On quenches in non-integrable quantum many-body systems: the one-dimensional Bose-Hubbard model revisited

Fabian Heidrich‐Meisner, Lode Pollet, Stefan Sorg +1 more

Giulio Biroli, Bruno Sciolla

Guillaume Roux

When a quantum many-body system undergoes a quench, the time-averaged density matrix $\overline{\ensuremath{\rho}}$ governs the time-averaged expectation value of any observable. It is therefore the key object to look at when comparing results with equilibrium predictions. We show that the weights of $\overline{\ensuremath{\rho}}$ can be efficiently computed with Lanczos diagonalization for relatively large Hilbert spaces. As an application, we investigate the crossover from perturbative to nonperturbative quenches in the nonintegrable Bose-Hubbard model: in finite systems, an approximate Boltzmann distribution is observed for small quenches, while for larger ones the distributions do not follow standard equilibrium predictions. Studying thermodynamical features, such as the energy fluctuations and the entropy, show that $\overline{\ensuremath{\rho}}$ bears a memory of the initial state.

Marcos Rigol

In a recent paper, Roux [Phys. Rev. A 79, 021608(R) (2009)] argued that thermalization in a Bose-Hubbard system, after a quantum quench, follows from the approximate Boltzmann distribution of the overlap between the initial state and the eigenstates of the final Hamiltonian. We show here that the distribution of the overlaps is in general not related to the canonical (or microcanonical) distribution and, hence, it cannot explain why thermalization occurs in quantum systems.

Sooshin Kim, Alexander Lukin, Matthew Rispoli +7 more

Corinna Kollath, Guillaume Roux, Giulio Biroli +1 more

Motivated by the role that spectral properties play for the dynamical evolution of a quantum many-body system, we investigate the level spacing statistics of the extended Bose–Hubbard model. In particular, we focus on the distribution of the ratio of adjacent level spacings, useful at large interactions, to distinguish between chaotic and non-chaotic regimes. After revisiting the bare Bose–Hubbard model, we study the effect of two different perturbations: next-nearest-neighbor hopping and nearest-neighbor interaction. The system size dependence is investigated together with the effect of the proximity to integrable points or lines. Lastly, we discuss the consequences of a cutoff in the number of onsite bosons on the level statistics.