Publications

Order by: publication date number of citations

• Higher-form symmetries, anomalous magnetohydrodynamics, and holography

  Arpit Das, Ruth Gregory, Nabil Iqbal

  SciPost Phys. 14, 163 (2023) · published 20 June 2023 | Toggle abstract · pdf

  In $U(1)$ Abelian gauge theory coupled to fermions, the non-conservation of the axial current due to the chiral anomaly is given by a dynamical operator $F_{\mu\nu} \tilde{F}^{\mu\nu}$ constructed from the field-strength tensor. We attempt to describe this physics in a universal manner by casting this operator in terms of the 2-form current for the 1-form symmetry associated with magnetic flux conservation. We construct a holographic dual with this symmetry breaking pattern and study some aspects of finite temperature anomalous magnetohydrodynamics. We explicitly calculate the charge susceptibility and the axial charge relaxation rate as a function of temperature and magnetic field and compare to recent lattice results. At small magnetic fields we find agreement with elementary hydrodynamics weakly coupled to an electrodynamic sector, but we find deviations at larger fields.

  6 citations

• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II

  J. M. Maillet, G. Niccoli, B. Pezelier

  SciPost Phys. 5, 026 (2018) · published 24 September 2018 | Toggle abstract · pdf

  This article is a direct continuation of [1] where we begun the study of the transfer matrix spectral problem for the cyclic representations of the trigonometric 6-vertex reflection algebra associated to the Bazhanov-Stroganov Lax operator. There we addressed this problem for the case where one of the K-matrices describing the boundary conditions is triangular. In the present article we consider the most general integrable boundary conditions, namely the most general boundary K-matrices satisfying the reflection equation. The spectral analysis is developed by implementing the method of Separation of Variables (SoV). We first design a suitable gauge transformation that enable us to put into correspondence the spectral problem for the most general boundary conditions with another one having one boundary K-matrix in a triangular form. In these settings the SoV resolution can be obtained along an extension of the method described in [1]. The transfer matrix spectrum is then completely characterized in terms of the set of solutions to a discrete system of polynomial equations in a given class of functions and equivalently as the set of solutions to an analogue of Baxter's T-Q functional equation. We further describe scalar product properties of the separate states including eigenstates of the transfer matrix.

  6 citations

• From combinatorial maps to correlation functions in loop models

  Linnea Grans-Samuelsson, Jesper Lykke Jacobsen, Rongvoram Nivesvivat, Sylvain Ribault, Hubert Saleur

  SciPost Phys. 15, 147 (2023) · published 9 October 2023 | Toggle abstract · pdf

  In two-dimensional statistical physics, correlation functions of the $O(N)$ and Potts models may be written as sums over configurations of non-intersecting loops. We define sums associated to a large class of combinatorial maps (also known as ribbon graphs). We allow disconnected maps, but not maps that include monogons. Given a map with $n$ vertices, we obtain a function of the moduli of the corresponding punctured Riemann surface. Due to the map's combinatorial (rather than topological) nature, that function is single-valued, and we call it an $n$-point correlation function. We conjecture that in the critical limit, such functions form a basis of solutions of certain conformal bootstrap equations. They include all correlation functions of the $O(N)$ and Potts models, and correlation functions that do not belong to any known model. We test the conjecture by counting solutions of crossing symmetry for four-point functions on the sphere.

  5 citations

• Spiking neuromorphic chip learns entangled quantum states

  Stefanie Czischek, Andreas Baumbach, Sebastian Billaudelle, Benjamin Cramer, Lukas Kades, Jan M. Pawlowski, Markus K. Oberthaler, Johannes Schemmel, Mihai A. Petrovici, Thomas Gasenzer, Martin Gärttner

  SciPost Phys. 12, 039 (2022) · published 26 January 2022 | Toggle abstract · pdf

  The approximation of quantum states with artificial neural networks has gained a lot of attention during the last years. Meanwhile, analog neuromorphic chips, inspired by structural and dynamical properties of the biological brain, show a high energy efficiency in running artificial neural-network architectures for the profit of generative applications. This encourages employing such hardware systems as platforms for simulations of quantum systems. Here we report on the realization of a prototype using the latest spike-based BrainScaleS hardware allowing us to represent few-qubit maximally entangled quantum states with high fidelities. Bell correlations of pure and mixed two-qubit states are well captured by the analog hardware, demonstrating an important building block for simulating quantum systems with spiking neuromorphic chips.

  5 citations

• Gauging tensor networks with belief propagation

  Joseph Tindall, Matt Fishman

  SciPost Phys. 15, 222 (2023) · published 1 December 2023 | Toggle abstract · pdf

  Effectively compressing and optimizing tensor networks requires reliable methods for fixing the latent degrees of freedom of the tensors, known as the gauge. Here we introduce a new algorithm for gauging tensor networks using belief propagation, a method that was originally formulated for performing statistical inference on graphical models and has recently found applications in tensor network algorithms. We show that this method is closely related to known tensor network gauging methods. It has the practical advantage, however, that existing belief propagation implementations can be repurposed for tensor network gauging, and that belief propagation is a very simple algorithm based on just tensor contractions so it can be easier to implement, optimize, and generalize. We present numerical evidence and scaling arguments that this algorithm is faster than existing gauging algorithms, demonstrating its usage on structured, unstructured, and infinite tensor networks. Additionally, we apply this method to improve the accuracy of the widely used simple update gate evolution algorithm.

