SciPost: SciPost Physics: issue detail

SciPost Physics

SciPost Physics Vol. 12 issue 6 (June 2022)

Previous issue | Vol. 12 issue 5

Vol. 13 issue 1 | Next issue

Stripes in the extended $t-t^\prime$ Hubbard model: A Variational Monte Carlo analysis

Vito Marino, Federico Becca, Luca F. Tocchio

SciPost Phys. 12, 180 (2022) · published 1 June 2022 | · pdf

By using variational quantum Monte Carlo techniques, we investigate the instauration of stripes (i.e., charge and spin inhomogeneities) in the Hubbard model on the square lattice at hole doping $\delta=1/8$, with both nearest- ($t$) and next-nearest-neighbor hopping ($t^\prime$). Stripes with different wavelengths $\lambda$ (denoting the periodicity of the charge inhomogeneity) and character (bond- or site-centered) are stabilized for sufficiently large values of the electron-electron interaction $U/t$. The general trend is that $\lambda$ increases going from negative to positive values of $t^\prime/t$ and decreases by increasing $U/t$. In particular, the $\lambda=8$ stripe obtained for $t^\prime=0$ and $U/t=8$ [L.F. Tocchio, A. Montorsi, and F. Becca, SciPost Phys. 7, 21 (2019)] shrinks to $\lambda=6$ for $U/t\gtrsim 10$. For $t^\prime/t<0$, the stripe with $\lambda=5$ is found to be remarkably stable, while for $t^\prime/t>0$, stripes with wavelength $\lambda=12$ and $\lambda=16$ are also obtained. In all these cases, pair-pair correlations are highly suppressed with respect to the uniform state (obtained for large values of $|t^\prime/t|$), suggesting that striped states are not superconducting at $\delta=1/8$.
A model of persistent breaking of continuous symmetry

Noam Chai, Anatoly Dymarsky, Mikhail Goykhman, Ritam Sinha, Michael Smolkin

SciPost Phys. 12, 181 (2022) · published 1 June 2022 | · pdf

We consider a UV-complete field-theoretic model in general dimensions, including $d=2+1$, that exhibits spontaneous breaking of continuous symmetry, persisting to arbitrarily large temperatures. Our model consists of two copies of the long-range vector models, with $O(m)$ and $O(N-m)$ global symmetry groups, perturbed by double-trace operators. Using conformal perturbation theory we find weakly-coupled IR fixed points for $N\geq 6$ that reveal a spontaneous breaking of global symmetry. Namely, at finite temperature the lower rank group is broken, with the pattern persisting at all temperatures due to scale-invariance. We provide evidence that the models in question are unitary and invariant under full conformal symmetry. Our work generalizes recent results, which considered the particular case of $m=1$ and reported persistent breaking of the discrete $\mathbb{Z}_2=O(1)$. Furthermore, we show that this model exhibits a continuous family of weakly interacting field theories at finite $N$.
Massive holographic QFTs in de Sitter

José Manuel Penín, Kostas Skenderis, Benjamin Withers

SciPost Phys. 12, 182 (2022) · published 1 June 2022 | · pdf

We study strongly coupled mass-deformed-CFT on a fixed de Sitter spacetime in three dimensions via holography. We elucidate the global causal structure of the four-dimensional spacetime dual to the de Sitter invariant vacuum state. The conformal boundaries of de Sitter appear as spacelike defects sourced by the mass deformation, which extend into the bulk as curvature singularities in AdS. We compute all one- and two-point functions of the deformed-CFT stress tensor and a scalar operator order-by-order in the mass deformation for a simple holographic model. These correlation functions admit a spectral representation as a sum of simple poles corresponding to normalisable modes in the bulk.
Global form of flavor symmetry groups in 4d N=2 theories of class S

