Critical behavior of the SU(3) ferromagnetic Heisenberg chain

Jee, Young-Ju; Lee, Kong-Ju-Bock; Schlottmann, P.

doi:10.1103/physrevb.39.2815

Cited by 10 publications

(10 citation statements)

References 19 publications

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“…For quantum quenches in the regime where bosonization provides a good approximation [86] the full time evolution of the probability distribution for certain observables can be obtained in a straightforward way. Finally, the case of integrable chains of higher spin could be studied both in equilibrium [87,88] and after a quench [84,89].…”

Section: Discussionmentioning

confidence: 99%

Full counting statistics in the transverse field Ising chain

2018

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We consider the full probability distribution for the transverse magnetization of a finite subsystem in the transverse field Ising chain. We derive a determinant representation of the corresponding characteristic function for general Gaussian states. We consider applications to the full counting statistics in the ground state, finite temperature equilibrium states, non-equilibrium steady states and time evolution after global quantum quenches. We derive an analytical expression for the time and subsystem size dependence of the characteristic function at sufficiently late times after a quantum quench. This expression features an interesting multiple light-cone structure.

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Section: Discussionmentioning

confidence: 99%

Full counting statistics in the transverse field Ising chain

2018

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“…The mathematical framework to study this limit is provided by the thermodynamic Bethe ansatz formalism [17], which we briefly review in the specific case of the SU (3)-invariant model, referring the reader to Refs. [69,70,[73][74][75][76] for more detail.…”

Section: The Thermodynamic Descriptionmentioning

confidence: 99%

Integrable quenches in nested spin chains I: the exact steady states

Piroli¹,

Vernier²,

Calabrese³

et al. 2019

J. Stat. Mech.

101

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We consider quantum quenches in the integrable SU (3)-invariant spin chain (Lai-Sutherland model) which admits a Bethe ansatz description in terms of two different quasiparticle species, providing a prototypical example of a model solvable by nested Bethe ansatz. We identify infinite families of integrable initial states for which analytic results can be obtained. We show that they include special families of two-site product states which can be related to integrable "soliton non-preserving" boundary conditions in an appropriate rotated channel. We present a complete analytical result for the quasiparticle rapidity distribution functions corresponding to the stationary state reached at large times after the quench from the integrable initial states. Our results are obtained within a Quantum Transfer Matrix (QTM) approach, which does not rely on the knowledge of the quasilocal conservation laws or of the overlaps between the initial states and the eigenstates of the Hamiltonian. Furthermore, based on an analogy with previous works, we conjecture analytic expressions for such overlaps: this allows us to employ the Quench Action method to derive a set of integral equations characterizing the quasi-particle distribution functions of the post-quench steady state. We verify that the solution to the latter coincides with our analytic result found using the QTM approach. Finally, we present a direct physical application of our results by providing predictions for the propagation of entanglement after the quench from such integrable states. arXiv:1811.00432v4 [cond-mat.stat-mech]

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“…The thermodynamic Bethe ansatz for the nested system of interest in this work has been widely studied in the literature, see, e.g., Refs. [129,130,[134][135][136][137]. Here we review the aspects which are relevant for our work.…”

Section: String Hypothesis and Thermodynamic Descriptionmentioning

confidence: 99%

Exact solution for the quench dynamics of a nested integrable system

Mestyán¹,

Bertini²,

Piroli³

et al. 2017

J. Stat. Mech.

111

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Integrable models provide an exact description for a wide variety of physical phenomena. For example nested integrable systems contain different species of interacting particles with a rich phenomenology in their collective behavior, which is the origin of the unconventional phenomenon of spin-charge separation. So far, however, most of the theoretical work in the study of non-equilibrium dynamics of integrable systems has been focusing on models with an elementary (i.e. not nested) Bethe ansatz. In this work we explicitly investigate quantum quenches in nested integrable systems, by generalizing the application of the Quench Action approach. Specifically, we consider the spin-1 Lai-Sutherland model, described, in the thermodynamic limit, by the theory of two different species of Bethe-ansatz particles, each one forming an infinite number of bound states. We focus on the situation where the quench dynamics starts from a simple matrix product state for which the overlaps with the eigenstates of the Hamiltonian are known. We fully characterize the post-quench steady state and perform several consistency checks for the validity of our results. Finally, we provide predictions for the propagation of entanglement and mutual information after the quench, which can be used as signature of the quasi-particle content of the model. arXiv:1705.00851v2 [cond-mat.stat-mech]

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Critical behavior of the SU(3) ferromagnetic Heisenberg chain

Cited by 10 publications

References 19 publications

Full counting statistics in the transverse field Ising chain

Full counting statistics in the transverse field Ising chain

Integrable quenches in nested spin chains I: the exact steady states

Exact solution for the quench dynamics of a nested integrable system

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