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SciPost Physics

SciPost Physics Vol. 18 issue 5 (May 2025)

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Single-particle spectra and magnetic susceptibility in the Emery model: A dynamical mean-field perspective

Yi-Ting Tseng, Mário O. Malcolms, Henri Menke, Marcel Klett, Thomas Schäfer, Philipp Hansmann

SciPost Phys. 18, 145 (2025) · published 1 May 2025 | · pdf

We investigate dynamical mean-field calculations of the three-band Emery model at the one- and two-particle level for material-realistic parameters of high-$T_c$ superconductors. Our study shows that even within dynamical mean-field theory, which accounts solely for temporal fluctuations, the intrinsic multi-orbital nature of the Emery model introduces effective non-local correlations. These correlations lead to a non-Curie-like temperature dependence of the magnetic susceptibility, consistent with nuclear magnetic resonance experiments in the pseudogap regime. By analyzing the temperature dependence of the uniform static spin susceptibility obtained by single-site and cluster dynamical mean-field theory, we find indications of emerging oxygen-copper singlet fluctuations, explicitly captured by the model. Despite correctly describing the hallmark of the pseudogap at the two-particle level, such as the drop in the Knight shift of nuclear magnetic resonance, dynamical mean-field theory fails to capture the spectral properties of the pseudogap.
Three-dimensional quantum Hall effect in topological amorphous metals

Jiong-Hao Wang, Yong Xu

SciPost Phys. 18, 146 (2025) · published 2 May 2025 | · pdf

Weyl semimetals have been theoretically predicted to become topological metals with anomalous Hall conductivity in amorphous systems. However, measuring the anomalous Hall conductivity in realistic materials, particularly those with multiple pairs of Weyl points, is a significant challenge. If a system respects time-reversal symmetry, then the anomalous Hall conductivity even vanishes. As such, it remains an open question how to probe the Weyl band like topology in amorphous materials. Here, we theoretically demonstrate that, under magnetic fields, a topological metal slab in amorphous systems exhibits three-dimensional quantum Hall effect, even in time-reversal invariant systems, thereby providing a feasible approach to exploring Weyl band like topology in amorphous materials. We unveil the topological origin of the quantized Hall conductance by calculating the Bott index. The index is carried by broadened Landau levels with bulk states spatially localized except at critical transition energies. The topological property also results in edge states localized at distinct hinges on two opposite surfaces.
Subsystem symmetry fractionalization and foliated field theory

Po-Shen Hsin, David T. Stephen, Arpit Dua, Dominic J. Williamson

SciPost Phys. 18, 147 (2025) · published 2 May 2025 | · pdf

Topological quantum matter exhibits a range of exotic phenomena when enriched by subdimensional symmetries. This includes new features beyond those that appear in the conventional setting of global symmetry enrichment. A recently discovered example is a type of subsystem symmetry fractionalization that occurs through a different mechanism to global symmetry fractionalization. In this work we extend the study of subsystem symmetry fractionalization through new examples derived from the general principle of embedding subsystem symmetry into higher-form symmetry. This leads to new types of symmetry fractionalization that are described by foliation dependent higher-form symmetries. This leads to field theories and lattice models that support previously unseen anomalous subsystem symmetry fractionalization. Our work expands the range of exotic topological physics that is enabled by subsystem symmetry in field theory and on the lattice.
A tale of $Z$+jet: SMEFT effects and the Lam-Tung relation

Rhorry Gauld, Ulrich Haisch, Joachim Weiss

SciPost Phys. 18, 148 (2025) · published 6 May 2025 | · pdf

We derive constraints on dimension-six light-quark dipole operators within the Standard Model (SM) effective field theory, based on measurements of $Z$ production at SLC and LEP, as well as $Z$+jet production at the LHC. Our new constraints exclude the parameter space that could potentially explain the observed discrepancy between theoretical predictions and experimental data for the Lam-Tung relation. With these updated limits, we model-independently determine the maximum possible influence that beyond-SM contributions could have on the angular coefficients $A_0$ and $A_2$, which enter the Lam-Tung relation.
Unfolding $E_{11}$

