Publications

Order by: publication date number of citations

• A degeneracy bound for homogeneous topological order

  Jeongwan Haah

  SciPost Phys. 10, 011 (2021) · published 20 January 2021 | Toggle abstract · pdf

  We introduce a notion of homogeneous topological order, which is obeyed by most, if not all, known examples of topological order including fracton phases on quantum spins (qudits). The notion is a condition on the ground state subspace, rather than on the Hamiltonian, and demands that given a collection of ball-like regions, any linear transformation on the ground space be realized by an operator that avoids the ball-like regions. We derive a bound on the ground state degeneracy $\mathcal D$ for systems with homogeneous topological order on an arbitrary closed Riemannian manifold of dimension $d$, which reads \[ \log \mathcal D \le c \mu (L/a)^{d-2}.\] Here, $L$ is the diameter of the system, $a$ is the lattice spacing, and $c$ is a constant that only depends on the isometry class of the manifold, and $\mu$ is a constant that only depends on the density of degrees of freedom. If $d=2$, the constant $c$ is the (demi)genus of the space manifold. This bound is saturated up to constants by known examples.

  18 citations

• Statistical mechanics of coupled supercooled liquids in finite dimensions

  Benjamin Guiselin, Ludovic Berthier, Gilles Tarjus

  SciPost Phys. 12, 091 (2022) · published 14 March 2022 | Toggle abstract · pdf

  We study the statistical mechanics of supercooled liquids when the system evolves at a temperature $T$ with a field $\epsilon$ linearly coupled to its overlap with a reference configuration of the same liquid sampled at a temperature $T_0$. We use mean-field theory to fully characterize the influence of the reference temperature $T_0$, and we mainly study the case of a fixed, low-$T_0$ value in computer simulations. We numerically investigate the extended phase diagram in the $(\epsilon,T)$ plane of model glass-forming liquids in spatial dimensions $d=2$ and $d=3$, relying on umbrella sampling and reweighting techniques. For both $2d$ and $3d$ cases, a similar phenomenology with nontrivial thermodynamic fluctuations of the overlap is observed at low temperatures, but a detailed finite-size analysis reveals qualitatively distinct behaviors. We establish the existence of a first-order transition line for nonzero $\epsilon$ ending in a critical point in the universality class of the random-field Ising model (RFIM) in $d=3$. In $d=2$ instead, no phase transition is found in large enough systems at least down to temperatures below the extrapolated calorimetric glass transition temperature $T_g$. Our results confirm that glass-forming liquid samples of limited size display the thermodynamic fluctuations expected for finite systems undergoing a random first-order transition. They also support the relevance of the physics of the RFIM for supercooled liquids, which may then explain the qualitative difference between $2d$ and $3d$ glass-formers.

  18 citations

• Quantum Gutzwiller approach for the two-component Bose-Hubbard model

  Victor E. Colussi, Fabio Caleffi, Chiara Menotti, Alessio Recati

  SciPost Phys. 12, 111 (2022) · published 29 March 2022 | Toggle abstract · pdf

  We study the effects of quantum fluctuations in the two-component Bose-Hubbard model generalizing to mixtures the quantum Gutzwiller approach introduced recently in [Phys. Rev. Research 2, 033276 (2020)]. As a basis for our study, we analyze the mean-field ground-state phase diagram and spectrum of elementary excitations, with particular emphasis on the quantum phase transitions of the model. Within the quantum critical regimes, we address both the superfluid transport properties and the linear response dynamics to density and spin probes of direct experimental relevance. Crucially, we find that quantum fluctuations have a dramatic effect on the drag between the superfluid species of the system, particularly in the vicinity of the paired and antipaired phases absent in the usual one-component Bose-Hubbard model. Additionally, we analyse the contributions of quantum corrections to the one-body coherence and density/spin fluctuations from the perspective of the collective modes of the system, providing results for the few-body correlations in all the regimes of the phase diagram.

  18 citations

• Loop amplitudes from precision networks

  Simon Badger, Anja Butter, Michel Luchmann, Sebastian Pitz, Tilman Plehn

  SciPost Phys. Core 6, 034 (2023) · published 25 April 2023 | Toggle abstract · pdf

  Evaluating loop amplitudes is a time-consuming part of LHC event generation. For di-photon production with jets we show that simple, Bayesian networks can learn such amplitudes and model their uncertainties reliably. A boosted training of the Bayesian network further improves the uncertainty estimate and the network precision in critical phase space regions. In general, boosted network training of Bayesian networks allows us to move between fit-like and interpolation-like regimes of network training.

  18 citations

• Conformal dispersion relations for defects and boundaries

  Lorenzo Bianchi, Davide Bonomi

  SciPost Phys. 15, 055 (2023) · published 8 August 2023 | Toggle abstract · pdf

  We derive a dispersion relation for two-point correlation functions in defect conformal field theories. The correlator is expressed as an integral over a (single) discontinuity that is controlled by the bulk channel operator product expansion (OPE). This very simple relation is particularly useful in perturbative settings where the discontinuity is determined by a subset of bulk operators. In particular, we apply it to holographic correlators of two chiral primary operators in $\mathcal{N}=4$ Super Yang-Mills theory in the presence of a supersymmetric Wilson line. With a very simple computation, we are able to reproduce and extend existing results. We also propose a second relation, which reconstructs the correlator from a double discontinuity, and is controlled by the defect channel OPE. Finally, for the case of codimension-one defects (boundaries and interfaces) we derive a dispersion relation which receives contributions from both OPE channels and we apply it to the boundary correlator in the O(N) critical model. We reproduce the order $\epsilon^2$ result in the $\epsilon$-expansion using as input a finite number of boundary CFT data.

