Abstract
We study ergodicity breaking in the clean Bose-Hubbard chain for small hopping strength. We see the existence of a non-ergodic 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 a glassy behaviour 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 with $L < 12$. Extrapolations of our scalings to larger system sizes should be taken with care, as discussed in the paper.
Highlights
Thermalization in classical Hamiltonian systems is well understood in terms of chaotic dynamics and the related essentially ergodic exploration of the phase space [1,2,3]
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
III, we study the ergodicity breaking by means of the behavior of the half-chain entanglement entropy whose volume-law behavior is in sharp contrast with the area-law behavior in many-body localized systems
Summary
Thermalization in classical Hamiltonian systems is well understood in terms of chaotic dynamics and the related essentially ergodic exploration of the phase space [1,2,3]. For small values of J, this model breaks ergodicity in a way remarkably different from many-body localization, where the eigenstates show instead an area-law behavior and the averaged entanglement entropy is constant with the system size. We see a nonergodic regime at small hoppings with properties that are clearly different from a many-body localized phase In this way, we confirm and extend the results of [42,43]. Given the system sizes that we are able to reach, we should keep in mind the possibility that this nonergodic regime is a finite-size effect and we do not know if it can be extrapolated towards the thermodynamic limit Some hint in this direction is provided by the behavior of the entanglement-entropy averages restricted to the highentropy states (see Sec. III), but the system sizes are too small for a definitive statement.
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