Nicolas Boulanger, Paul P. Cook, Josh A. O'Connor, Peter West

SciPost Phys. 18, 149 (2025) · published 6 May 2025 | · pdf

We work out the unfolded formulation of the fields in the non-linear realisation of $E_{11}$. Using the connections in this formalism, we propose, at the linearised level, an infinite number of first-order duality relations between the dual fields in $E_{11}$. In this way, we introduce extra fields that do not belong to $E_{11}$ and we investigate their origin. The equations of motion of the fields are obtained by taking derivatives and higher traces of the duality relations.
MACK: Mismodeling addressed with contrastive knowledge

Liam Rankin Sheldon, Dylan Sheldon Rankin, Philip Harris

SciPost Phys. 18, 150 (2025) · published 6 May 2025 | · pdf

The use of machine learning methods in high energy physics typically relies on large volumes of precise simulation for training. As machine learning models become more complex they can become increasingly sensitive to differences between this simulation and the real data collected by experiments. We present a generic methodology based on contrastive learning which is able to greatly mitigate this negative effect. Crucially, the method does not require prior knowledge of the specifics of the mismodeling. While we demonstrate the efficacy of this technique using the task of jet-tagging at the Large Hadron Collider, it is applicable to a wide array of different tasks both in and out of the field of high energy physics.
Spectral anomalies and broken symmetries in maximally chaotic quantum maps

Laura Shou, Amit Vikram, Victor Galitski

SciPost Phys. 18, 151 (2025) · published 12 May 2025 | · pdf

Spectral statistics such as the level spacing statistics and spectral form factor (SFF) are widely expected to accurately identify "ergodicity," including the presence of underlying macroscopic symmetries, in generic quantum systems ranging from quantized chaotic maps to interacting many-body systems. By studying various quantizations of maximally chaotic maps that break a discrete classical symmetry upon quantization, we demonstrate that this approach can be misleading and fail to detect macroscopic symmetries. Notably, the same classical map can exhibit signatures of different random matrix symmetry classes in short-range spectral statistics depending on the quantization. While the long-range spectral statistics encoded in the early time ramp of the SFF are more robust and correctly identify macroscopic symmetries in several common quantizations, we also demonstrate analytically and numerically that the presence of Berry-like phases in the quantization leads to spectral anomalies, which break this correspondence. Finally, we provide numerical evidence that long-range spectral rigidity remains directly correlated with ergodicity in the quantum dynamical sense of visiting a complete orthonormal basis.
New physics through flavor tagging at FCC-ee

Admir Greljo, Hector Tiblom, Alessandro Valenti

SciPost Phys. 18, 152 (2025) · published 12 May 2025 | · pdf

Leveraging recent advancements in machine learning-based flavor tagging, we develop an optimal analysis for measuring the hadronic cross-section ratios $R_b$, $R_c$, and $R_s$ at the FCC-ee during its $WW$, $Zh$, and $t\bar{t}$ runs. Our results indicate up to a two-order-of-magnitude improvement in precision, providing an unprecedented test of the SM. Using these observables, along with $R_\ell$ and $R_t$, we project sensitivity to flavor non-universal four-fermion (4F) interactions within the SMEFT, contributing both at the tree-level and through the renormalization group (RG). We highlight a subtle complementarity with RG-induced effects at the FCC-ee's $Z$-pole. Our analysis demonstrates significant improvements over the current LEP-II and LHC bounds in probing flavor-conserving 4F operators involving heavy quark flavors and all lepton flavors. As an application, we explore simplified models addressing current $B$-meson anomalies, demonstrating that FCC-ee can effectively probe the relevant parameter space. Finally, we design optimized search strategies for quark flavor-violating 4F interactions.
Intrinsically/purely gapless-SPT from non-invertible duality transformations

