Publications

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• Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries

  Sahand Seifnashri

  SciPost Phys. 16, 098 (2024) · published 9 April 2024 | Toggle abstract · pdf

  We study 't Hooft anomalies of global symmetries in 1+1d lattice Hamiltonian systems. We consider anomalies in internal and lattice translation symmetries. We derive a microscopic formula for the "anomaly cocycle" using topological defects implementing twisted boundary conditions. The anomaly takes value in the cohomology group $H^3(G,U(1)) × H^2(G,U(1))$. The first factor captures the anomaly in the internal symmetry group $G$, and the second factor corresponds to a generalized Lieb-Schultz-Mattis anomaly involving $G$ and lattice translation. We present a systematic procedure to gauge internal symmetries (that may not act on-site) on the lattice. We show that the anomaly cocycle is the obstruction to gauging the internal symmetry while preserving the lattice translation symmetry. As an application, we construct anomaly-free chiral lattice gauge theories. We demonstrate a one-to-one correspondence between (locality-preserving) symmetry operators and topological defects, which is essential for the results we prove. We also discuss the generalization to fermionic theories. Finally, we construct non-invertible lattice translation symmetries by gauging internal symmetries with a Lieb-Schultz-Mattis anomaly.

  34 citations

• Hidden symmetry of Bogoliubov de Gennes quasi-particle eigenstates and universal relations in flat band superconducting bipartite lattices

  Georges Bouzerar, Maxime Thumin

  SciPost Phys. Core 7, 018 (2024) · published 9 April 2024 | Toggle abstract · pdf

  Unconventional flat band (FB) superconductivity, as observed in van der Waals heterostructures, could open promising avenues towards high-T$_c$ materials. In FBs, pairings and superfluid weight scale linearly with the interaction parameter, such an unusual behaviour justifies and encourages strategies to promote FB engineering. Bipartite lattices (BLs) which naturally host FBs could be particularly interesting candidates. Within Bogoliubov de Gennes theory and in the framework of the attractive Hubbard model in BLs, a hidden symmetry of the quasi-particle eigenstates is revealed. As a consequence, we demonstrate universal relations for the pairings and the superfluid weight that are independent of the characteristics of the hopping term. Remarkably, it is shown that these general properties are insensitive to disorder as long as the bipartite character is protected.

  5 citations

• Heat and charge transport in interacting nanoconductors driven by time-modulated temperatures

  Rosa López, Pascal Simon, Minchul Lee

  SciPost Phys. 16, 094 (2024) · published 5 April 2024 | Toggle abstract · pdf

  We investigate the quantum transport of the heat and the charge through a quantum dot coupled to fermionic contacts under the influence of time modulation of temperatures. We derive, within the nonequilibrium Keldysh Green's function formalism, generic formulas for the charge and heat currents by extending the concept of gravitational field introduced by Luttinger to the dynamically driven system and by identifying the correct form of dynamical contact energy. In linear response regime our formalism is validated from satisfying the Onsager reciprocity relations and demonstrates its utility to reveal nontrivial dynamical effects of the Coulomb interaction on charge and energy relaxations.

  5 citations

• Thermalization of long range Ising model in different dynamical regimes: A full counting statistics approach

  Nishan Ranabhat, Mario Collura

  SciPost Phys. Core 7, 017 (2024) · published 5 April 2024 | Toggle abstract · pdf

  We study the thermalization of the transverse field Ising chain with a power law decaying interaction $\sim 1/r^{\alpha}$ following a global quantum quench of the transverse field in two different dynamical regimes. The thermalization behavior is quantified by comparing the full probability distribution function (PDF) of the evolving states with the corresponding thermal state given by the canonical Gibbs ensemble (CGE). To this end, we used the matrix product state (MPS)-based Time Dependent Variational Principle (TDVP) algorithm to simulate both real time evolution following a global quantum quench and the finite temperature density operator. We observe that thermalization is strongly suppressed in the region with strong confinement for all interaction strengths $\alpha$, whereas thermalization occurs in the region with weak confinement.

  6 citations

• Generalized charges, part I: Invertible symmetries and higher representations

  Lakshya Bhardwaj, Sakura Schäfer-Nameki

  SciPost Phys. 16, 093 (2024) · published 4 April 2024 | Toggle abstract · pdf

  $q$-charges describe the possible actions of a generalized symmetry on $q$-dimensional operators. In Part I of this series of papers, we describe $q$-charges for invertible symmetries; while the discussion of $q$-charges for non-invertible symmetries is the topic of Part II. We argue that $q$-charges of a standard global symmetry, also known as a 0-form symmetry, correspond to the so-called $(q+1)$-representations of the 0-form symmetry group, which are natural higher-categorical generalizations of the standard notion of representations of a group. This generalizes already our understanding of possible charges under a 0-form symmetry! Just like local operators form representations of the 0-form symmetry group, higher-dimensional extended operators form higher-representations. This statement has a straightforward generalization to other invertible symmetries: $q$-charges of higher-form and higher-group symmetries are $(q+1)$-representations of the corresponding higher-groups. There is a natural extension to higher-charges of non-genuine operators (i.e. operators that are attached to higher-dimensional operators), which will be shown to be intertwiners of higher-representations. This brings into play the higher-categorical structure of higher-representations. We also discuss higher-charges of twisted sector operators (i.e. operators that appear at the boundary of topological operators of one dimension higher), including operators that appear at the boundary of condensation defects.

