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arXiv:cond-mat/0612030 · Physical Review Letters

Strongly Correlated Fermions after a Quantum Quench

Salvatore R. Manmana, Stefan Weßel, R. M. Noack, A. Muramatsu

Published May 25, 2007• 316 citations
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Abstract

Using the adaptive time-dependent density-matrix renormalization group method, we study the time evolution of strongly correlated spinless fermions on a one-dimensional lattice after a sudden change of the interaction strength. For certain parameter values, two different initial states (e.g., metallic and insulating) lead to observables which become indistinguishable after relaxation. We find that the resulting quasistationary state is nonthermal. This result holds for both integrable and nonintegrable variants of the system.

DOI
10.1103/physrevlett.98.210405

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We provide evidence that the relaxation dynamics of one-dimensional, metallic Fermi systems resulting out of an abrupt amplitude change of the two-particle interaction has aspects which are universal in the Luttinger liquid sense: the leading long-time behavior of certain observables is described by universal functions of the equilibrium Luttinger liquid parameter and the renormalized velocity. We analytically derive those functions for the Tomonaga-Luttinger model and verify our hypothesis of universality by considering spinless lattice fermions within the framework of the density-matrix renormalization group.
Particle entanglement provides information on quantum correlations in systems of indistinguishable particles. Here, we study the one-particle entanglement entropy for an integrable model of spinless, interacting fermions both at equilibrium and after an interaction quantum quench. Using both large-scale exact diagonalization and time-dependent density matrix renormalization group calculations, we numerically compute the one-body reduced density matrix for the $J\ensuremath{-}V$ model, as well as its postquench dynamics. We include an analysis of the fermionic momentum distribution, showcasing its time evolution after a quantum quench. Our numerical results, extrapolated to the thermodynamic limit, can be compared with field theoretic bosonization in the Tomonaga-Luttinger liquid regime. Excellent agreement is obtained using an interaction cutoff that can be determined uniquely in the ground state.
We investigate the non-equilibrium relaxation dynamics of a one dimensional system of interacting spinless fermions near the XXZ integrable point. We observe two qualitatively different regimes: close to integrability and for low energies the relaxation proceeds in two steps (prethermalization scenario), while for large energies and/or away from integrability the dynamics develops in a single step. When the integrability breaking parameter is below a certain finite threshold and the energy of the system is sufficiently low the lifetime of the metastable states increases abruptly by several orders of magnitude, resembling the physics of glassy systems. This is reflected in a sudden jump in the relaxation timescales. We present results for finite but large systems and for large times compared to standard numerical methods. Our approach is based on the construction of equations of motion for one- and two-particle correlation functions using projection operator techniques.
We obtain the exact time evolution for the one-dimensional integrable fermionic 1/r1/r1/r Hubbard model after a sudden change of its interaction parameter, starting from either a metallic or a Mott-insulating eigenstate. In all cases the system relaxes to a new steady state, showing that the presence of the Mott gap does not inhibit relaxation. The properties of the final state are described by a generalized Gibbs ensemble. We discuss under which conditions such ensembles provide the correct statistical description of isolated integrable systems in general. We find that generalized Gibbs ensembles do predict the properties of the steady state correctly, provided that the observables or initial states are sufficiently uncorrelated in terms of the constants of motion.
We study the sudden expansion of strongly correlated fermions in a one-dimensional lattice, utilizing the time-dependent density-matrix renormalization group method. Our focus is on the behavior of experimental observables such as the density, the momentum distribution function, and the density and spin structure factors. As our main result, we show that correlations in the transient regime can be accurately described by equilibrium reference systems. In addition, we find that the expansion from a Mott insulator produces distinctive peaks in the momentum distribution function at $k\ensuremath{\approx}\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$, accompanied by the onset of power-law correlations.