Linhao Li, Masaki Oshikawa, Yunqin Zheng

SciPost Phys. 18, 153 (2025) · published 13 May 2025 | · pdf

The Kennedy-Tasaki (KT) transformation was used to construct the gapped symmetry protected topological (SPT) phase from the symmetry breaking phase with open boundary condition, and was generalized in our proceeding work [Phys. Rev. B 108, 214429 (2023)] on a ring by sacrificing the unitarity, and should be understood as a non-invertible duality transformation. In this work, we further apply the KT transformation to systematically construct gapless symmetry protected topological phases. This construction reproduces the known examples of (intrinsically) gapless SPT where the non-trivial topological features come from the gapped sectors by means of decorated defect constructions. We also construct new (intrinsically) purely gapless SPTs where there are no gapped sectors, hence are beyond the decorated defect construction. This construction elucidates the field theory description of the various gapless SPTs, and can also be applied to analytically study the stability of various gapless SPT models on the lattice under certain symmetric perturbations.
The complex Liouville string: The matrix integral

Scott Collier, Lorenz Eberhardt, Beatrix Mühlmann, Victor A. Rodriguez

SciPost Phys. 18, 154 (2025) · published 13 May 2025 | · pdf

We propose a duality between the complex Liouville string and a two-matrix integral. The complex Liouville string is defined by coupling two Liouville theories with complex central charges $c = 13 ± i \lambda$ on the worldsheet. The matrix integral is characterized by its spectral curve which allows us to compute the perturbative string amplitudes recursively via topological recursion. This duality constitutes a controllable instance of holographic duality. The leverage on the theory is provided by the rich analytic structure of the string amplitudes that we discussed in [arXiv:2409.18759] and allows us to perform numerous tests on the duality.
SKATR: A self-supervised summary transformer for SKA

Ayodele Ore, Caroline Heneka, Tilman Plehn

SciPost Phys. 18, 155 (2025) · published 14 May 2025 | · pdf

The Square Kilometer Array will initiate a new era of radio astronomy by allowing 3D imaging of the Universe during Cosmic Dawn and Reionization. Modern machine learning is crucial to analyze the highly structured and complex signal. However, accurate training data is expensive to simulate, and supervised learning may not generalize. We introduce a self-supervised vision transformer, SKATR, whose learned encoding can be cheaply adapted for downstream tasks on 21cm maps. Focusing on regression and generative inference of astrophysical and cosmological parameters, we demonstrate that SKATR representations are maximally informative and that SKATR generalizes out-of-domain to differently-simulated, noised, and higher-resolution datasets.
The club sandwich: Gapless phases and phase transitions with non-invertible symmetries

Lakshya Bhardwaj, Lea E. Bottini, Daniel Pajer, Sakura Schäfer-Nameki

SciPost Phys. 18, 156 (2025) · published 14 May 2025 | · pdf

We provide a generalization of the Symmetry Topological Field Theory (SymTFT) framework to characterize phase transitions and gapless phases with categorical symmetries. The central tool is the club sandwich, which extends the SymTFT setup to include an interface between two topological orders: there is a symmetry boundary, which is gapped, and a physical boundary that may be gapless, but in addition, there is also a gapped interface in the middle. The club sandwich generalizes so-called Kennedy-Tasaki (KT) transformations. Building on the results in [L. Bhardwaj et al., Phys. Rev. Lett. 133, 161601 (2024); L. Bhardwaj et al., SciPost Phys. 18, 032 (2025)] on gapped phases with categorical symmetries, we construct gapless theories describing phase transitions with non-invertible symmetries by applying suitable KT transformations on known phase transitions provided by the critical Ising model and the 3-state Potts model. We also describe in detail the order parameters in these gapless theories characterizing the phase transitions, which are generally mixtures of conventional and string-type order parameters mixed together by the action of categorical symmetries. Additionally, removing the physical boundary from the club sandwiches results in club quiches, which characterize all possible gapped boundary phases with (possibly non-invertible) symmetries that can arise on the boundary of a bulk gapped phase. We also provide a mathematical characterization of gapped boundary phases with symmetries as pivotal tensor functors whose targets are pivotal multi-fusion categories.
Intertwined order of generalized global symmetries

