Publications

Order by: publication date number of citations

• Entanglement and interaction in a topological quantum walk

  Alberto D. Verga, Ricardo Gabriel Elias

  SciPost Phys. 5, 019 (2018) · published 31 August 2018 | Toggle abstract · pdf

  We study the quantum walk of two interacting particles on a line with an interface separating two topologically distinct regions. The interaction induces a localization-delocalization transition of the edge state at the interface. We characterize the transition through the entanglement between the two particles.

  8 citations

• Interacting edge states of fermionic symmetry-protected topological phases in two dimensions

  Joseph Sullivan, Meng Cheng

  SciPost Phys. 9, 016 (2020) · published 5 August 2020 | Toggle abstract · pdf

  Recently, it has been found that there exist symmetry-protected topological phases of fermions, which have no realizations in non-interacting fermionic systems or bosonic models. We study the edge states of such an intrinsically interacting fermionic SPT phase in two spatial dimensions, protected by $\mathbb{Z}_4\times\mathbb{Z}_2^T$ symmetry. We model the edge Hilbert space by replacing the internal $\mathbb{Z}_4$ symmetry with a spatial translation symmetry, and design an exactly solvable Hamiltonian for the edge model. We show that at low-energy the edge can be described by a two-component Luttinger liquid, with nontrivial symmetry transformations that can only be realized in strongly interacting systems. We further demonstrate the symmetry-protected gaplessness under various perturbations, and the bulk-edge correspondence in the theory.

  8 citations

• Navigating through the O(N) archipelago

  Benoit Sirois

  SciPost Phys. 13, 081 (2022) · published 4 October 2022 | Toggle abstract · pdf

  A novel method for finding allowed regions in the space of CFT-data, coined navigator method, was recently proposed in arXiv:2104.09518. Its efficacy was demonstrated in the simplest example possible, i.e. that of the mixed-correlator study of the 3D Ising Model. In this paper, we would like to show that the navigator method may also be applied to the study of the family of $d$-dimensional $O(N)$ models. We will aim to follow these models in the $(d,N)$ plane. We will see that the "sailing" from island to island can be understood in the context of the navigator as a parametric optimization problem, and we will exploit this fact to implement a simple and effective path-following algorithm. By sailing with the navigator through the $(d,N)$ plane, we will provide estimates of the scaling dimensions $(\Delta_{\phi},\Delta_{s},\Delta_{t})$ in the entire range $(d,N) \in [3,4] \times [1,3]$. We will show that to our level of precision, we cannot see the non-unitary nature of the $O(N)$ models due to the fractional values of $d$ or $N$ in this range. We will also study the limit $N \xrightarrow[]{} 1$, and see that we cannot find any solution to the unitary mixed-correlator crossing equations below $N=1$.

  8 citations

• On classical and hybrid shadows of quantum states

  Saumya Shivam, Curt W. von Keyserlingk, Shivaji L. Sondhi

  SciPost Phys. 14, 094 (2023) · published 4 May 2023 | Toggle abstract · pdf

  Classical shadows are a computationally efficient approach to storing quantum states on a classical computer for the purposes of estimating expectation values of local observables, obtained by performing repeated random measurements. In this note we offer some comments on this approach. We note that the resources needed to form classical shadows with bounded relative error depend strongly on the target state. We then comment on the advantages and limitations of using classical shadows to simulate many-body dynamics. In addition, we introduce the notion of a hybrid shadow, constructed from measurements on a part of the system instead of the entirety, which provides a framework to gain more insight into the nature of shadow states as one reduces the size of the subsystem measured, and a potential alternative to compressing quantum states.

  8 citations

• Stabilizing the Laughlin state of light: Dynamics of hole fractionalization

  Pavel D. Kurilovich, Vladislav D. Kurilovich, José Lebreuilly, Steven M. Girvin

  SciPost Phys. 13, 107 (2022) · published 14 November 2022 | Toggle abstract · pdf

  Particle loss is the ultimate challenge for preparation of strongly correlated many-body states of photons. An established way to overcome the loss is to employ a stabilization setup that autonomously injects new photons in place of the lost ones. However, as we show, the effectiveness of such a stabilization setup is compromised for fractional quantum Hall states. There, a hole formed by a lost photon can separate into several remote quasiholes none of which can be refilled by injecting a photon locally. By deriving an exact expression for the steady-state density matrix, we demonstrate that isolated quasiholes proliferate in the steady state which damages the quality of the state preparation. The motion of quasiholes leading to their separation is allowed by a repeated process in which a photon is first lost and then quickly refilled in the vicinity of the quasihole. We develop the theory of this dissipative quasihole dynamics and show that it has diffusive character. Our results demonstrate that fractionalization might present an obstacle for both creation and stabilization of strongly-correlated states with photons.

  8 citations

• Emulating twisted double bilayer graphene with a multiorbital optical lattice

  Junhyun Lee, J. H. Pixley

  SciPost Phys. 13, 033 (2022) · published 25 August 2022 | Toggle abstract · pdf

  This work theoretically explores how to emulate twisted double bilayer graphene with ultracold atoms in multiorbital optical lattices. In particular, the quadratic band touching of Bernal stacked bilayer graphene is emulated using a square optical lattice with $p_x$, $p_y$, and $d_{x^2−y^2}$ orbitals on each site, while the effects of a twist are captured through the application of an incommensurate potential. The quadratic band touching is stable until the system undergoes an Anderson like delocalization transition in momentum space, which occurs concomitantly with a strongly renormalized single particle spectrum inducing flat bands, which is a generalization of the magic-angle condition realized in Dirac semimetals. The band structure is described perturbatively in the quasiperiodic potential strength, which captures miniband formation and the existence of magic-angles that qualitatively agrees with the exact numerical results in the appropriate regime. We identify several magic-angle conditions that can either have part or all of the quadratic band touching point become flat. In each case, these are accompanied by a diverging density of states and the delocalization of plane wave eigenstates. It is discussed how these transitions and phases can be observed in ultracold atom experiments.

