Universal diffusive decay of correlations in gapped one-dimensional systems

Rapp, Ákos; Zaránd, Gergely

doi:10.1140/epjb/e2008-00465-5

Cited by 13 publications

(21 citation statements)

References 27 publications

(91 reference statements)

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“…The semiclassical approach considered in this work concerns quantum systems with multiple species of long-lived quasiparticle excitations distinguished by some internal degree of freedom [different species]. The method was introduced in [5,6] to describe low-temperature correlations in a transverse field Ising chain, and, then, applied for the study of several systems both in [7][8][9] and out of [14-20, 31, 32, 86] equilibrium. The main idea is that when the density of quasiparticles is low, they propagate along classical trajectories.…”

Section: A Semiclassical Approachmentioning

confidence: 99%

Transport in the sine-Gordon field theory: From generalized hydrodynamics to semiclassics

2019

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The semiclassical approach introduced by Sachdev and collaborators proved to be extremely successful in the study of quantum quenches in massive field theories, both in homogeneous and inhomogeneous settings. While conceptually very simple, this method allows one to obtain analytic predictions for several observables when the density of excitations produced by the quench is small. At the same time, a novel generalized hydrodynamic (GHD) approach, which captures exactly many asymptotic features of the integrable dynamics, has recently been introduced. Interestingly, also this theory has a natural interpretation in terms of semiclassical particles and it is then natural to compare the two approaches. This is the objective of this work: we carry out a systematic comparison between the two methods in the prototypical example of the sine-Gordon field theory. In particular, we study the "bipartitioning protocol" where the two halves of a system initially prepared at different temperatures are joined together and then left to evolve unitarily with the same Hamiltonian. We identify two different limits in which the semiclassical predictions are analytically recovered from GHD: a particular non-relativistic limit and the low temperature regime. Interestingly, the transport of topological charge becomes sub-ballistic in these cases. Away from these limits we find that the semiclassical predictions are only approximate and, in contrast to the latter, the transport is always ballistic. This statement seems to hold true even for the so-called "hybrid" semiclassical approach, where finite time DMRG simulations are used to describe the evolution in the internal space. arXiv:1904.02696v1 [cond-mat.stat-mech]

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Section: A Semiclassical Approachmentioning

confidence: 99%

Transport in the sine-Gordon field theory: From generalized hydrodynamics to semiclassics

2019

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“…Here we intend to pursue another, semiclassical route to understand non-equlibrium steady state physics, an approach that has been successfully applied to compute dynamical correlation functions both at finite temperature [33][34][35][36][37] and out of equilibrium after a quantum quench [38][39][40][41]. This approach is applicable to gapped one dimensional systems with quasiparticles possessing some topological or symmetry-protected internal quantum numbers µ which we shall refer to in what follows as 'spin'.…”

Section: Introductionmentioning

confidence: 99%

Semiclassical theory of front propagation and front equilibration following an inhomogeneous quantum quench

2018

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We use a semiclassical approach to study out of equilibrium dynamics and transport in quantum systems with massive quasiparticle excitations having internal quantum numbers. In the universal limit of low energy quasiparticles, the system is described in terms of a classical gas of colored hardcore particles. Starting from an inhomogeneous initial state, in this limit we give analytic expressions for the space and time dependent spin density and spin current profiles. Depending on the initial state, the spin transport is found to be ballistic or diffusive. In the ballistic case we identify a "second front" that moves more slowly than the maximal quasiparticle velocity. Our analytic results also capture the diffusive broadening of this ballistically propagating front. To go beyond the universal limit, we study the effect of non-trivial scattering processes in the O(3) non-linear sigma model by performing Monte Carlo simulations, and observe local equilibration around the second front in terms of the densities of the particle species. arXiv:1712.09466v3 [cond-mat.stat-mech]

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“…Here we shall follow a complementary and more intuitive approach, and study the evolution of dynamical correlations after a quantum quench by extending the semiclassical approach of Refs. 18,[22][23][24][25][39][40][41][42][43][44][45] to study small quenches in the gapped phase of the sine-Gordon model. The sine-Gordon model is a paradigmatic model providing the low energy effective description of a wide range of one-dimensional systems including spin chains, spin ladders, and cold atomic gases [46][47][48][49][50][51] .…”

Section: Introductionmentioning

confidence: 99%

Quantum quenches in the sine-Gordon model: A semiclassical approach

Kormos¹,

Zaránd²

2016

Phys. Rev. E

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We compute the time evolution of correlation functions after quantum quenches in the sine-Gordon model within the semiclassical approximation, which is expected to yield accurate results for small and slow quenches producing slow quasiparticles with low density. We demonstrate this by reproducing results of a recent form-factor calculation of the relaxation of expectation values [B. Bertini, D. Schuricht, and F. H. L. Essler, J. Stat. Mech. (2014) P100351742-546810.1088/1742-5468/2014/10/P10035]. Extending these results, we find that-in the universal limit of vanishingly small quasiparticle velocities-the expectation values of most vertex operators do not decay to zero. We give analytic expressions for the relaxation of dynamic correlation functions and show that they have diffusive behavior for large timelike separation.

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Universal diffusive decay of correlations in gapped one-dimensional systems

Cited by 13 publications

References 27 publications

Transport in the sine-Gordon field theory: From generalized hydrodynamics to semiclassics

Transport in the sine-Gordon field theory: From generalized hydrodynamics to semiclassics

Semiclassical theory of front propagation and front equilibration following an inhomogeneous quantum quench

Quantum quenches in the sine-Gordon model: A semiclassical approach

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