Breakdown of thermalization in finite one-dimensional systems

We use quantum quenches to study the dynamics and thermalization of hardcore bosons in finite one-dimensional lattices. We perform exact diagonalizations and find that, far away from integrability, few-body observables thermalize. We then study the breakdown of thermalization as one approaches an integrable point. This is found to be a smooth process in which the predictions of standard statistical mechanics continuously worsen as the system moves toward integrability. We establish a direct connection between the presence or absence of thermalization and the validity or failure of the eigenstate thermalization hypothesis, respectively.Comment: 9 pages, 13 figures, as publishe

Comment on "Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined" [arXiv:0810.3720]

In a recent paper Roux [Phys. Rev. A 79, 021608(R) (2009), arXiv:0810.3720] argued that thermalization in a Bose-Hubbard system, after a 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.Comment: 2 pages, 1 figure, as publishe

Analytical and numerical study of trapped strongly correlated bosons in two- and three-dimensional lattices

We study the ground-state properties of trapped inhomogeneous systems of hardcore bosons in two- and three-dimensional lattices. We obtain our results both numerically, using quantum Monte Carlo techniques, and via several analytical approximation schemes, such as the Gutzwiller-mean-field approach, a cluster-mean-field method and a spin-wave analysis which takes quantum fluctuations into account. We first study the homogeneous case, for which simple analytical expressions are obtained for all observables of interest, and compare the results with the numerical ones. We obtain the equation of state of the system along with other thermodynamic properties such as the free energy, kinetic energy, superfluid density, condensate fraction and compressibility. In the presence of a trap, superfluid and insulating domains coexist in the system. We show that the spin-wave-based method reproduces the quantum Monte-Carlo results for global as well as for local quantities with a high degree of accuracy. We also discuss the validity of the local density approximation in those systems. Our analysis can be used to describe bosons in optical lattices where the onsite interaction U is much larger than the hopping amplitude t.Comment: 14 pages, 14 figure

Confinement control by optical lattices

It is shown that the interplay of a confining potential with a periodic potential leads for free particles to states spatially confined on a fraction of the total extension of the system. A more complex `slicing' of the system can be achieved by increasing the period of the lattice potential. These results are especially relevant for fermionic systems, where interaction effects are in general strongly reduced for a single species at low temperatures.Comment: Revtex file, 13 pages, 18 figures. References added. Published versio