arXiv subjects

Spyros Sotiriadis

Publications and source records attributed to Spyros Sotiriadis.

33 records · Page 2Linked to original sources

arXiv2017

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.

cond-mat.stat-mech↗

arXiv2016

Memory-preserving equilibration after a quantum quench in a 1d critical model

One of the fundamental principles of statistical physics is that only partial information about a system's state is required for its macroscopic description. This is not only true for thermal ensembles, but also for the unconventional ensemble, known as Generalized Gibbs Ensemble (GGE), that is expected to describe the relaxation of integrable systems after a quantum quench. By analytically studying the quench dynamics in a prototypical one-dimensional critical model, the massless free bosonic field theory, we find evidence of a novel type of equilibration characterized by the preservation of an enormous amount of memory of the initial state that is accessible by local measurements. In particular, we show that the equilibration retains memory of non-Gaussian initial correlations, in contrast to the case of massive free evolution which erases all such memory. The GGE in its standard form, being a Gaussian ensemble, fails to predict correctly the equilibrium values of local observables, unless the initial state is Gaussian itself. Our findings show that the equilibration of a broad class of quenches whose evolution is described by Luttinger liquid theory with an initial state that is non-Gaussian in terms of the bosonic field, is not correctly captured by the corresponding bosonic GGE, raising doubts about the validity of the latter in general one-dimensional gapless integrable systems such as the Lieb-Liniger model. We also propose that the same experiment by which the GGE was recently observed [Langen et al., Science 348 (2015) 207-211] can also be used to observe its failure, simply by starting from a non-Gaussian initial state.

cond-mat.stat-mech↗

arXiv2016

Cluster expansion for ground states of local Hamiltonians

A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quench.

cond-mat.stat-mech↗

arXiv2016

Equilibration and GGE in interacting-to-free Quantum Quenches in dimensions d>1

Ground states of interacting QFTs are non-gaussian states, i.e. their connected n-point correlation functions do not vanish for n>2, in contrast to the free QFT case. We show that when the ground state of an interacting QFT evolves under a free massive QFT for a long time (a scenario that can be realised by a Quantum Quench), the connected correlation functions decay and all local physical observables equilibrate to values that are given by a gaussian density matrix that keeps memory only of the two-point initial correlation function. The argument hinges upon the fundamental physical principle of cluster decomposition, which is valid for the ground state of a general QFT. An analogous result was already known to be valid in the case of d=1 spatial dimensions, where it is a special case of the so-called Generalised Gibbs Ensemble (GGE) hypothesis, and we now generalise it to higher dimensions. Moreover in the case of massless free evolution, despite the fact that the evolution may not lead to equilibration but unbounded increase of correlations with time instead, the GGE gives correctly the leading order asymptotic behaviour of correlation functions in the thermodynamic and large time limit. The demonstration is performed in the context of bosonic relativistic QFT, but the arguments apply more generally.

hep-th↗

arXiv2015

Probing Klein tunneling through quantum quenches

We study the interplay between an inhomogeneous quantum quench of the external potential in a system of relativistic fermions in one dimension and the well-known Klein tunneling. We find that the large time evolution is characterized by particle production at a constant rate which we derive analytically. The produced particles can be physically interpreted according to a semiclassical picture and the state reached in the long time limit can be classified as a non-equilibrium-steady-state. Such a quantum quench can be used in order to observe macroscopic effects of Klein tunneling in transport, raising the possibility of an experimental implementation.

cond-mat.stat-mech↗

arXiv2015

Quench echo and work statistics in integrable quantum field theories

We propose a boundary thermodynamic Bethe ansatz calculation technique to obtain the Loschmidt echo and the statistics of the work done when a global quantum quench is performed on an integrable quantum field theory. We derive an analytic expression for the lowest edge of the probability density function and find that it exhibits universal features, in the sense that its scaling form depends only on the statistics of excitations. We perform numerical calculations on the sinh-Gordon model, a deformation of the free boson theory, and we obtain that by turning on the interaction the density function develops fermionic properties. The calculations are facilitated by a previously unnoticed property of the thermodynamic Bethe ansatz construction.

cond-mat.stat-mech↗

arXiv2014

Validity of the GGE for quantum quenches from interacting to noninteracting models

In the majority of the analytical verifications of the conjecture that the Generalised Gibbs Ensemble describes the large time asymptotics of local observables in quantum quench problems, both the post-quench and the pre-quench Hamiltonians are essentially noninteracting. We test this conjecture studying the field correlations in the more general case of an arbitrary pre-quench Hamiltonian, while keeping the post-quench one noninteracting. We first show that in the previously studied special case of a noninteracting pre-quench Hamiltonian, the validity of the conjecture is a consequence of Wick's theorem. We then show that it is also valid in the general case of an arbitrary interacting pre-quench Hamiltonian, but this time as a consequence of the cluster decomposition property of the initial state, which is a fundamental principle for generic physical states. For arbitrary initial states that do not satisfy the cluster decomposition property, the above conjecture is not generally true. As a byproduct of our investigation we obtain an analytical derivation of earlier numerical results for the large time evolution of correlations after a quantum quench of the interaction in the Lieb-Liniger model from a nonzero value to zero.

