Eigenstate thermalization to non-monotonic distributions in strongly-interacting chaotic lattice gases

TL;DR

Isolated quantum many-body systems with finite spectra can exhibit equilibrium energy distributions that deviate from the standard Fermi-Dirac and Bose-Einstein forms. The authors study two chaotic lattice models (2D Fermi-Hubbard and 1D Bose-Hubbard) via exact diagonalization, examining level statistics, the local density of states (LDOS), and orbital occupations to compare interacting and non-interacting shells. They find that strong interactions broaden the LDOS with width $\Gamma$, mixing microcanonical shells of opposite temperatures and producing non-monotonic, non-FD/BE orbital occupation distributions that persist in large systems while ETH remains valid. The work thus reveals a qualitative departure from conventional thermal distributions in chaotic many-body systems and suggests that these effects could be observed in cold-atom experiments, enriching the understanding of chaos, ergodicity, and LDOS in quantum thermalization.

Abstract

We find non-monotonic equilibrium energy distributions, qualitatively different from the Fermi-Dirac and Bose-Einstein forms, in strongly-interacting many-body chaotic systems. The effect emerges in systems with finite energy spectra, supporting both positive and negative temperatures, in the regime of quantum ergodicity. The results are supported by exact diagonalization calculations for chaotic Fermi-Hubbard and Bose-Hubbard models, when they have Wigner-Dyson statistics of energy spectra and demonstrate eigenstate thermalization. The proposed effects may be observed in experiments with cold atoms in optical lattices.

Figures (6)

• Figure 1: 1B orbital occupations for (a) the FH model with the interaction strengths $V=0$ (dashed lines), $V=1$ (pluses), and $V=10$ (solid lines), averaged over microcanonical shells with the mean energies $-6$ (black), $0$ (green), and $6$ (red) and (b) the 1D BH model with the interaction strengths $V=0$ (dashed lines), $V=0.3$(pluses), and $V=3$ (solid lines), averaged over microcanonical shells with the mean energies $-1.2$ (black), $-0.17$ (green), and $1.2$ (red).
• Figure 2: 1B orbital occupations for different $\tilde{\Gamma}$. (a) The FH model with $\tilde{N}=0.2$ and $\tilde{E}=0.1$. (b) The 2D BH model with $\tilde{N}=0.2$ and $\tilde{E}=-0.1$. (c) The 1D BH model with $\tilde{N}=0.2$ and $\tilde{E}=-0.1$. The green lines show the FD or BE distributions corresponding to $\tilde{E}$.
• Figure 3: One-body orbital energy as a function of the orbital label $k$ for small and large FH models.
• Figure 4: (a) Level spacing ratio (black line) vs. interaction strength for the FH model. Dashed lines show $\left\langle r\right\rangle$ for the Poisson and GOE statistics. The green line shows NPC. (b) The same for the 1D BH model.
• Figure 5: Ratio of eigenstate-to-eigenstate fluctuation variances for the non-integrable to ones for the integrable systems eigenstates vs. interaction strength for: (a) the FH model averaged over the microcanonical shell with the mean energy $0$; (b) the 1D BH model with the mean shell energy $-5.14$.