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

By S. Sotiriadis, Pasquale Calabrese. 2014

132 citations recorded by the source corpus.

In the majority of analytical verifications of the conjecture that the Generalized Gibbs Ensemble (GGE) describes the large time asymptotics of local observables in quantum quench problems, both post- and pre-quench Hamiltonians are essentially noninteracting. We test this conjecture studying 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 this conjecture is more generally valid for 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.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c594c953fe9086b9b11250c27ada40516b979453

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

The Quench Action (2016, background): “Perhaps one could extend these all the way to any initial state satisfying cluster decomposition, these being representative of the generic case (see for example ([143]).”
Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles (2016, background): “While for integrable systems composed of non-interacting particles it is clear which conserved qu antities should be taken into account, for integrable syste m with interacting particles, such as the XXZ model, this is st ll an open question [266, 267, 268, 269, 270, 271].”
Quench dynamics and relaxation in isolated integrable quantum spin chains (2016, unknown): “It is essential for our purposes that the initial density matrix ( ) ρ 0 has a cluster decomposition property [128] [ ( ) ( ) ( )] [ ( ) ( )] [ ( ) ( )] → ρ ρ ρ = | − | ∞ O O O O x y x y lim Tr 0 Tr 0 Tr 0 , x y (12)”
Generalized Gibbs ensemble in integrable lattice models (2016, background): “Since then, the validity of the GGE to describe observables in integrable systems after equilibration has been demonstrated in a wide range of 1D models including: Luttinger liquids [39, 40, 41], the 1/r fermionic Hubbard model [42], the sine-Gordon model [43], the transverse field Ising model [44, ”