Many-body localization and particle multioccupancy in the disordered Bose-Hubbard model

TL;DR

This work investigates how particle statistics influence many-body localization in the disordered Bose-Hubbard model. By combining Van Vleck perturbation theory (applicable to the higher-energy sector) with an algebraic projection approach (for the lower-energy sector), the study reveals a robust cluster MBL phase at high energies without finite-size drift, while a drift toward thermal behavior emerges at low energies due to emergent spin/fermion statistics. The results imply a Bose–Fermi distinction can create a mobility edge between cluster MBL and thermal regions and establish dBH as a suitable platform for exploring nonergodic eigenstate matter in cold-atom experiments. The methods provide a pathway to analyze large systems beyond exact diagonalization and connect the bosonic problem to effective disordered spin models, potentially guiding future explorations of MBL in interacting bosonic platforms.

Abstract

We study the potential influence of the particle multi-occupations on the stability of many-body localization in the disordered Bose-Hubbard model. Within the higher-energy section of the dynamical phase diagram, we find that there is no apparent finite-size boundary drift between the thermal phase and the many-body localized regime. We substantiate this observation by introducing the Van Vleck perturbation theory into the field of many-body localization. The appropriateness of this method rests largely on the peculiar Hilbert-space structure enabled by the particles' Bose statistics. The situation is reversed in the lower-energy section of the dynamical phase diagram, where the significant finite-size boundary drift pushes the putative many-body localized regime up to the greater disorder strengths. We utilize the algebraic projection method to make a connection linking the disordered Bose-Hubbard model in the lower-energy section to an intricate disordered spin chain model. This issue of the finite-size drift could hence be analogous to what happens in the disordered Heisenberg chain. Both trends might be traced back to the particles' intrinsic or emergent single-occupancy constraint like the spin-$1/2$, hard-core boson, or spinless fermion degrees of freedom.

Figures (4)

• Figure 1: The sequence of the small-size dynamical phase diagrams of the dBH chain model (\ref{['hamdbh']}) with $N=\frac{L}{2}$. The color contours are derived from the level-spacing ratio $r$ computed by ED and averaged over a sufficient amount of random samples (see the main text for details). Here, the axes $\varepsilon$ and $\mu$ stand for the normalized energy and the disorder strength, respectively.
• Figure 2: The companion sequence of the small-size dynamical phase diagrams of the dBH chain model (\ref{['hamdbh']}) with $N=\frac{L}{2}$. The color contours are drawn from the quantity of the maximal site occupation $\textrm{max}(n_i)/N$ (see its definition in the main text) computed via ED and averaged over many random realizations.
• Figure 3: Perturbative estimates of the level-spacing ratio $r$ for the top blocks $n_{\textrm{max}}=N,\ N-1,\ N-2$ and bottom blocks $n_{\textrm{max}}=1,\ 2$ as a function of the dBH chain length $L$. These scaling results are obtained by the Van Vleck algorithm and averaged over at least $100$ random samples at weak disorder $\mu=2J$. Here, the top dashed line gives the prediction of the level-spacing ratio suitable for the Gaussian orthogonal ensemble, $r_{\rm GOE}\approx0.536$, while the bottom dashed line gives the corresponding prediction for the ensemble obeying the Poisson statistics, $r_{\rm Poi.}\approx0.386$.
• Figure 4: Comparison between the averaged level-spacing ratio obtained from the ED, $r_{\rm ED}$, and obtained from the perturbative Van Vleck method, $r_{\rm pert.}$. The detailed procedure of how to extract $r_{\rm ED}$ from Figs. \ref{['pic8']} and \ref{['pic_ni']} is explained in the main text. The $r_{\rm pert.}$ values are directly read out from Fig. \ref{['pic_vv']}, thus here we have focused on the weak-disorder regime specified by $\mu=2J$. The two dashed lines are defined as in Fig. \ref{['pic_vv']}.