Lakshya Bhardwaj

SciPost Phys. 12, 183 (2022) · published 7 June 2022 | · pdf

We provide a systematic method to deduce the global form of flavor symmetry groups in 4d N=2 theories obtained by compactifying 6d N=(2,0) superconformal field theories (SCFTs) on a Riemann surface carrying regular punctures and possibly outer-automorphism twist lines. Apriori, this method only determines the group associated to the manifest part of the flavor symmetry algebra, but often this information is enough to determine the group associated to the full enhanced flavor symmetry algebra. Such cases include some interesting and well-studied 4d N=2 SCFTs like the Minahan-Nemeschansky theories. The symmetry groups obtained via this method match with the symmetry groups obtained using a Lagrangian description if such a description arises in some duality frame. Moreover, we check that the proposed symmetry groups are consistent with the superconformal indices available in the literature. As another application, our method finds distinct global forms of flavor symmetry group for pairs of interacting 4d N=2 SCFTs (recently pointed out in the literature) whose Coulomb branch dimensions, flavor algebras and levels coincide (along with other invariants), but nonetheless are distinct SCFTs.
Long-term memory magnetic correlations in the Hubbard model: A dynamical mean-field theory analysis

Clemens Watzenböck, Martina Fellinger, Karsten Held, Alessandro Toschi

SciPost Phys. 12, 184 (2022) · published 7 June 2022 | · pdf

We investigate the onset of a not-decaying asymptotic behavior of temporal magnetic correlations in the Hubbard model in infinite dimensions. This long-term memory feature of dynamical spin correlations can be precisely quantified by computing the difference between the zero-frequency limit of the Kubo susceptibility and the corresponding static isothermal one. Here, we present a procedure for reliably evaluating this difference starting from imaginary time-axis data, and apply it to the testbed case of the Mott-Hubbard metal-insulator transition (MIT). At low temperatures, we find long-term memory effects in the entire Mott regime, abruptly ending at the first order MIT. This directly reflects the underlying local moment physics and the associated degeneracy in the many-electron spectrum. At higher temperatures, a more gradual onset of an infinitely-long time-decay of magnetic correlations occurs in the crossover regime, not too far from the Widom line emerging from the critical point of the MIT. Our work has relevant algorithmic implications for the analytical continuation of dynamical susceptibilities in strongly correlated regimes and offers a new perspective for unveiling fundamental properties of the many-particle spectrum of the problem under scrutiny.
Shallow trimers of two identical fermions and one particle in resonant regimes

Pascal Naidon, Ludovic Pricoupenko, Christiane Schmickler

SciPost Phys. 12, 185 (2022) · published 7 June 2022 | · pdf

We consider two identical fermions interacting in the p-wave channel. Each fermion also interacts with another particle in the vicinity of an s-wave resonance. We find that in addition to the Kartavtsev-Malykh universal trimer states resulting from the s-wave particle-fermion interaction, the fermion-fermion p-wave interaction induces one or two shallow trimers in a large domain of the control parameters, including a borromean regime where the ground-state trimer exists in the absence of dimers at any mass ratio between the fermions and the particle. A generic picture of the trimer spectrum emerges from this work in terms of the low-energy parameters of the interactions.
The 3d twisted index and wall-crossing

Mathew Bullimore, Andrea E.V. Ferrari, Heeyeon Kim

SciPost Phys. 12, 186 (2022) · published 8 June 2022 | · pdf

We study the twisted index of 3d $\mathcal{N}=2$ supersymmetric gauge theories on $S^1 \times \Sigma$ in the presence of a real FI parameter deformation. This parameter induces a 1d FI parameter for the effective supersymmetric quantum mechanics on $S^1$. Using supersymmetric localisation, the twisted index can be expressed as a contour integral. We show that the contour prescription is modified in the presence of the 1d FI parameter, leading to wall-crossing phenomena for the twisted index. In particular, we derive a general wall-crossing formula for abelian gauge theories. We also examine the origin of wall-crossing as change of stability condition in the algebro-geometric interpretation of the twisted index. These ideas are illustrated for abelian theories with $\mathcal{N}=4$ supersymmetry and in a non-abelian example that reproduces wall-crossing phenomena associated to moduli spaces of stable pairs.
Comparing machine learning and interpolation methods for loop-level calculations