  18 citations

• Tensor network Python (TeNPy) version 1

  Johannes Hauschild, Jakob Unfried, Sajant Anand, Bartholomew Andrews, Marcus Bintz, Umberto Borla, Stefan Divic, Markus Drescher, Jan Geiger, Martin Hefel, Kévin Hémery, Wilhelm Kadow, Jack Kemp, Nico Kirchner, Vincent S. Liu, Gunnar Möller, Daniel Parker, Michael Rader, Anton Romen, Samuel Scalet, Leon Schoonderwoerd, Maximilian Schulz, Tomohiro Soejima, Philipp Thoma, Yantao Wu, Philip Zechmann, Ludwig Zweng, Roger S. K. Mong, Michael P. Zaletel, Frank Pollmann

  SciPost Phys. Codebases 41 (2024) · published 26 November 2024 | Toggle abstract · pdf

  TeNPy (short for 'Tensor Network Python') is a python library for the simulation of strongly correlated quantum systems with tensor networks. The philosophy of this library is to achieve a balance of readability and usability for new-comers, while at the same time providing powerful algorithms for experts. The focus is on MPS algorithms for 1D and 2D lattices, such as DMRG ground state search, as well as dynamics using TEBD, TDVP, or MPO evolution. This article is a companion to the recent version 1.0 release of TeNPy and gives a brief overview of the package.

  18 citations

• A time-dependent regularization of the Redfield equation

  Antonio D'Abbruzzo, Vasco Cavina, Vittorio Giovannetti

  SciPost Phys. 15, 117 (2023) · published 27 September 2023 | Toggle abstract · pdf

  We introduce a new regularization of the Redfield equation based on a replacement of the Kossakowski matrix with its closest positive semidefinite neighbor. Unlike most of the existing approaches, this procedure is capable of retaining the time dependence of the Kossakowski matrix, leading to a completely positive divisible quantum process. Using the dynamics of an exactly-solvable three-level open system as a reference, we show that our approach performs better during the transient evolution, if compared to other approaches like the partial secular master equation or the universal Lindblad equation. To make the comparison between different regularization schemes independent from the initial state, we introduce a new quantitative approach based on the Choi-Jamiołkowski isomorphism.

  18 citations

• An invitation to the principal series

  Tarek Anous, Jim Skulte

  SciPost Phys. 9, 028 (2020) · published 1 September 2020 | Toggle abstract · pdf

  Scalar unitary representations of the isometry group of $d$-dimensional de Sitter space $SO(1,d)$ are labeled by their conformal weights $\Delta$. A salient feature of de Sitter space is that scalar fields with sufficiently large mass compared to the de Sitter scale $1/\ell$ have complex conformal weights, and physical modes of these fields fall into the unitary continuous principal series representation of $SO(1,d)$. Our goal is to study these representations in $d=2$, where the relevant group is $SL(2,\mathbb{R})$. We show that the generators of the isometry group of dS$_2$ acting on a massive scalar field reproduce the quantum mechanical model introduced by de Alfaro, Fubini and Furlan (DFF) in the early/late time limit. Motivated by the ambient dS$_2$ construction, we review in detail how the DFF model must be altered in order to accommodate the principal series representation. We point out a difficulty in writing down a classical Lagrangian for this model, whereas the canonical Hamiltonian formulation avoids any problem. We speculate on the meaning of the various de Sitter invariant vacua from the point of view of this toy model and discuss some potential generalizations.

  18 citations

• Euler-scale dynamical fluctuations in non-equilibrium interacting integrable systems

  Gabriele Perfetto, Benjamin Doyon

  SciPost Phys. 10, 116 (2021) · published 27 May 2021 | Toggle abstract · pdf

  We derive an exact formula for the scaled cumulant generating function of the time-integrated current associated to an arbitrary ballistically transported conserved charge. Our results rely on the Euler-scale description of interacting, many-body, integrable models out of equilibrium given by the generalized hydrodynamics, and on the large deviation theory. Crucially, our findings extend previous studies by accounting for inhomogeneous and dynamical initial states in interacting systems. We present exact expressions for the first three cumulants of the time-integrated current. Considering the non-interacting limit of our general expression for the scaled cumulant generating function, we further show that for the partitioning protocol initial state our result coincides with previous results of the literature. Given the universality of the generalized hydrodynamics, the expression obtained for the scaled cumulant generating function is applicable to any interacting integrable model obeying the hydrodynamic equations, both classical and quantum.

  18 citations

• Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters

  Jonas Richter, Tjark Heitmann, Robin Steinigeweg

  SciPost Phys. 9, 031 (2020) · published 3 September 2020 | Toggle abstract · pdf

  We study quantum quenches in the transverse-field Ising model defined on different lattice geometries such as chains, two- and three-leg ladders, and two-dimensional square lattices. Starting from fully polarized initial states, we consider the dynamics of the transverse and the longitudinal magnetization for quenches to weak, strong, and critical values of the transverse field. To this end, we rely on an efficient combination of numerical linked cluster expansions (NLCEs) and a forward propagation of pure states in real time. As a main result, we demonstrate that NLCEs comprising solely rectangular clusters provide a promising approach to study the real-time dynamics of two-dimensional quantum many-body systems directly in the thermodynamic limit. By comparing to existing data from the literature, we unveil that NLCEs yield converged results on time scales which are competitive to other state-of-the-art numerical methods.

  18 citations