  49 citations

• A lattice pairing-field approach to ultracold Fermi gases

  Florian Ehmann, Joaquín E. Drut, Jens Braun

  SciPost Phys. 16, 091 (2024) · published 3 April 2024 | Toggle abstract · pdf

  We develop a pairing-field formalism for ab initio studies of non-relativistic two-component fermions on a (d+1)-dimensional spacetime lattice. More specifically, we focus on theories where the interaction between the two components can be described by the exchange of a corresponding pairing field. The introduction of a pairing field may indeed be convenient for studies of, e.g., the finite-temperature phase structure and critical behavior of, e.g., ultracold atomic Fermi gases. Moreover, such a formalism allows to directly compute the momentum and frequency dependence of the pair propagator, from which the pair-correlation function can be extracted. For a first illustration of the application of our formalism, we compute the density equation of state and the superfluid order parameter for a gas of unpolarized fermions in (0+1) dimensions by employing the complex Langevin approach to surmount the sign problem.

  1 citation

• Higher-group symmetry in finite gauge theory and stabilizer codes

  Maissam Barkeshli, Yu-An Chen, Po-Shen Hsin, Ryohei Kobayashi

  SciPost Phys. 16, 089 (2024) · published 3 April 2024 | Toggle abstract · pdf

  A large class of gapped phases of matter can be described by topological finite group gauge theories. In this paper, we show how such gauge theories possess a higher-group global symmetry, which we study in detail. We derive the $d$-group global symmetry and its 't Hooft anomaly for topological finite group gauge theories in $(d+1)$ space-time dimensions, including non-Abelian gauge groups and Dijkgraaf-Witten twists. We focus on the 1-form symmetry generated by invertible (Abelian) magnetic defects and the higher-form symmetries generated by invertible topological defects decorated with lower dimensional gauged symmetry-protected topological (SPT) phases. We show that due to a generalization of the Witten effect and charge-flux attachment, the 1-form symmetry generated by the magnetic defects mixes with other symmetries into a higher group. We describe such higher-group symmetry in various lattice model examples. We discuss several applications, including the classification of fermionic SPT phases in (3+1)D for general fermionic symmetry groups, where we also derive a simpler formula for the $[O_5] ∈ H^5(BG, U(1))$ obstruction that has appeared in prior work. We also show how the $d$-group symmetry is related to fault-tolerant non-Pauli logical gates and a refined Clifford hierarchy in stabilizer codes. We discover new logical gates in stabilizer codes using the $d$-group symmetry, such as a controlled Z gate in the (3+1) D $\mathbb{Z}_2$ toric code.

  25 citations

• Abelian combinatorial gauge symmetry

  Hongji Yu, Dmitry Green, Andrei E. Ruckenstein, Claudio Chamon

  SciPost Phys. Core 7, 014 (2024) · published 26 March 2024 | Toggle abstract · pdf

  Combinatorial gauge symmetry is a principle that allows us to construct lattice gauge theories with two key and distinguishing properties: a) only one- and two-body interactions are needed; and b) the symmetry is exact rather than emergent in an effective or perturbative limit. The ground state exhibits topological order for a range of parameters. This paper is a generalization of the construction to any finite Abelian group. In addition to the general mathematical construction, we present a physical implementation in superconducting wire arrays, which offers a route to the experimental realization of lattice gauge theories with static Hamiltonians.

  1 citation

• Quantum parameter estimation with many-body fermionic systems and application to the Hall effect

  Olivier Giraud, Mark-Oliver Goerbig, Daniel Braun

  SciPost Phys. 16, 085 (2024) · published 25 March 2024 | Toggle abstract · pdf

  We calculate the quantum Fisher information for a generic many-body fermionic system in a pure state depending on a parameter. We discuss the situations where the parameter is imprinted in the basis states, in the state coefficients, or both. In the case where the parameter dependence of coefficients results from a Hamiltonian evolution, we derive a particularly simple expression for the quantum Fisher information. We apply our findings to the quantum Hall effect, and evaluate the quantum Fisher information associated with the optimal measurement of the magnetic field for a system in the ground state of the effective Hamiltonian. The occupation of electron states with high momentum enforced by the Pauli principle leads to a "super-Heisenberg" scaling of the sensitivity with a power law that depends on the geometry of the sensor.

  1 citation

• Anomalous Luttinger equivalence between temperature and curved spacetime: From black holes to thermal quenches

  Baptiste Bermond, Maxim Nikolaevich Chernodub, Adolfo G. Grushin, David Carpentier

  SciPost Phys. 16, 084 (2024) · published 25 March 2024 | Toggle abstract · pdf

  Building on the idea of Tolman and Ehrenfest that heat has weight, Luttinger established a deep connection between gravitational fields and thermal transport. However, this relation does not include anomalous quantum fluctuations that become paramount in strongly curved spacetime. In this work, we revisit the celebrated Tolman-Ehrenfest and Luttinger relations and show how to incorporate the quantum energy scales associated with these fluctuations, captured by gravitational anomalies of quantum field theories. We point out that such anomalous fluctuations naturally occur in the quantum atmosphere of a black hole. Our results reveal that analogous fluctuations are also observable in thermal conductors in flat-space time provided local temperature varies strongly. As a consequence, we establish that the gravitational anomalies manifest themselves naturally in non-linear thermal response of a quantum wire. In addition, we propose a systematic way to identify thermal analogues of black hole's anomalous quantum fluctuations associated to gravitational anomalies. We identify their signatures in propagating energy waves following a thermal quench, as well as in the energy density of heating Floquet states induced by repeated thermal quenches.

  5 citations