Ibrahim Chahrour, James D. Wells

SciPost Phys. 12, 187 (2022) · published 8 June 2022 | · pdf

The need to approximate functions is ubiquitous in science, either due to empirical constraints or high computational cost of accessing the function. In high-energy physics, the precise computation of the scattering cross-section of a process requires the evaluation of computationally intensive integrals. A wide variety of methods in machine learning have been used to tackle this problem, but often the motivation of using one method over another is lacking. Comparing these methods is typically highly dependent on the problem at hand, so we specify to the case where we can evaluate the function a large number of times, after which quick and accurate evaluation can take place. We consider four interpolation and three machine learning techniques and compare their performance on three toy functions, the four-point scalar Passarino-Veltman $D_0$ function, and the two-loop self-energy master integral $M$. We find that in low dimensions ($d = 3$), traditional interpolation techniques like the Radial Basis Function perform very well, but in higher dimensions ($d=5, 6, 9$) we find that multi-layer perceptrons (a.k.a neural networks) do not suffer as much from the curse of dimensionality and provide the fastest and most accurate predictions.
Symmetries, safety, and self-supervision

Barry M. Dillon, Gregor Kasieczka, Hans Olischlager, Tilman Plehn, Peter Sorrenson, Lorenz Vogel

SciPost Phys. 12, 188 (2022) · published 9 June 2022 | · pdf

Collider searches face the challenge of defining a representation of high-dimensional data such that physical symmetries are manifest, the discriminating features are retained, and the choice of representation is new-physics agnostic. We introduce JetCLR to solve the mapping from low-level data to optimized observables though self-supervised contrastive learning. As an example, we construct a data representation for top and QCD jets using a permutation-invariant transformer-encoder network and visualize its symmetry properties. We compare the JetCLR representation with alternative representations using linear classifier tests and find it to work quite well.
Destruction of localization by thermal inclusions: Anomalous transport and Griffiths effects in the Anderson and André-Aubry-Harper models

Xhek Turkeshi, Damien Barbier, Leticia F. Cugliandolo, Marco Schirò, Marco Tarzia

SciPost Phys. 12, 189 (2022) · published 9 June 2022 | · pdf

We discuss and compare two recently proposed toy models for anomalous transport and Griffiths effects in random systems near the Many-Body Localization transitions: the random dephasing model, which adds thermal inclusions in an Anderson Insulator as local Markovian dephasing channels that heat up the system, and the random Gaussian Orthogonal Ensemble (GOE) approach which models them in terms of ensembles of random regular graphs. For these two settings we discuss and compare transport and dissipative properties and their statistics. We show that both types of dissipation lead to similar Griffiths-like phenomenology, with the GOE bath being less effective in thermalising the system due to its finite bandwidth. We then extend these models to the case of a quasi-periodic potential as described by the André-Aubry-Harper model coupled to random thermal inclusions, that we show to display, for large strength of the quasiperiodic potential, a similar phenomenology to the one of the purely random case. In particular, we show the emergence of subdiffusive transport and broad statistics of the local density of states, suggestive of Griffiths like effects arising from the interplay between quasiperiodic localization and random coupling to the baths.
The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap

Jaychandran Padayasi, Abijith Krishnan, Max A. Metlitski, Ilya A. Gruzberg, Marco Meineri

SciPost Phys. 12, 190 (2022) · published 9 June 2022 | · pdf

This paper studies the critical behavior of the 3d classical $\mathrm{O}(N)$ model with a boundary. Recently, one of us established that upon treating $N$ as a continuous variable, there exists a critical value $N_c > 2$ such that for $2 \leq N < N_c$ the model exhibits a new extraordinary-log boundary universality class, if the symmetry preserving interactions on the boundary are enhanced. $N_c$ is determined by a ratio of universal amplitudes in the normal universality class, where instead a symmetry breaking field is applied on the boundary. We study the normal universality class using the numerical conformal bootstrap. We find truncated solutions to the crossing equation that indicate $N_c \approx 5$. Additionally, we use semi-definite programming to place rigorous bounds on the boundary CFT data of interest to conclude that $N_c > 3$, under a certain positivity assumption which we check in various perturbative limits.
$\mathrm{T}\overline{\mathrm{T}}$-deformed 1d Bose gas