Benjamin Moy, Eduardo Fradkin

SciPost Phys. 18, 157 (2025) · published 15 May 2025 | · pdf

We investigate the interplay of generalized global symmetries in 2+1 dimensions in a lattice model that couples a $\mathbb{Z}_N$ clock model to a $\mathbb{Z}_N$ gauge theory via a topological interaction. This coupling binds the charges of one symmetry to the disorder operators of the other, and when these composite objects condense, they give rise to emergent generalized symmetries with mixed 't Hooft anomalies. These anomalies result in phases with ordinary symmetry breaking, topological order, and symmetry-protected topological (SPT) order, where the different types of order are not independent but intimately related. We further explore the gapped boundary states of these exotic phases and develop theories for phase transitions between them. Additionally, we extend this lattice model to incorporate a non-invertible global symmetry, which can be spontaneously broken, leading to domain walls with non-trivial fusion rules.
On the topology of solutions to random continuous constraint satisfaction problems

Jaron Kent-Dobias

SciPost Phys. 18, 158 (2025) · published 15 May 2025 | · pdf

We consider the set of solutions to $M$ random polynomial equations whose $N$ variables are restricted to the $(N-1)$-sphere. Each equation has independent Gaussian coefficients and a target value $V_0$. When solutions exist, they form a manifold. We compute the average Euler characteristic of this manifold in the limit of large $N$, and find different behavior depending on the target value $V_0$, the ratio $\alpha=M/N$, and the variances of the coefficients. We divide this behavior into five phases with different implications for the topology of the solution manifold. When $M=1$ there is a correspondence between this problem and level sets of the energy in the spherical spin glasses. We conjecture that the transition energy dividing two of the topological phases corresponds to the energy asymptotically reached by gradient descent from a random initial condition, possibly resolving an open problem in out-of-equilibrium dynamics. However, the quality of the available data leaves the question open for now.
Tighter lower bounds on quantum annealing times

Luis Pedro García-Pintos, Mrunmay Sahasrabudhe, Christian Arenz

SciPost Phys. 18, 159 (2025) · published 16 May 2025 | · pdf

We derive lower bounds on the time needed for a quantum annealer to prepare the ground state of a target Hamiltonian. These bounds do not depend on the annealing schedule and can take the local structure of the Hamiltonian into account. Consequently, the bounds are computable without knowledge of the annealer's dynamics and, in certain cases, scale with the size of the system. We discuss spin systems where the bounds are polynomially tighter than existing bounds, qualitatively capturing the scaling of the exact annealing times as a function of the number of spins.
Spin-chain based quantum thermal machines

Edoardo Maria Centamori, Michele Campisi, Vittorio Giovannetti

SciPost Phys. 18, 160 (2025) · published 16 May 2025 | · pdf

We study the performance of quantum thermal machines in which the working fluid of the model is represented by a many-body quantum system that is periodically connected with external baths via local couplings. A formal characterization of the limit cycles of the set-up is presented in terms of the mixing properties of the quantum channel that describes the evolution of the fluid over a thermodynamic cycle. For the special case in which the system is a collection of spin $1/2$ particles coupled via magnetization preserving Hamiltonians, a full characterization of the possible operational regimes (i.e., thermal engine, refrigerator, heater and thermal accelerator) is provided: in this context we show in fact that the different regimes only depend upon a limited number of parameters (essentially the ratios of the energy gaps associated with the local Hamiltonians of the parts of the network which are in direct thermal contact with the baths).
Crystallography, group cohomology, and Lieb–Schultz–Mattis constraints

Chunxiao Liu, Weicheng Ye

SciPost Phys. 18, 161 (2025) · published 20 May 2025 | · pdf

We compute the mod-2 cohomology ring for three-dimensional (3D) space groups and establish a connection between them and the lattice structure of crystals with space group symmetry. This connection allows us to obtain a complete set of Lieb-Schultz-Mattis constraints, specifying the conditions under which a unique, symmetric, gapped ground state cannot exist in 3D lattice magnets. We associate each of these constraints with an element in the third mod-2 cohomology of the space group, when the internal symmetry acts on-site and its projective representations are classified by powers of $\mathbb{Z}_2$. We demonstrate the relevance of our results to the study of $U(1)$ quantum spin liquids on the 3D pyrochlore lattice. We determine, through anomaly matching, the symmetry fractionalization patterns of both electric and magnetic charges, extending previous results from projective symmetry group classifications.
Monopole breaking of Chern-Weil symmetries

