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arXiv:2209.11290 · Journal of High Energy Physics

Entanglement of stationary states in the presence of unstable quasiparticles

Dávid X. Horváth, Pasquale Calabrese, Olalla A. Castro-Alvaredo

Published Apr 19, 2023• 1 citation

Abstract

Abstract The effect of unstable quasiparticles in the out-of-equilibrium dynamics of certain integrable systems has been the subject of several recent studies. In this paper we focus on the stationary value of the entanglement entropy density, its growth rate, and related functions, after a quantum quench. We consider several quenches, each of which is characterised by a corresponding squeezed coherent state. In the quench action approach, the coherent state amplitudes K(θ) become input data that fully characterise the large-time stationary state, thus also the corresponding Yang-Yang entropy. We find that, as function of the mass of the unstable particle, the entropy growth rate has a global minimum signalling the depletion of entropy that accompanies a slowdown of stable quasiparticles at the threshold for the formation of an unstable excitation. We also observe a separation of scales governed by the interplay between the mass of the unstable particle and the quench parameter, separating a non-interacting regime described by free fermions from an interacting regime where the unstable particle is present. This separation of scales leads to a double-plateau structure of many functions, where the relative height of the plateaux is related to the ratio of central charges of the UV fixed points associated with the two regimes, in full agreement with conformal field theory predictions. The properties of several other functions of the entropy and its growth rate are also studied in detail, both for fixed quench parameter and varying unstable particle mass and viceversa.

DOI: 10.1007/jhep04(2023)091

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A typical working condition in the study of quantum quenches is that the initial state produces a distribution of quasiparticle excitations with an opposite-momentum-pair structure.In this work we investigate the dynamical and stationary properties of the entanglement entropy after a quench from initial states which do not have such structure: instead of pairs of excitations they generate ν-plets of correlated excitations with ν > 2. Our study is carried out focusing on a system of non-interacting fermions on the lattice.We study the time evolution of the entanglement entropy showing that the standard semiclassical formula is not applicable.We propose a suitable generalisation which correctly describes the entanglement entropy evolution and perfectly matches numerical data.We finally consider the relation between the thermodynamic entropy of the stationary state and the diagonal entropy, showing that when there is no pair structure their ratio depends on the details of the initial state and lies generically between 1/2 and 1.

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Global quantum quench with a finite quench rate which crosses critical points is known to lead to universal scaling of correlation functions as functions of the quench rate. In this work, we explore scaling properties of the entanglement entropy of a subsystem in a harmonic chain during a mass quench which asymptotes to finite constant values at early and late times and for which the dynamics is exactly solvable. When the initial state is the ground state, we find that for large enough subsystem sizes the entanglement entropy becomes independent of size. This is consistent with Kibble–Zurek scaling for slow quenches, and with recently discussed “fast quench scaling” for quenches fast compared to physical scales, but slow compared to UV cutoff scales.

Abstract Recently, a non-trivial relation between the quasi-particle spectrum and entanglement entropy production was discovered in non-integrable quenches in the paramagnetic Ising quantum spin chain. Here we study the dynamics of analogous quenches in the quantum Potts spin chain. Tuning the parameters of the system, we observe a sudden increase in the entanglement production rate, which is shown to be related to the appearance of new quasiparticle excitations in the post-quench spectrum. Our results demonstrate the generality of the effect and support its interpretation as the non-equilibrium version of the well-known Gibbs paradox related to mixing entropy which appears in systems with a non-trivial quasi-particle spectrum.

The time evolution of the entanglement entropy is a key concept to understand the structure of a nonequilibrium quantum state. In a large class of models, such evolution can be understood in terms of a semiclassical picture of moving quasiparticles spreading the entanglement throughout the system. However, it is not yet known how the entanglement splits between the sectors of an internal local symmetry of a quantum many-body system. Here, guided by the examples of conformal field theories and free-fermion chains, we show that the quasiparticle picture can be adapted to this goal, leading to a general conjecture for the charged entropies whose Fourier transform gives the desired symmetry-resolved entanglement

{S}_{n}(q)

. We point out two physically relevant effects that should be easily observed in atomic experiments: a delay time for the onset of

{S}_{n}(q)

which grows linearly with $|\mathrm{\ensuremath{\Delta}}q|$ (the difference between the charge

q

and its mean value) and an effective equipartition when $|\mathrm{\ensuremath{\Delta}}q|$ is much smaller than the subsystem size.