36 research outputs found
Quasi locality of the GGE in interacting-to-free quenches in relativistic field theories
We study the quench dynamics in continuous relativistic quantum field theory,
more specifically the locality properties of the large time stationary state.
After a quantum quench in a one-dimensional integrable model, the expectation
values of local observables are expected to relax to a Generalized Gibbs
Ensemble (GGE), constructed out of the conserved charges of the model.
Quenching to a free bosonic theory, it has been shown that the system indeed
relaxes to a GGE described by the momentum mode occupation numbers. We first
address the question whether the latter can be written directly in terms of
local charges and we find that, in contrast to the lattice case, this is not
possible in continuous field theories. We then investigate the less stringent
requirement of the existence of a sequence of truncated local GGEs that
converges to the correct steady state, in the sense of the expectation values
of the local observables. While we show that such a sequence indeed exists, in
order to unequivocally determine the so-defined GGE, we find that information
about the expectation value of the recently discovered quasi-local charges is
in the end necessary, the latter being the suitable generalization of the local
charges while passing from the lattice to the continuum. Lastly, we study the
locality properties of the GGE and show that the latter is completely
determined by the knowledge of the expectation value of a countable set of
suitably defined quasi-local charges
Lack of thermalization for integrability-breaking impurities
We investigate the effects of localized integrability-breaking perturbations
on the large times dynamics of thermodynamic quantum and classical systems. In
particular, we suddenly activate an impurity which breaks the integrability of
an otherwise homogeneous system. We focus on the large times dynamics and on
the thermalization properties of the impurity, which is shown to have mere
perturbative effects even at infinite times, thus preventing thermalization.
This is in clear contrast with homogeneous integrability-breaking terms, which
display the prethermalization paradigm and are expected to eventually cause
thermalization, no matter the weakness of the integrability-breaking term.
Analytic quantitative results are obtained in the case where the bulk
Hamiltonian is free and the impurity interacting.Comment: 21 pages, 6 figure
Non-Equilibrium Steady State generated by a moving defect: the supersonic threshold
We consider the dynamics of a system of free fermions on a 1D lattice in the
presence of a defect moving at constant velocity. The defect has the form of a
localized time-dependent variation of the chemical potential and induces at
long times a Non-Equilibrium Steady State (NESS), which spreads around the
defect. We present a general formulation which allows recasting the
time-dependent protocol in a scattering problem on a static potential. We
obtain a complete characterization of the NESS. In particular, we show a strong
dependence on the defect velocity and the existence of a sharp threshold when
such velocity exceeds the speed of sound. Beyond this value, the NESS is not
produced and remarkably the defect travels without significantly perturbing the
system. We present an exact solution for a like defect traveling with
an arbitrary velocity and we develop a semiclassical approximation which
provides accurate results for smooth defects.Comment: 18 pages, 13 figure
The sine-Gordon model from coupled condensates: a Generalized Hydrodynamics viewpoint
The sine-Gordon model captures the low-energy effective dynamics of a wealth
of one-dimensional quantum systems, stimulating the experimental efforts in
building a versatile quantum simulator of this field theory and fueling the
parallel development of new theoretical toolkits able to capture
far-from-equilibrium settings. In this work, we analyze the realization of
sine-Gordon from the interference pattern of two one-dimensional
quasicondensates: we argue the emergent field theory is well described by its
classical limit and develop its large-scale description based on Generalized
Hydrodynamics. We show how, despite sine-Gordon being an integrable field
theory, trap-induced inhomogeneities cause instabilities of excitations and
provide exact analytical results to capture this effect.Comment: 21 pages, 7 figure
Entanglement spreading and quasiparticle picture beyond the pair structure
The quasi-particle picture is a powerful tool to understand the entanglement spreading in many-body quantum systems after a quench. As an input, the structure of the excitations' pattern of the initial state must be provided, the common choice being pairwise-created excitations. However, several cases exile this simple assumption. In this work, we investigate weakly-interacting to free quenches in one dimension. This results in a far richer excitations' pattern where multiplets with a larger number of particles are excited. We generalize the quasi-particle ansatz to such a wide class of initial states, providing a small-coupling expansion of the Renyi entropies. Our results are in perfect agreement with iTEBD numerical simulations
Exact Thermodynamics and Transport in the Classical Sine-Gordon Model
We revisit the exact thermodynamic description of the classical sine-Gordon
field theory, a notorious integrable model. We found that existing results in
the literature based on the soliton-gas picture did not correctly take into
account light, but extended, solitons and thus led to incorrect results. This
issue is regularized upon requantization: we derive the correct thermodynamics
by taking the semiclassical limit of the quantum model. Our results are then
extended to transport settings by means of Generalized Hydrodynamics.Comment: 33 pages, 4 figure
Generalized hydrodynamics of classical integrable field theory: the sinh-Gordon model
Using generalized hydrodynamics (GHD), we develop the Euler hydrodynamics of
classical integrable field theory. Classical field GHD is based on a known
formalism for Gibbs ensembles of classical fields, that resembles the
thermodynamic Bethe ansatz of quantum models, which we extend to generalized
Gibbs ensembles (GGEs). In general, GHD must take into account both solitonic
and radiative modes of classical fields. We observe that the quasi-particle
formulation of GHD remains valid for radiative modes, even though these do not
display particle-like properties in their precise dynamics. We point out that
because of a UV catastrophe similar to that of black body radiation, radiative
modes suffer from divergences that restrict the set of finite-average
observables; this set is larger for GGEs with higher conserved charges. We
concentrate on the sinh-Gordon model, which only has radiative modes, and study
transport in the domain-wall initial problem as well as Euler-scale
correlations in GGEs. We confirm a variety of exact GHD predictions, including
those coming from hydrodynamic projection theory, by comparing with Metropolis
numerical evaluations.Comment: 41 pages, 9 figure
Spreading of entanglement and correlations after a quench with intertwined quasiparticles
We extend the semiclassical picture for the spreading of entanglement and correlations to quantum quenches with several species of quasiparticles that have non-trivial pair correlations in momentum space. These pair correlations are, for example, relevant in inhomogeneous lattice models with a periodically-modulated Hamiltonian parameter. We provide explicit predictions for the spreading of the entanglement entropy in the space-time scaling limit. We also predict the time evolution of one- and two-point functions of the order parameter for quenches within the ordered phase. We test all our predictions against exact numerical results for quenches in the Ising chain with a modulated transverse field and we find perfect agreement