Nonergodic behavior of the clean Bose-Hubbard chain

Abstract

We study ergodicity breaking in the clean Bose-Hubbard chain for small hopping strength. We see the existence of a nonergodic regime by means of indicators as the half-chain entanglement entropy of the eigenstates, the average level spacing ratio, the properties of the eigenstate-expectation distribution of the correlation and the scaling of the inverse participation ratio averages. We find that this ergodicity breaking is different from many-body localization because the average half-chain entanglement entropy of the eigenstates obeys volume law. This ergodicity breaking appears unrelated to the spectrum being organized in quasidegenerate multiplets at small hopping and finite system sizes, so in principle, it can survive also for larger system sizes. We find that some imbalance oscillations in time which could mark the existence of glassy behavior in space are well described by the dynamics of a single symmetry-breaking doublet and quantitatively captured by a perturbative effective XXZ model. We show that the amplitude of these oscillations vanishes in the large-size limit. Our findings are numerically obtained for systems for L < 12. Extrapolations of our scalings to larger system sizes should be taken with care, as discussed in the paper.

Nonergodic dynamics of the one-dimensional Bose-Hubbard model with a trapping potential

“…We see that when the trapping potential is as weak as Ω/J ≤ 0.02, r is close to the Wigner-Dyson (Poisson) value in a region of small (large) U/J. This behavior is consistent with the previous work in the absence of the trapping potential [30,34]. As we will see below, the nonergodic behaviors appear in the Poisson distribution regime.…”

“…In this case, nonergodic dynamics have been found in a strongly interacting regime when there is no trapping potential [32,34]. We show that the presence of a weak trapping potential does not break the nonergodic behaviors caused by the large interaction.…”

“…In this paper, we study nonergodic behaviors of the 1D Bose-Hubbard model. The previous works investigated level-spacing statistics, expectation values of physical quantities of the eigenstates and dynamics, and showed that strong interparticle interactions lead to the nonergodicity even when the system is homogeneous [30][31][32][33][34]. From these works, it can be expected that the nonergodic behaviors are likely due to the Hilbert-space fragmentation.…”

The ergodic and non-ergodic phases in one dimensional clean Jaynes-Cummings-Hubbard system

“…Eigenenergy is scaled as ǫ ≡ (E − E min )/(E max − E min ) ∈ [0, 1], then the eigenstates can be chosen around energy targets [48][49][50]. In the random matrix theory, the discrimination between ergodic and non-ergodic regimes can depend on spectral statistics [34,51]. We can capture the statistical features of spectrum by the level spacing ratios [52,53], r n = min(δ n+1 /δ n , δ n /δ n+1 ), where δ n = E n+1 − E n is the nth level spacing and the eigenenergies are arranged in an ascending order.…”

“…Later, it was found that the large tilt potential can also produce a similar effect to the disorder, resulting in the non-ergodic many-body systems [28][29][30][31], which has been realized in the latest experiments [32]. In addition, the existence of non-ergodic behaviors is also found for a one-dimensional uniform Josephson junction chain at higher energies or weak Josephson coupling [33] and a clean Bose Hubbard chain under weak tunneling strength [34]. Interesting questions thus arise and need to be clarified, e.g., whether there are other factors that can lead to the ergodicity breaking?…”