Eduardo García-Valdecasas, Matthew Reece, Motoo Suzuki

SciPost Phys. 18, 162 (2025) · published 20 May 2025 | · pdf

Gauge theories in $d$ dimensions with a nontrivial fundamental group admit a $(d-3)$-form magnetic symmetry and a $(d-5)$-form instantonic symmetry. These are examples of Chern-Weil symmetries, with conserved currents built out of the gauge field strength, which can only be explicitly broken through violations of the Bianchi identity. For U(1) gauge theory, it is clear that magnetic monopoles violate not only the $(d-3)$-form magnetic symmetry but also lower-form symmetries like the instantonic symmetry. It is also known that an improved instanton number symmetry current, which is conserved, can be constructed in the case that the magnetic monopole admits a dyonic excitation. We study the generalization to other gauge groups, showing that magnetic monopoles also violate instantonic symmetries for nonabelian groups like PSU($n$), and that dyon modes can restore such symmetries. Furthermore, we show that in many (but not all) examples where a gauge group $G$ is Higgsed to a gauge group $H$, the structure of monopoles and dyons emerging from the Higgsing process explicitly breaks the instantonic symmetries of $H$ to those of $G$. The meaning of explicit breaking of a $(d-5)$-form symmetry is clearest for $d > 4$, but these results also extend to $d = 4$, where the breaking is interpreted as an obstruction to coupling the theory to a background axion field.
Fusion rules and structure constants of E-series minimal models

Rongvoram Nivesvivat, Sylvain Ribault

SciPost Phys. 18, 163 (2025) · published 21 May 2025 | · pdf

In the ADE classification of Virasoro minimal models, the E-series is the sparsest: their central charges $c=1-6\frac{(p-q)^2}{pq}$ are not dense in the half-line $c∈ (-∞,1)$, due to $q=12,18,30$ taking only 3 values — the Coxeter numbers of $E_6, E_7, E_8$. The E-series is also the least well understood, with few known results beyond the spectrum. Here, we use a semi-analytic bootstrap approach for numerically computing 4-point correlation functions. We deduce non-chiral fusion rules, i.e. which 3-point structure constants vanish. These vanishings can be explained by constraints from null vectors, interchiral symmetry, simple currents, extended symmetries, permutations, and parity, except in one case for $q=30$. We conjecture that structure constants are given by a universal expression built from the double Gamma function, times polynomial functions of $\cos(\pi\frac{p}{q})$ with values in $\mathbb{Q}\big(\cos(\frac{\pi}{q})\big)$, which we work out explicitly for $q=12$. We speculate on generalizing E-series minimal models to generic integer values of $q$, and recovering loop CFTs as $p,q\to ∞$.
A radial variable for de Sitter two-point functions

Manuel Loparco, Jiaxin Qiao, Zimo Sun

SciPost Phys. 18, 164 (2025) · published 21 May 2025 | · pdf

We introduce a "radial" two-point invariant for quantum field theory in de Sitter (dS) analogous to the radial coordinate used in conformal field theory. We show that the two-point function of a free massive scalar in the Bunch-Davies vacuum has an exponentially convergent series expansion in this variable with positive coefficients only. Assuming a convergent Källén-Lehmann decomposition, this result is then generalized to the two-point function of any scalar operator non-perturbatively. A corollary of this result is that, starting from two-point functions on the sphere, an analytic continuation to an extended complex domain is admissible. dS two-point configurations live inside or on the boundary of this domain, and all the paths traced by analytic continuation between dS and the sphere or between dS and Euclidean Anti-de Sitter are also contained within this domain.
Stabilizer disentangling of conformal field theories

Martina Frau, Poetri Sonya Tarabunga, Mario Collura, Emanuele Tirrito, Marcello Dalmonte