  5 citations

• Stationarization and Multithermalization in spin glasses

  Pierluigi Contucci, Federico Corberi, Jorge Kurchan, Emanuele Mingione

  SciPost Phys. 10, 113 (2021) · published 26 May 2021 | Toggle abstract · pdf

  We develop further the study of a system in contact with a multibath having different temperatures at widely separated timescales. We consider those systems that do not thermalize in finite times when in contact with an ordinary bath but may do so in contact with a multibath. Thermodynamic integration is possible, thus allowing one to recover the stationary distribution on the basis of measurements performed in a `multi-reversible' transformation. We show that following such a protocol the system is at each step described by a generalization of the Boltzmann-Gibbs distribution, that has been studied in the past. Guerra's bound interpolation scheme for spin-glasses is closely related to this: by translating it into a dynamical setting, we show how it may actually be implemented in practice. The phase diagram plane of temperature vs "number of replicas", long studied in spin-glasses, in our approach becomes simply that of the two temperatures the system is in contact with. We suggest that this representation may be used to directly compare phenomenological and mean-field inspired models.Finally, we show how an approximate out of equilibrium probability distribution may be inferred experimentally on the basis of measurements along an almost reversible transformation.

  5 citations

• Towards non-invertible anomalies from generalized Ising models

  Shang Liu, Wenjie Ji

  SciPost Phys. 15, 150 (2023) · published 10 October 2023 | Toggle abstract · pdf

  We present a general approach to the bulk-boundary correspondence of noninvertible topological phases, including both topological and fracton orders. This is achieved by a novel bulk construction protocol where solvable $(d+1)$-dimensional bulk models with noninvertible topology are constructed from the so-called generalized Ising (GI) models in $d$ dimensions. The GI models can then terminate on the boundaries of the bulk models. The construction generates abundant examples, including not only prototype ones such as $\mathbb{Z}_2$ toric code models in any dimensions no less than two, and the X-cube fracton model, but also more diverse ones such as the $\mathbb{Z}_2× \mathbb{Z}_2$ topological order, the 4d $\mathbb{Z}_2$ topological order with pure-loop excitations, etc. The boundary of the solvable model is potentially anomalous and corresponds to precisely only sectors of the GI model that host certain total symmetry charges and/or satisfy certain boundary conditions. We derive a concrete condition for such bulk-boundary correspondence. The condition is violated only when the bulk model is either trivial or fracton ordered. A generalized notion of Kramers-Wannier duality plays an important role in the construction. Also, utilizing the duality, we find an example where a single anomalous theory can be realized on the boundaries of two distinct bulk fracton models, a phenomenon not expected in the case of topological orders. More generally, topological orders may also be generated starting with lattice models beyond the GI models, such as those with symmetry protected topological orders, through a variant bulk construction, which we provide in an appendix.

  5 citations

• Magnetic flux response of non-Hermitian topological phases

  Marco Michael Denner, Frank Schindler

  SciPost Phys. 14, 107 (2023) · published 11 May 2023 | Toggle abstract · pdf

  We derive the response of non-Hermitian topological phases with intrinsic point gap topology to localized magnetic flux insertions. In two spatial dimensions, we identify the necessary and sufficient conditions for a flux skin effect that localizes an extensive number of in-gap modes at a flux core. In three dimensions, we furthermore establish the existence of: a flux spectral jump, where flux tube insertion fills up the entire point gap only at a single parallel crystal momentum; a higher-order flux skin effect, which occurs at the ends of flux tubes in presence of pseudo-inversion symmetry; and a flux Majorana mode that represents a spectrally isolated mid-gap state in the complex energy plane. We uniquely associate each non-Hermitian symmetry class with intrinsic point gap topology with one of these cases or a trivial flux response, and discuss possible experimental realizations.

  5 citations

• Anisotropic higher rank $\mathbb{Z}_N$ topological phases on graphs

  Hiromi Ebisu, Bo Han

  SciPost Phys. 14, 106 (2023) · published 11 May 2023 | Toggle abstract · pdf

  We study unusual gapped topological phases where they admit $\mathbb{Z}_N$ fractional excitations in the same manner as topologically ordered phases, yet their ground state degeneracy depends on the local geometry of the system. Placing such phases on 2D lattice, composed of an arbitrary connected graph and 1D line, we find that the fusion rules of quasiparticle excitations are described by the Laplacian of the graph and that the number of superselection sectors is related to the kernel of the Laplacian. Based on this analysis, we further show that the ground state degeneracy is given by $\bigl[N\times \prod_{i}\text{gcd}(N, p_i)\bigr]^2$, where $p_i$'s are invariant factors of the Laplacian that are greater than one and gcd stands for the greatest common divisor. We also discuss braiding statistics between quasiparticle excitations.

  5 citations

• The Return of the Singularities: Applications of the Smeared Null Energy Condition

  Ben Freivogel, Eleni-Alexandra Kontou, Dimitrios Krommydas

  SciPost Phys. 13, 001 (2022) · published 15 July 2022 | Toggle abstract · pdf

  The classic singularity theorems of General Relativity rely on energy conditions that can be violated in semiclassical gravity. Here, we provide motivation for an energy condition obeyed by semiclassical gravity: the smeared null energy condition (SNEC), a proposed bound on the weighted average of the null energy along a finite portion of a null geodesic. We then prove a semiclassical singularity theorem using SNEC as an assumption. This theorem extends the Penrose theorem to semiclassical gravity. We also apply our bound to evaporating black holes and the traversable wormhole of Maldacena-Milekhin-Popov, and comment on the relationship of our results to other proposed semiclassical singularity theorems.

  5 citations