Yunfeng Jiang

SciPost Phys. 12, 191 (2022) · published 10 June 2022 | · pdf

$\mathrm{T}\overline{\mathrm{T}}$ deformation was originally proposed as an irrelevant solvable deformation for 2d relativistic quantum field theories (QFTs). The same family of deformations can also be defined for integrable quantum spin chains which was first studied in the context of integrability in AdS/CFT. In this paper, we construct such deformations for yet another type of models, which describe a collection of particles moving in 1d and interacting in an integrable manner. The prototype of such models is the Lieb-Liniger model. This shows that such deformations can be defined for a very wide range of systems. We study the finite volume spectrum and thermodynamics of the $\mathrm{T}\overline{\mathrm{T}}$-deformed Lieb-Liniger model. We find that for one sign of the deformation parameter $(\lambda<0)$, the deformed spectrum becomes complex when the volume of the system is smaller than certain critical value, signifying the break down of UV physics. For the other sign $(\lambda>0)$, there exists an upper bound for the temperature, similar to the Hagedorn behavior of the $\mathrm{T}\overline{\mathrm{T}}$ deformed QFTs. Both behaviors can be attributed to the fact that $\mathrm{T}\overline{\mathrm{T}}$ deformation changes the size the particles. We show that for $\lambda>0$, the deformation increases the spaces between particles which effectively increases the volume of the system. For $\lambda<0$, $\mathrm{T}\overline{\mathrm{T}}$ deformation fattens point particles to finite size hard rods. This is similar to the observation that the action of $\mathrm{T}\overline{\mathrm{T}}$-deformed free boson is the Nambu-Goto action, which describes bosonic strings -- also an extended object with finite size.
Physical representations for scattering amplitudes and the wavefunction of the universe

Paolo Benincasa, William J. Torres Bobadilla

SciPost Phys. 12, 192 (2022) · published 10 June 2022 | · pdf

The way we organise perturbation theory is of fundamental importance both for computing the observables of relevance and for extracting fundamental physics out of them. If on one hand the different ways in which the perturbative observables can be written make manifest different features ({\it e.g.} symmetries as well as principles such as unitarity, causality and locality), on the other hand precisely demanding that some concrete features are manifest lead to different ways of organising perturbation theory. In the context of flat-space scattering amplitudes, a number of them are already known and exploited, while much less is known for cosmological observables. In the present work, we show how to systematically write down both the wavefunction of the universe and the flat-space scattering amplitudes, in such a way that they manifestly show physical poles only. We make use of the invariant definition of such observables in terms of {\it cosmological polytopes} and their {\it scattering facet}. In particular, we show that such representations correspond to triangulations of such objects through hyperplanes identified by the intersection of their facets outside of them. All possible triangulations of this type generate the different representations. This allows us to provide a general proof for the conjectured all-loop causal representation of scattering amplitudes. Importantly, all such representations can be viewed as making explicit a subset of compatible singularities, and our construction provides a way to extend Steinmann relations to higher codimension singularities for both the flat-space scattering amplitudes and the cosmological wavefunction.
Real-time ab initio description of the photon-echo mechanisms in extended systems: the case study of bulk GaAs