  8 citations

• On spectrally flowed local vertex operators in AdS$_3$

  Sergio Iguri, Nicolas Kovensky

  SciPost Phys. 13, 115 (2022) · published 23 November 2022 | Toggle abstract · pdf

  We provide a novel local definition for spectrally flowed vertex operators in the $SL(2,\mathbb{R})$-WZW model, generalising the proposal of Maldacena and Ooguri in [arXiv:hep-th/0111180] for the singly-flowed case to all $\omega>1$. This allows us to establish the precise connection between the computation of correlators using the so-called spectral flow operator, and the methods introduced recently by Dei and Eberhardt in [arXiv:2105.12130] based on local Ward identities. We show that the auxiliary variable $y$ used in the latter paper arises naturally from a point-splitting procedure in the space-time coordinate. The recursion relations satisfied by spectrally flowed correlators, which take the form of partial differential equations in $y$-space, then correspond to null-state conditions for generalised spectral flowed operators. We highlight the role of certain $SL(2,\mathbb{R})$ discrete module isomorphisms in this context, and prove the validity of the conjecture put forward in [arXiv:2105.12130] for $y$-space structure constants of three-point functions with arbitrary spectral flow charges.

  8 citations

• dS$\boldsymbol{_2}$ as excitation of AdS$\boldsymbol{_2}$

  Florian Ecker, Daniel Grumiller, Robert McNees

  SciPost Phys. 13, 119 (2022) · published 5 December 2022 | Toggle abstract · pdf

  We introduce a family of 2D dilaton gravity models with state-dependent constant curvature so that dS$_2$ emerges as an excitation of AdS$_2$. Curiously, the strong coupling region corresponds to the asymptotic region geometrically. Apart from these key differences, many features resemble the Almheiri--Polchinski model. We discuss perturbative and non-perturbative thermodynamical stability, bubble nucleation through matter shockwaves, and semiclassical backreaction effects. In some of these models, we find that low temperatures are dominated by AdS$_2$ but high temperatures are dominated by dS$_2$, concurrent with a recent proposal by Susskind.

  8 citations

• Emergent XY* transition driven by symmetry fractionalization and anyon condensation

  Michael Schuler, Louis-Paul Henry, Yuan-Ming Lu, Andreas M. Läuchli

  SciPost Phys. 14, 001 (2023) · published 11 January 2023 | Toggle abstract · pdf

  Anyons in a topologically ordered phase can carry fractional quantum numbers with respect to the symmetry group of the considered system, one example being the fractional charge of the quasiparticles and quasiholes in the fractional quantum Hall effect. When such symmetry-fractionalized anyons condense, the resulting phase must spontaneously break the symmetry and display a local order parameter. In this paper, we study the phase diagram and anyon condensation transitions of a $\mathbb{Z}_2$ topological order perturbed by Ising interactions in the Toric Code. The interplay between the global (``onsite'') Ising ($\mathbb{Z}_2$) symmetry and the lattice space group symmetries results in a non-trivial symmetry fractionalization class for the anyons, and is shown to lead to two characteristically different confined, symmetry-broken phases. To understand the anyon condensation transitions, we use the recently introduced critical torus energy spectrum technique to identify a line of emergent 2+1D XY* transitions ending at a fine-tuned (Ising$^2$)* critical point. We provide numerical evidence for the occurrence of two symmetry breaking patterns predicted by the specific symmetry fractionalization class of the condensed anyons in the explored phase diagram. In combination with large-scale quantum Monte Carlo simulations we measure unusually large critical exponents $\eta$ for the scaling of the correlation function at the continuous anyon condensation transitions, and we further identify lines of (weakly) first order transitions in the phase diagram. As an important additional result, we discuss the phase diagram of a resulting 2+1D Ashkin-Teller model, where we demonstrate that torus spectroscopy is capable of identifying emergent XY/O(2) critical behaviour, thereby solving some longstanding open questions in the domain of the 3D Ashkin-Teller models. To establish the generality of our results, we propose a field theoretical description capturing the transition from a $\mathbb{Z}_2$ topological order to either $\mathbb{Z}_2$ symmetry broken phase, which is in excellent agreement with the numerical results.

  8 citations

• $\mathcal{I}$/$c$-extremization in M/F-duality

  Marieke van Beest, Sebastjan Cizel, Sakura Schäfer-Nameki, James Sparks

  SciPost Phys. 9, 029 (2020) · published 1 September 2020 | Toggle abstract · pdf

  We study the holographic dual to $c$-extremization for 2d $(0,2)$ superconformal field theories (SCFTs) that have an AdS$_3$ dual realized in Type IIB with varying axio-dilaton, i.e. F-theory. M/F-duality implies that such AdS$_3$ solutions can be mapped to AdS$_2$ solutions in M-theory, which are holographically dual to superconformal quantum mechanics (SCQM), obtained by dimensional reduction of the 2d SCFTs. We analyze the corresponding map between holographic $c$-extremization in F-theory and $\mathcal{I}$-extremization in M-theory, where in general the latter receives corrections relative to the F-theory result.

  8 citations