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arXiv:1210.1424 · Condensed Matter Physics

The two-state Bose-Hubbard model in the hard-core boson limit: Non-ergodicity and the Bose-Einstein condensation

Stasyuk, Stasyuk

Published Sep 19, 2012• 4 citations
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Abstract

The Bose-Einstein condensation in the hard-core boson limit (HCB) of the Bose-Hubbard model with two local states and the particle hopping in the excited band only is investigated.For the purpose of considering the nonergodicity, a single-particle spectral density is calculated in the random phase approximation by means of the temperature boson Green functions.The non-ergodic contribution to the momentum distribution function of particles (connected with the static density fluctuations) increases significantly and becomes comparable with the ergodic contribution in the superfluid phase near the tricritical point.

DOI
10.5488/cmp.15.33002

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The Bose-Einstein condensation in the hard-core boson limit (HCB) of the Bose-Hubbard model with two local states and the particle hopping in the excited band only is investigated.For the purpose of considering the nonergodicity, a single-particle spectral density is calculated in the random phase approximation by means of the temperature boson Green functions.The non-ergodic contribution to the momentum distribution function of particles (connected with the static density fluctuations) increases significantly and becomes comparable with the ergodic contribution in the superfluid phase near the tricritical point.
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Building on large-scale quantum Monte Carlo simulations, we investigate the zero-temperature phase diagram of hard-core bosons in a random potential on site-centered Cayley trees with branching number K=2K=2K=2. In order to follow how the Bose-Einstein condensate (BEC) is affected by the disorder, we focus on both the zero-momentum density, probing the quantum coherence, and the one-body density matrix (1BDM) whose largest eigenvalue monitors the off-diagonal long-range order. We further study its associated eigenstate which brings useful information about the real-space properties of this leading eigenmode. Upon increasing randomness, we find that the system undergoes a quantum phase transition at finite disorder strength between a long-range ordered BEC state, fully ergodic at large scale, and a new disordered Bose glass regime showing conventional localization for the coherence fraction while the 1BDM displays a nontrivial algebraic vanishing BEC density together with a nonergodic occupation in real space. These peculiar properties can be analytically captured by a simple phenomenological description on the Cayley tree which provides a physical picture of the Bose glass regime.
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The spectrum of phonon-like collective excitations in the system of Bose-atoms in optical lattice (more generally, in the system of quantum particles described by the Bose-Hubbard model) is investigated.Such excitations appear due to displacements of particles with respect to their local equilibrium positions.The two-level model taking into account the transitions of bosons between the ground state and the first excited state in potential wells, as well as interaction between them, is used.Calculations are performed within the random phase approximation in the hard-core boson limit.It is shown that excitation spectrum in normal phase consists of the one exciton-like band, while in the phase with BE condensate an additional band appears.The positions, spectral weights and widths of bands strongly depend on chemical potential of bosons and temperature.The conditions of stability of a system with respect to the lowering of symmetry and displacement modulation are discussed.