Marco D'Alessandro, Davide Sangalli

SciPost Phys. 12, 193 (2022) · published 13 June 2022 | · pdf

In this paper we present an ab initio real-time analysis of free polarization decay and photon echo in extended systems. As a prototype material, we study bulk GaAs driven by ultra-short laser pulses of 10 fs (energy spread of 0.4 eV), with frequency tuned in the continuum of the optical spectrum. We compute the electronic polarization P(t), and define a computational procedure to extract the echo signal in the dipole approximation. Results are obtained in both the low and high field regime, and compared with a two-levels system (TLS) model, with parameters extracted from the ab initio simulations. ab initio results are in optimal agreement with the TLS in the low-field case, whereas some differences are observed in the high-field regime where the multi-band nature of GaAs becomes relevant. In the high field regime we compute the pulse area, and look for fluences with pulse area close to {\pi}. We highlight that such fluences are well below the damage threshold of GaAs. However a unique value of the area cannot be defined, due to the strong dependence of the transition dipoles in the energy window excited by the laser pulse.
Rényi entropies and negative central charges in non-Hermitian quantum systems

Yi-Ting Tu, Yu-Chin Tzeng, Po-Yao Chang

SciPost Phys. 12, 194 (2022) · published 13 June 2022 | · pdf

Quantum entanglement is one essential element to characterize many-body quantum systems. However, the entanglement measures are mostly discussed in Hermitian systems. Here, we propose a natural extension of entanglement and R\'enyi entropies to non-Hermitian quantum systems. There have been other proposals for the computation of these quantities, which are distinct from what is proposed in the current paper. We demonstrate the proposed entanglement quantities which are referred to as generic entanglement and R\'enyi entropies. These quantities capture the desired entanglement properties in non-Hermitian critical systems, where the low-energy properties are governed by the non-unitary conformal field theories (CFTs). We find excellent agreement between the numerical extrapolation of the negative central charges from the generic entanglement/R\'enyi entropy and the non-unitary CFT prediction. Furthermore, we apply the generic entanglement/R\'enyi entropy to symmetry-protected topological phases with non-Hermitian perturbations. We find the generic $n$-th R\'enyi entropy captures the expected entanglement property, whereas the traditional R\'enyi entropy can exhibit unnatural singularities due to its improper definition.
Entanglement entropy in quantum spin chains with broken parity number symmetry

Arash Jafarizadeh, M. A. Rajabpour

SciPost Phys. 12, 195 (2022) · published 14 June 2022 | · pdf

Consider a generic quantum spin chain that can be mapped to free quadratic fermions via Jordan-Wigner (JW) transformation. In the presence of arbitrary boundary magnetic fields, this Hamiltonian is no longer a quadratic Hamiltonian after JW transformation. Using ancillary sites and enlarging the Hamiltonian we first introduce a bigger quadratic Hamiltonian. Then we diagonalize this enlarged Hamiltonian in its most generic form and show that all the states are degenerate because of the presence of a zero mode. The eigenstates of the original spin chain with boundary magnetic fields can be derived after appropriate projection. We study in-depth the properties of the eigenstates of the enlarged Hamiltonian. In particular, we find: 1) the eigenstates in configuration bases, 2) calculate all the correlation functions, 3) find the reduced density matrices, 4) calculate the entanglement entropy. We show that the generic eigenstate of the enlarged Hamiltonian (including the eigenstates of the original spin chain) breaks the parity number symmetry and consequently one needs to take care of some technicalities regarding the calculation of the reduced density matrix and entanglement entropy. Interestingly we show that the entanglement structure of these eigenstates is quite universal and independent of the Hamiltonian. We support our results by applying them to a couple of examples.
Edge physics at the deconfined transition between a quantum spin Hall insulator and a superconductor

Ruochen Ma, Liujun Zou, Chong Wang

SciPost Phys. 12, 196 (2022) · published 14 June 2022 | · pdf

We study the edge physics of the deconfined quantum phase transition (DQCP) between a spontaneous quantum spin Hall (QSH) insulator and a spin-singlet superconductor (SC). Although the bulk of this transition is in the same universality class as the paradigmatic deconfined Neel to valence-bond-solid transition, the boundary physics has a richer structure due to proximity to a quantum spin Hall state. We use the parton trick to write down an effective field theory for the QSH-SC transition in the presence of a boundary. We calculate various edge properties in an $N\to\infty$ limit. We show that the boundary Luttinger liquid in the QSH state survives at the phase transition, but only as "fractional" degrees of freedom that carry charge but not spin. The physical fermion remains gapless on the edge at the critical point, with a universal jump in the fermion scaling dimension as the system approaches the transition from the QSH side. The critical point could be viewed as a gapless analogue of the quantum spin Hall state but with the full $SU(2)$ spin rotation symmetry, which cannot be realized if the bulk is gapped.
Josephson junctions of topological nodal superconductors

