Single-particle and many-body analyses of a quasiperiodic integrable system after a quench

Abstract

In general, isolated integrable quantum systems have been found to relax to an apparent equilibrium state in which the expectation values of few-body observables are described by the generalized Gibbs ensemble. However, recent work has shown that relaxation to such a generalized statistical ensemble can be precluded by localization in a quasiperiodic lattice system. Here we undertake complementary single-particle and many-body analyses of noninteracting spinless fermions and hard-core bosons within the Aubry-André model to gain insight into this phenomenon. Our investigations span both the localized and delocalized regimes of the quasiperiodic system, as well as the critical point separating the two. Considering first the case of spinless fermions, we study the dynamics ofthe momentum distribution function and characterize the effects of real-space and momentum-space localization on the relevant single-particle wave functions and correlation functions. We show that although some observables do not relax in the delocalized and localized regimes, the observables that do relax in these regimes do so in a manner consistent with a recently proposed Gaussian equilibration scenario, whereas relaxation at the critical point has a more exotic character We also construct various statistical ensembles from the many-body eigenstates of the fermionic and bosonic Hamiltonians and study the effect of localization on their properties. PACS number (s): 03.75.Kk, 05.70.Ln, 02.30.Ik, 05.30.Jp 0(7)= lim ^ f r'^oo X' Jo O{X) ^aa = {Ô)DE, (3)which defines the expectation value of Ô in the DE [5]. The DE involves as many constraints as the dimension ofthe manybody Hilbert space (the overlaps of the initial state with the eigenstates of H), which grows exponentially with system size. By contrast, for models that can be mapped to noninteracting Hamiltonians, the GGE involves a number of constraints that is only polynomially large in the size ofthe system [19]. It may, therefore, appear surprising that the predictions of the GGE

Time fluctuations in isolated quantum systems of interacting particles

“…The fluctuations were again shown to scale exponentially with system size. Yet, in the particular case of an integrable Hamiltonian quadratic in the canonical Fermi operators or mapped onto one, where the nonresonant conditions are not satisfied, it was shown analytically [14] and numerically [15][16][17] that the time fluctuations of one-body or quadratic observables scale as 1/ √ L, L being the system size. These findings motivate the questions: How do the time fluctuations scale with L in the case of integrable systems that cannot be mapped to free particles?…”

Effects of the interplay between initial state and Hamiltonian on the thermalization of isolated quantum many-body systems

“…We can then talk about equilibration in a probabilistic sense. The rate of decay of these fluctuations with system size depends on the system investigated [36][37][38][39][40][41][42][43]. The important fact for us here is that for the models we study the temporal fluctuations are indeed small and should vanish for very large systems [36].…”

Quantum quenches in the thermodynamic limit. II. Initial ground states

“…We assume thatρ I is not stationary underĤ. As discussed in numerical [1,[5][6][7][8][9][10][11][12] and analytical [13][14][15][16][17][18][19] studies, if an observableÔ equilibrates, its expectation value after equilibration can be computed asÔ…”