Publications

Order by: publication date number of citations

• Superintegrable cellular automata and dual unitary gates from Yang-Baxter maps

  Tamás Gombor, Balázs Pozsgay

  SciPost Phys. 12, 102 (2022) · published 22 March 2022 | Toggle abstract · pdf

  We consider one dimensional block cellular automata, where the local update rules are given by Yang-Baxter maps, which are set theoretical solutions of the Yang-Baxter equations. We show that such systems are superintegrable: they possess an exponentially large set of conserved local charges, such that the charge densities propagate ballistically on the chain. For these quantities we observe a complete absence of "operator spreading". In addition, the models can also have other local charges which are conserved only additively. We discuss concrete models up to local dimensions $N\le 4$, and show that they give rise to rich physical behaviour, including non-trivial scattering of particles and the coexistence of ballistic and diffusive transport. We find that the local update rules are classical versions of the "dual unitary gates" if the Yang-Baxter maps are non-degenerate. We discuss consequences of dual unitarity, and we also discuss a family of dual unitary gates obtained by a non-integrable quantum mechanical deformation of the Yang-Baxter maps.

  10 citations

• Bose-Einstein condensate in an elliptical waveguide

  Luca Salasnich

  SciPost Phys. Core 5, 015 (2022) · published 22 March 2022 | Toggle abstract · pdf

  We investigate the effects of spatial curvature for an atomic Bose-Einstein condensate confined in an elliptical waveguide. The system is well described by an effective 1D Gross-Pitaevskii equation with a quantum-curvature potential, which has the shape of a double-well but crucially depends on the eccentricity of the ellipse. The ground state of the system displays a quantum phase transition from a two-peak configuration to a one-peak configuration at a critical attractive interaction strength. In correspondence of this phase transition the superfluid fraction strongly reduces and goes to zero for a sufficiently attractive Bose-Bose interaction.

  2 citations

• Sub-GeV dark matter models and direct detection

  Tongyan Lin

  SciPost Phys. Lect. Notes 43 (2022) · published 18 March 2022 | Toggle abstract · pdf

  Lecture notes for Les Houches Summer School 2021: Dark Matter. These lectures give a brief introduction to sub-GeV dark matter models, and then reviews theory and approaches to direct detection of sub-GeV dark matter.

  4 citations

• Measurable signatures of bosonic fractional Chern insulator states and their fractional excitations in a quantum-gas microscope

  Botao Wang, Xiao-Yu Dong, André Eckardt

  SciPost Phys. 12, 095 (2022) · published 17 March 2022 | Toggle abstract · pdf

  The recent progress in engineering topological band structures in optical-lattice systems makes it promising to study fractional Chern insulator states in these systems. Here we consider a realistic finite system of a few repulsively interacting bosons on a square lattice with magnetic flux and sharp edges, as it can be realized in quantum-gas microscopes. We investigate under which conditions a fractional Chern insulator state corresponding to the Laughlin-like state at filling $\nu=1/2$ can be stabilized and its fractional excitations probed. Using numerical simulations, we find an incompressible bulk density at the expected filling for systems, whose linear extent is as small as 6-8 sites. This is a promising result, since such small systems are favorable with respect to the required adiabatic state preparation. Moreover, we also see very clear signatures of excitations with fractional charge in response both to static pinning potentials and dynamical flux insertion. Since the compressible edges, which are found to feature chiral currents, can serve as a reservoir, these observations are robust against changes in the total particle number. Our results suggest that signatures of both a fractional Chern insulator state and its fractional excitations can be found under realistic experimental conditions.