Ranjani Seshadri, Maxim Khodas, Dganit Meidan

SciPost Phys. 12, 197 (2022) · published 23 June 2022 | · pdf

Transition metal dichalcogenides (TMDs) offer a unique platform to study unconventional superconductivity, owing to the presence of strong spin-orbit coupling and a remarkable stability to an in-plane magnetic field. A recent study found that when an in-plane field applied to a superconducting monolayer TMD is increased beyond the Pauli critical limit, a quantum phase transition occurs into a topological nodal superconducting phase which hosts Majorana flat bands. We study the current-phase relation of this nodal superconductor in a Josephson junction geometry. We find that the nodal superconductivity is associated with an energy-phase relation that depends on the momentum transverse to the current direction, with a $4\pi$ periodicity in between pairs of nodal points. We interpret this response as a result of a series of quantum phase transitions, driven by the transverse momentum, which separate a topological trivial phase and two distinct topologically non-trivial phases characterized by different winding invariants. This analysis sheds light on the stability of the Majorana flat bands to symmetry-breaking perturbations.
Matchmakereft: automated tree-level and one-loop matching

Adrián Carmona, Achilleas Lazopoulos, Pablo Olgoso, José Santiago

SciPost Phys. 12, 198 (2022) · published 23 June 2022 | · pdf

We introduce matchmakereft, a fully automated tool to compute the tree-level and one-loop matching of arbitrary models onto arbitrary effective theories. Matchmakereft performs an off-shell matching, using diagrammatic methods and the background field method when gauge theories are involved. The large redundancy inherent to the off-shell matching together with explicit gauge invariance offers a significant number of non-trivial checks of the results provided. These results are given in the physical basis but several intermediate results, including the matching in the Green basis before and after canonical normalization, are given for flexibility and the possibility of further cross-checks. As a non-trivial example we provide the complete matching in the Warsaw basis up to one loop of an extension of the Standard Model with a charge -1 vector-like lepton singlet. Matchmakereft has been built with generality, flexibility and efficiency in mind. These ingredients allow matchmakereft to have many applications beyond the matching between models and effective theories. Some of these applications include the one-loop renormalization of arbitrary theories (including the calculation of the one-loop renormalization group equations for arbitrary theories); the translation between different Green bases for a fixed effective theory or the check of (off-shell) linear independence of the operators in an effective theory. All these applications are performed in a fully automated way by matchmakereft.
On the logarithmic bipartite fidelity of the open XXZ spin chain at $Δ=-1/2$

Christian Hagendorf, Gilles Parez

SciPost Phys. 12, 199 (2022) · published 24 June 2022 | · pdf

The open XXZ spin chain with the anisotropy $\Delta=-\frac12$ and a one-parameter family of diagonal boundary fields is studied at finite length. A determinant formula for an overlap involving the spin chain's ground-state vectors for different lengths is found. The overlap allows one to obtain an exact finite-size formula for the ground state's logarithmic bipartite fidelity. The leading terms of its asymptotic series for large chain lengths are evaluated. Their expressions confirm the predictions of conformal field theory for the fidelity.
On the dynamic distinguishability of nodal quasi-particles in overdoped cuprates