cond-mat.stat-mech↗

arXiv2014

Boundary State in an Integrable Quantum Field Theory Out of Equilibrium

We study a quantum quench of the mass and the interaction in the Sinh-Gordon model starting from a large initial mass and zero initial coupling. Our focus is on the determination of the expansion of the initial state in terms of post-quench excitations. We argue that the large energy profile of the involved excitations can be relevant for the late time behaviour of the system and common regularization schemes are unreliable. We therefore proceed in determining the initial state by first principles expanding it in a systematic and controllable fashion on the basis of the asymptotic states. Our results show that, for the special limit of pre-quench parameters we consider, it assumes a squeezed state form that has been shown to evolve so as to exhibit the equilibrium behaviour predicted by the Generalized Gibbs Ensemble.

cond-mat.stat-mech↗

arXiv2013

Quench dynamics of a Tonks-Girardeau gas released from a harmonic trap

We consider the non-equilibrium dynamics of a gas of impenetrable bosons released from a harmonic trapping potential to a circle. The many body dynamics is solved analytically and the time dependence of all the physically relevant correlations is described. We prove that, for large times and in the thermodynamic limit, the reduced density matrix of any subsystem converges to a generalized Gibbs ensemble as a consequence of the integrability of the model. We discuss the approach to the stationary behavior at late times. We also describe the time-dependence of the entanglement entropy which attains a very simple form in the stationary state.

cond-mat.quant-gas↗

arXiv2013

Statistics of the work done by splitting a one-dimensional quasi-condensate

Motivated by experiments on splitting one-dimensional quasi-condensates, we study the statistics of the work done by a quantum quench in a bosonic system. We discuss the general features of the probability distribution of the work and focus on its behaviour at the lowest energy threshold, which develops an edge singularity. A formal connection between this probability distribution and the critical Casimir effect in thin classical films shows that certain features of the edge singularity are universal as the post-quench gap tends to zero. Our results are quantitatively illustrated by an exact calculation for non-interacting bosonic systems. The effects of finite system size, dimensionality, and non-zero initial temperature are discussed in detail.

cond-mat.stat-mech↗

arXiv2013

Equilibration of a Tonks-Girardeau gas following a trap release

We study the non-equilibrium dynamics of a Tonks-Girardeau gas released from a parabolic trap to a circle. We present the exact analytic solution of the many body dynamics and prove that, for large times and in a properly defined thermodynamic limit, the reduced density matrix of any finite subsystem converges to a generalized Gibbs ensemble. The equilibration mechanism is expected to be the same for all one-dimensional systems.

cond-mat.quant-gas↗

arXiv2012

Zamolodchikov-Faddeev Algebra and Quantum Quenches in Integrable Field Theories

We analyze quantum quenches in integrable models and in particular the determination of the initial state in the basis of eigenstates of the post-quench hamiltonian. This leads us to consider the set of transformations of creation and annihilation operators that respect the Zamolodchikov-Faddeev algebra satisfied by integrable models. We establish that the Bogoliubov transformations hold only in the case of quantum quenches in free theories. In the most general case of interacting theories, we identify two classes of transformations. The first class induces a change in the S-matrix of the theory but not of its ground state, whereas the second class results in a "dressing" of the operators. As examples of our approach we consider the transformations associated with a change of the interaction in the Sinh-Gordon and the Lieb-Liniger model.

cond-mat.stat-mech↗

arXiv2010

Quantum quench in interacting field theory: a self-consistent approximation

We study a composite quantum quench of the energy gap and the interactions in the interacting ϕ^4 model using a self-consistent approximation. Firstly we review the results for free theories where a quantum quench of the energy gap or mass leads for long times to stationary behaviour with thermal characteristics. An exception to this rule is the 2d case with zero mass after the quench. In the composite quench however we find that the effect of the interactions in our approximation is simply to effectively change the value of the mass. This means on the one hand that the interacting model also exhibits the same stationary behaviour and on the other hand that this is now true even for the massless 2d case.

quant-ph↗

arXiv2009

Quantum Quench from a Thermal Initial State

We consider a quantum quench in a system of free bosons, starting from a thermal initial state. As in the case where the system is initially in the ground state, any finite subsystem eventually reaches a stationary thermal state with a momentum-dependent effective temperature. We find that this can, in some cases, even be lower than the initial temperature. We also study lattice effects and discuss more general types of quenches.

cond-mat.stat-mech↗

arXiv2008

Inhomogeneous Quantum Quenches

We study the problem of a quantum quench in which the initial state is the ground state of an inhomogeneous hamiltonian, in two different models, conformal field theory and ordinary free field theory, which are known to exhibit thermalisation of finite regions in the homogeneous case. We derive general expressions for the evolution of the energy flow and correlation functions, as well as the entanglement entropy in the conformal case. Comparison of the results of the two approaches in the regime of their common validity shows agreement up to a point further discussed. Unlike the thermal analogue, the evolution in our problem is non-diffusive and can be physically interpreted using an intuitive picture of quasiparticles emitted from the initial time hypersurface and propagating semiclassically.

cond-mat.stat-mech↗