Quasilocal charges and progress towards the complete GGE for field theories with nondiagonal scattering

Vernier, Éric; Cubero, Axel Cortés

doi:10.1088/1742-5468/aa5288

Cited by 45 publications

(51 citation statements)

References 122 publications

(435 reference statements)

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“…More general examples of expectation values of local charges of the sine-Gordon model can be found in Ref. [97]. Note that a form like (35) holds for all expectation values of local conserved charge densities in any TBA solvable model.…”

Section: Thermodynamic Bethe Ansatzmentioning

confidence: 99%

“…Note that the coupling pattern of the different species corresponds to the topology of the D p+1 Dynkin diagram [96]. The standard assumption of TBA is that, in the thermodynamic limit, the root densities {ρ k (θ)} p k=0 of a given eigenstate of the Hamiltonian fully specify the expectation values of all local observables in that eigenstate.…”

Section: Thermodynamic Bethe Ansatzmentioning

confidence: 99%

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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: Thermodynamic Bethe Ansatzmentioning

confidence: 99%

Section: Thermodynamic Bethe Ansatzmentioning

confidence: 99%

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

2019

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“…where a nm is the same as in (5), and g n is defined in (13). Finally, the GGE macrostate densities ρ n are obtained by substituting the solutions of (18) in the TBA equations (5).…”

Section: B Tba Description Of Homogeneous Quenchesmentioning

confidence: 99%

Towards a generalized hydrodynamics description of Rényi entropies in integrable systems

Alba

2019

Phys. Rev. B

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We investigate the steady-state Rényi entanglement entropies after a quench from a piecewise homogeneous initial state in integrable models. In the quench protocol two macroscopically different chains (leads) are joined together at the initial time, and the subsequent dynamics is studied. We study the entropies of a finite subsystem at the interface between the two leads. The density of Rényi entropies coincides with that of the entropies of the Generalized Gibbs Ensemble (GGE) that describes the interface between the chains. By combining the Generalized Hydrodynamics (GHD) treatment of the quench with the Bethe ansatz approach for the Rényi entropies, we provide exact results for quenches from several initial states in the anisotropic Heisenberg chain (XXZ chain), although the approach is applicable, in principle, to any low-entangled initial state and any integrable model. An interesting protocol that we consider is the expansion quench, in which one of the two leads is prepared in the vacuum of the model excitations. An intriguing feature is that for moderately large anisotropy the transport of bound-state is not allowed. Moreover, we show that there is a "critical" anisotropy, below which bound-state transport is permitted. This is reflected in the steady-state entropies, which for large enough anisotropy do not contain information about the bound states. Finally, we benchmark our results against time-dependent Density Matrix Renormalization Group (tDMRG) simulations. arXiv:1807.01800v2 [cond-mat.stat-mech]

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“…Amazingly, many of these examples have been experimentally realized [9][10][11][12][13][14][15][16][17].Integrable models are characterized by the presence of infinitely many conserved chargesQ j , which can be used to exactly determine their thermodynamics [25]. In recent times, the importance of quasi-local charges has moreover been underlined [26][27][28][29][30][31][32][33][34][35].The last decade has witnessed exact results reaching out-of-equilibrium protocols as well: great attention has been devoted to the homogeneous sudden quantum quench [36] (see also Ref. [37] and reference therein).…”

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confidence: 99%

Generalized Hydrodynamics with Space-Time Inhomogeneous Interactions

2019

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We provide a new hydrodynamic framework to describe out-of-equilibrium integrable systems with space-time inhomogeneous interactions. Our result builds up on the recently-introduced Generalized Hydrodynamics (GHD). The method allows to analytically describe the dynamics during generic space-time-dependent smooth modulations of the interactions. As a proof of concept, we study experimentally-motivated interaction quenches in the trapped interacting Bose gas, which cannot be treated with current analytical or numerical methods. We also benchmark our results in the XXZ spin chain and in the classical Sinh-Gordon model.Introduction. -Exploring the out-of-equilibrium behavior of quantum many-body systems is nowadays among the most active research areas in physics, due to a successful synergy between theoretical and experimental advances [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].How, and in which sense, does a coarse-grained thermodynamic description emerge through dynamical evolution in isolated out-of-equilibrium many-body systems? One-dimensional systems represent an ideal playground to address this question: there, remarkably powerful tools exist, both theoretical (such as conformal field theory [18] and integrability [19,20]) and computational (such as Matrix Product States methods [21]).Integrability is ubiquitous in the low-dimensional world, with applications ranging from spin chains [19] to continuum models (having Lorentz [20] or Galilean [22,23] invariance, or neither [24]). Amazingly, many of these examples have been experimentally realized [9][10][11][12][13][14][15][16][17].Integrable models are characterized by the presence of infinitely many conserved chargesQ j , which can be used to exactly determine their thermodynamics [25]. In recent times, the importance of quasi-local charges has moreover been underlined [26][27][28][29][30][31][32][33][34][35].The last decade has witnessed exact results reaching out-of-equilibrium protocols as well: great attention has been devoted to the homogeneous sudden quantum quench [36] (see also Ref. [37] and reference therein). Due to the conserved quantities, the system exhibits local relaxation to a state that is not thermal [38][39][40][41][42][43][44][45][46], but rather emerges from a Quench Action [47,48] or (where applicable) a Generalized Gibbs Ensemble [49,50] which accounts for all the relevant charges.More recently, the focus has been on quenches from spatially inhomogeneous systems. A new theoretical toolbox, dubbed Generalized Hydrodynamics (GHD) [51,52] allows to address this problem. In Ref. [51,52] GHD dealt with inhomogeneous states evolving under a homogeneous Hamiltonian. Several applications have been explored , extending the initial findings to describe the entanglement spreading [79][80][81][82][83][84], including diffusive corrections [85][86][87][88] or applying it to classical field theories [89][90][91][92]. Very recently, it has been shown that GHD FIG. 1: Prototypical experimental setup that can be addressed with our method...

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Quasilocal charges and progress towards the complete GGE for field theories with nondiagonal scattering

Cited by 45 publications

References 122 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

Towards a generalized hydrodynamics description of Rényi entropies in integrable systems

Generalized Hydrodynamics with Space-Time Inhomogeneous Interactions

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