Kamran Behnia

SciPost Phys. 12, 200 (2022) · published 24 June 2022 | · pdf

La$_{1.67}$Sr$_{0.33}$CuO$_4$ is not a superconductor and its resistivity follows a purely T$^2$ temperature dependence at very low temperatures. La$_{1.71}$Sr$_{0.29}$CuO$_4$, on the other hand, has a superconducting ground state together with a T-Linear term in its resistivity. The concomitant emergence of these two features below a critical doping is mystifying. Here, I notice that the electron-electron collision rate in the Fermi liquid above the doping threshold is unusually large. The scattering time of nodal quasi-particles expressed in a dimensionless parameter $\zeta$ is very close to what has been found in liquid $^3$He at its melting pressure. In the latter case, fermionic particles become dynamically distinguishable by excess of interaction. Ceasing to be dynamically indistinguishable, nodal electrons will be excluded from the Fermi sea. Such non-degenerate carriers will then scatter the degenerate ones within a phase space growing linearly with temperature.
A constructive theory of the numerically accessible many-body localized to thermal crossover

Philip J D Crowley, Anushya Chandran

SciPost Phys. 12, 201 (2022) · published 24 June 2022 | · pdf

The many-body localised (MBL) to thermal crossover observed in exact diagonalisation studies remains poorly understood as the accessible system sizes are too small to be in an asymptotic scaling regime. We develop a model of the crossover in short 1D chains in which the MBL phase is destabilised by the formation of many-body resonances. The model reproduces several properties of the numerically observed crossover, including an apparent correlation length exponent $\nu=1$, exponential growth of the Thouless time with disorder strength, linear drift of the critical disorder strength with system size, scale-free resonances, apparent $1/\omega$ dependence of disorder-averaged spectral functions, and sub-thermal entanglement entropy of small subsystems. In the crossover, resonances induced by a local perturbation are rare at numerically accessible system sizes $L$ which are smaller than a \emph{resonance length} $\lambda$. For $L \gg \sqrt{\lambda}$ (in lattice units), resonances typically overlap, and this model does not describe the asymptotic transition. The model further reproduces controversial numerical observations which Refs. [Suntajs et al 2019, Sels & Polkovnikov 2020] claimed to be inconsistent with MBL. We thus argue that the numerics to date is consistent with a MBL phase in the thermodynamic limit.
Gauging U(1) symmetry in (2+1)d topological phases

Meng Cheng, Chao-Ming Jian

SciPost Phys. 12, 202 (2022) · published 27 June 2022 | · pdf

We study the gauging of a global U(1) symmetry in a gapped system in (2+1)d. The gauging procedure has been well-understood for a finite global symmetry group, which leads to a new gapped phase with emergent gauge structure and can be described algebraically using the mathematical framework of modular tensor category (MTC). We develop a categorical description of U(1) gauging in an MTC, taking into account the dynamics of U(1) gauge field absent in the finite group case. When the ungauged system has a non-zero Hall conductance, the gauged theory remains gapped and we determine the complete set of anyon data for the gauged theory. On the other hand, when the Hall conductance vanishes, we argue that gauging has the same effect of condensing a special Abelian anyon nucleated by inserting $2\pi$ U(1) flux. We apply our procedure to the SU(2)$_k$ MTCs and derive the full MTC data for the $\mathbb{Z}_k$ parafermion MTCs. We also discuss a dual U(1) symmetry that emerges after the original U(1) symmetry of an MTC is gauged.
An ideal rapid-cycle Thouless pump

Savvas Malikis, Vadim Cheianov

SciPost Phys. 12, 203 (2022) · published 27 June 2022 | · pdf

Thouless pumping is a fundamental instance of quantized transport, which is topologically protected. Although its theoretical importance, the adiabaticity condition is an obstacle for further practical applications. Here, focusing on the Rice-Mele model, we provide a family of finite-frequency examples that ensure both the absence of excitations and the perfect quantization of the pumped charge at the end of each cycle. This family, which contains an adiabatic protocol as a limiting case, is obtained through a mapping onto the zero curvature representation of the Euclidean sinh-Gordon equation.
Geodesic geometry of 2+1-D Dirac materials subject to artificial, quenched gravitational singularities