  9 citations

• Time-reversal-broken Weyl semimetal in the Hofstadter regime

  Faruk Abdulla, Ankur Das, Sumathi Rao, Ganpathy Murthy

  SciPost Phys. Core 5, 014 (2022) · published 16 March 2022 | Toggle abstract · pdf

  We study the phase diagram for a lattice model of a time-reversal-broken three-dimensional Weyl semimetal (WSM) in an orbital magnetic field $B$ with a flux of $p/q$ per unit cell ($0\le p \le q-1$), with minimal crystalline symmetry. We find several interesting phases: (i) WSM phases with $2q$, $4q$, $6q$, and $8q$ Weyl nodes and corresponding surface Fermi arcs, (ii) a layered Chern insulating (LCI) phase, gapped in the bulk, but with gapless surface states, (iii) a phase in which some bulk bands are gapless with Weyl nodes, coexisting with others that are gapped but topologically nontrivial, adiabatically connected to an LCI phase, (iv) a new gapped trivially insulating phase (I$'$) with (non-topological) counter-propagating surface states, which could be gapped out in the absence of crystal symmetries. Importantly, we are able to obtain the phase boundaries analytically for all $p,q$. Analyzing the gaps for $p=1$ and very large $q$ enables us to smoothly take the zero-field limit, even though the phase diagrams look ostensibly very different for $q=1, B=0$, and $q\to\infty, B\to 0$.

  6 citations

• Photoemission spectral functions from the three-body Green's function

  Gabriele Riva, Timothée Audinet, Matthieu Vladaj, Pina Romaniello, J. Arjan Berger

  SciPost Phys. 12, 093 (2022) · published 15 March 2022 | Toggle abstract · pdf

  We present an original strategy for the calculation of direct and inverse photo-emission spectra from first principles. The main goal is to go beyond the standard Green's function approaches, such as the $GW$ method, in order to find a good description not only of the quasiparticles but also of the satellite structures, which are of particular importance in strongly correlated materials. To this end we use as a key quantity the three-body Green's function, or, more precisely, its hole-hole-electron and electron-electron-hole parts, and we show how the one-body Green's function, and hence the corresponding spectral function, can be retrieved from it. We show that, contrary to the one-body Green's function, information about satellites is already present in the non-interacting three-body Green's function. Therefore, simple approximations to the three-body self-energy, which is defined by the Dyson equation for the three-body Green's function and which contains many-body effects, can still yield accurate spectral functions. In particular, the self-energy can be chosen to be static which could simplify a self-consistent solution of the Dyson equation. We give a proof of principle of our strategy by applying it to the Hubbard dimer, for which the exact self-energy is available.

  6 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.

  10 citations

• Coarse-grained curvature tensor on polygonal surfaces

  Charlie Duclut, Aboutaleb Amiri, Joris Paijmans, Frank Jülicher

  SciPost Phys. Core 5, 011 (2022) · published 11 March 2022 | Toggle abstract · pdf

  Using concepts from integral geometry, we propose a definition for a local coarse-grained curvature tensor that is well-defined on polygonal surfaces. This coarse-grained curvature tensor shows fast convergence to the curvature tensor of smooth surfaces, capturing with accuracy not only the principal curvatures but also the principal directions of curvature. Thanks to the additivity of the integrated curvature tensor, coarse-graining procedures can be implemented to compute it over arbitrary patches of polygons. When computed for a closed surface, the integrated curvature tensor is identical to a rank-2 Minkowski tensor. We also provide an algorithm to extend an existing C++ package, that can be used to compute efficiently local curvature tensors on triangulated surfaces.

  2 citations

• Berry-Chern monopoles and spectral flows

  Pierre Delplace

  SciPost Phys. Lect. Notes 39 (2022) · published 10 March 2022 | Toggle abstract · pdf

  This lecture note adresses the correspondence between spectral flows, often associated to unidirectional modes, and Chern numbers associated to degeneracy points. The notions of topological indices (Chern numbers, analytical indices) are introduced for non specialists with a wave physics or condensed matter background. The correspondence is detailed with several examples, including the Dirac equations in two dimensions, Weyl fermions in three dimensions, the shallow water model in fluid dynamics and other generalizations.

  12 citations

• Enstrophy from symmetry

  Raja Marjieh, Natalia Pinzani-Fokeeva, Amos Yarom

  SciPost Phys. 12, 085 (2022) · published 9 March 2022 | Toggle abstract · pdf

  We study symmetry principles associated with the approximately conserved enstrophy current, responsible for the inverse energy cascade in non relativistic 2+1 dimensional turbulence. We do so by identifying the accidental symmetry associated with enstrophy current conservation in a recently realized effective action principle for hydrodynamics. Our analysis deals with both relativistic and non relativistic effective actions and their associated symmetries.

  3 citations