SciPost Phys. 18, 165 (2025) · published 22 May 2025 | · pdf

Understanding how entanglement can be reduced through simple operations is crucial for both classical and quantum algorithms. We investigate the entanglement properties of lattice models hosting conformal field theories cooled via local Clifford operations, a procedure we refer to as stabilizer disentangling. We uncover two distinct regimes: a constant gain regime, where disentangling is volume-independent, and a log-gain regime, where disentanglement increases with volume, characterized by a reduced effective central charge. In both cases, disentangling efficiency correlates with the target state magic, with larger magic leading to more effective cooling. The dichotomy between the two cases stems from mutual stabilizer Rényi entropy, which influences the entanglement cooling process. We provide an analytical understanding of such effect in the context of cluster Ising models, that feature disentangling global Clifford operations. Our findings indicate that matrix product states possess subclasses based on the relationship between entanglement and magic, and clarifying the potential of new classes of variational states embedding Clifford dynamics within matrix product states.
Orbifolds of chiral fermionic CFTs and their duality

Kohki Kawabata, Shinichiro Yahagi

SciPost Phys. 18, 166 (2025) · published 26 May 2025 | · pdf

We consider chiral fermionic conformal field theories (CFTs) constructed from lattices and investigate their orbifolds under reflection and shift $\mathbb{Z}_2$ symmetries. For lattices based on binary error-correcting codes, we show the duality between reflection and shift orbifolds using a triality structure inherited from the binary codes. Additionally, we systematically compute the partition functions of the orbifold theories for both binary and nonbinary codes. Finally, we explore applications of this code-based construction in the search for supersymmetric CFTs and chiral fermionic CFTs without continuous symmetries.
Knowledge-dependent optimal Gaussian strategies for phase estimation

Ricard Ravell Rodríguez, Simon Morelli

SciPost Phys. 18, 167 (2025) · published 27 May 2025 | · pdf

When estimating an unknown phase rotation of a continuous-variable system with homodyne detection, the optimal probe state strongly depends on the value of the estimated parameter. In this article, we identify the optimal pure single-mode Gaussian probe states depending on the knowledge of the estimated phase parameter before the measurement. We find that for a large prior uncertainty, the optimal probe states are close to coherent states, a result in line with findings from noisy parameter estimation. However, with increasingly precise estimates of the parameter, it becomes beneficial to put more of the available energy into the squeezing of the probe state. Surprisingly, there is a clear jump, where the optimal probe state changes abruptly to a squeezed vacuum state, which maximizes the Fisher information for this estimation task. We use our results to study repeated measurements and compare different methods to adapt the probe state based on the changing knowledge of the parameter according to the previous findings.
Charting the space of ground states with tensor networks

Marvin Qi, David T. Stephen, Xueda Wen, Daniel Spiegel, Markus J. Pflaum, Agnès Beaudry, Michael Hermele

SciPost Phys. 18, 168 (2025) · published 28 May 2025 | · pdf

We employ matrix product states (MPS) and tensor networks to study topological properties of the space of ground states of gapped many-body systems. We focus on families of states in one spatial dimension, where each state can be represented as an injective MPS of finite bond dimension. Such states are short-range entangled ground states of gapped local Hamiltonians. To such parametrized families over $X$ we associate a gerbe, which generalizes the line bundle of ground states in zero-dimensional families (\textit{i.e.} in few-body quantum mechanics). The nontriviality of the gerbe is measured by a class in $H^3(X, \Z)$, which is believed to classify one-dimensional parametrized systems. We show that when the gerbe is nontrivial, there is an obstruction to representing the family of ground states with an MPS tensor that is continuous everywhere on $X$. We illustrate our construction with two examples of nontrivial parametrized systems over $X=S^3$ and $X = \R P^2 × S^1$. Finally, we sketch using tensor network methods how the construction extends to higher dimensional parametrized systems, with an example of a two-dimensional parametrized system that gives rise to a nontrivial 2-gerbe over $X = S^4$.
Coherent deflection of atomic samples and positional mesoscopic superpositions

Luis Felipe Alves da Silva, Leandro M. R. Rocha, Miled H. Y. Moussa

SciPost Phys. 18, 169 (2025) · published 28 May 2025 | · pdf

We present a protocol based on the interplay between superradiance and superabsorption to achieve the coherent deflection of an atomic sample due to the momentum transfer from the atoms to a cavity field. The coherent character of this momentum transfer, causing the atomic sample to deflect as a whole, follows from the collective nature of the atomic superradiant pulse and its superabsorption by the cavity field. The protocol is then used for the construction of positional mesoscopic atomic superpositions in cavity quantum electrodynamics.