Seth M. Davis, Matthew S. Foster

SciPost Phys. 12, 204 (2022) · published 27 June 2022 | · pdf

The spatial modulation of the Fermi velocity for gapless Dirac electrons in quantum materials is mathematically equivalent to the problem of massless fermions on a certain class of curved spacetime manifolds. We study null geodesic lensing through these manifolds, which are dominated by curvature singularities, such as nematic singularity walls (where the Dirac cone flattens along one direction). Null geodesics lens across these walls, but do so by perfectly collimating to a local transit angle. Nevertheless, nematic walls can trap null geodesics into stable or metastable orbits characterized by repeated transits. We speculate about the role of induced one-dimensionality for such bound orbits in 2D dirty d-wave superconductivity.
Fractons, dipole symmetries and curved spacetime

Leo Bidussi, Jelle Hartong, Emil Have, Jørgen Musaeus, Stefan Prohazka

SciPost Phys. 12, 205 (2022) · published 28 June 2022 | · pdf

We study complex scalar theories with dipole symmetry and uncover a no-go theorem that governs the structure of such theories and which, in particular, reveals that a Gaussian theory with linearly realised dipole symmetry must be Carrollian. The gauging of the dipole symmetry via the Noether procedure gives rise to a scalar gauge field and a spatial symmetric tensor gauge field. We construct a worldline theory of mobile objects that couple gauge invariantly to these gauge fields. We systematically develop the canonical theory of a dynamical symmetric tensor gauge field and arrive at scalar charge gauge theories in both Hamiltonian and Lagrangian formalism. We compute the dispersion relation of the modes of this gauge theory, and we point out an analogy with partially massless gravitons. It is then shown that these fractonic theories couple to Aristotelian geometry, which is a non-Lorentzian geometry characterised by the absence of boost symmetries. We generalise previous results by coupling fracton theories to curved space and time. We demonstrate that complex scalar theories with dipole symmetry can be coupled to general Aristotelian geometries as long as the symmetric tensor gauge field remains a background field. The coupling of the scalar charge gauge theory requires a Lagrange multiplier that restricts the Aristotelian geometries.
Bootstrapping mixed MN correlators in 3D

Stefanos R. Kousvos, Andreas Stergiou

SciPost Phys. 12, 206 (2022) · published 28 June 2022 | · pdf

The recent emergence of the modern conformal bootstrap method for the study of conformal field theories (CFTs) has enabled the revisiting of old problems in classical critical phenomena described by three-dimensional CFTs. The study of such CFTs with $O(m)^n \rtimes S_n$ global symmetry, also known as MN models, is pursued in this work. Systems of mixed correlators involving scalar operators in two different representations of the global symmetry group are considered. Isolated allowed regions are found in parameter space for various values of $m$ and $n$. These "islands" can be separated into two qualitative groups: those close to the unitarity bound and those further away. As a by-product of our analysis generic tensor structures required to bootstrap any $G^n \rtimes S_n$ theory with $G$ arbitrary are worked out.
Exact hydrodynamic solution of a double domain wall melting in the spin-1/2 XXZ model

Stefano Scopa , Pasquale Calabrese, Jérôme Dubail

SciPost Phys. 12, 207 (2022) · published 28 June 2022 | · pdf

We investigate the non-equilibrium dynamics of a one-dimensional spin-1/2 XXZ model at zero-temperature in the regime $|\Delta|< 1$, initially prepared in a product state with two domain walls i.e, $|\downarrow\dots\downarrow\uparrow\dots\uparrow\downarrow\dots\downarrow\rangle$. At early times, the two domain walls evolve independently and only after a calculable time a non-trivial interplay between the two emerges and results in the occurrence of a split Fermi sea. For $\Delta=0$, we derive exact asymptotic results for the magnetization and the spin current by using a semi-classical Wigner function approach, and we exactly determine the spreading of entanglement entropy exploiting the recently developed tools of quantum fluctuating hydrodynamics. In the interacting case, we analytically solve the Generalized Hydrodynamics equation providing exact expressions for the conserved quantities. We display some numerical results for the entanglement entropy also in the interacting case and we propose a conjecture for its asymptotic value.