From Quantum Chaos to a Reversed Quantum Disentangled Liquid in a Disorder-Free Spin Ladder

Abstract

The mechanisms by which isolated interacting quantum systems evade thermalization extend beyond disorder-induced many-body localization, encompassing a growing class of interaction-driven phenomena. We investigate a spin-1/2 ladder with asymmetric XY leg couplings and tunable Ising interactions on the rungs, and identify the microscopic origin of many-body localization (MBL) in this setting. Through a suite of diagnostics -including entanglement dynamics, fidelity susceptibility, adiabatic gauge potential norms, level-spacing statistics and entropy of eigenstates- we uncover a reentrant progression of dynamical regimes as the rung coupling Jz is varied: integrable behavior at Jz=0, quantum chaos at intermediate Jz, and a robust nonthermal regime at strong coupling. In the latter regime, we demonstrate the emergence of a reversed quantum disentangled liquid (reversed-QDL), where the light species thermalizes while the heavy species remains localized. The strong-coupling limit further yields emergent local integrals of motion anchored in a fixed-point structure, providing a microscopic origin of the observed quasi-MBL dynamics. These results establish reversed-QDL as a distinct, disorder-free route to nonergodicity and broaden the classification of dynamical phases in quantum matter.

Figures (10)

• Figure 1: (Color online) Schematic illustration of the two-leg spin-$\frac{1}{2}$ ladder model. Blue and red spheres denote spins on the lower ($\tau$) and upper ($\sigma$) legs, respectively, which are coupled via XY interactions $J$ and $J'$. Rung couplings $J_z$ introduce inter-leg Ising interactions. The dashed green line denotes the bipartition used to measure entanglement entropy.
• Figure 2: (Color online) Time evolution of the half-cut entanglement entropy $S_{\mathrm{ent}}(t)$ for various values of inter-leg Ising coupling $J_z$, computed for a spin-1/2 ladder of size $L = 8$ with periodic boundary conditions and $J'=0.001$. The system exhibits a crossover from rapid thermalization at weak coupling ($J_z \ll 1$) to slow, logarithmic growth characteristic of quasi-many-body localization ($J_z \gg 1$). For $J_z = 10$, the labeled times $t_1$, $t_2$ and $t_3$ respectively mark the rapid rise due to local interactions, the onset and crossover to the logarithmic growth regime, highlighting the separation of dynamical timescales inherent to quasi-MBL. (Inset) The entropy saturation value plotted against system size at $J_z=0.01$ demonstrates a clear volume-law scaling, supports the identification of a chaotic phase.
• Figure 3: (Color online) Dimension-weighted average of fidelity susceptibility $\chi_{\mathrm{typ}}^{\mathrm{avg}}/D_{\mathrm{eff}}$ as a function of $J_z$ for ladder lengths $L=10, 12$. A clear peak appears near $J_z \simeq 1$, signaling a dynamical crossover. (Inset) Rescaled AGP norm $\|A_\lambda\|^2 / L$ as a function of system size for different values of $J_z$ on a logarithmic scale. For $J_z=0$ (integrable case), the scaling of $\|A_\lambda\|^2$ is linear in $L$, while for small nonzero $J_z$ values the norm grows exponentially, with $J_z=0.01$ showing clear chaotic behavior. Near $J_z \simeq 1$, deviations from exponential scaling appear, and for larger $J_z$, the exponential growth is strongly reduced. The AGP results are computed in the total-magnetization sector $\mathcal{S}^z_{\mathrm{tot}}=0$ and averaged over all $(k,\mathcal{Z})$ symmetry sectors.
• Figure 4: (Color online) Normalized average entropy $S_{\mathrm{avg}}$ versus $J_z$ for system sizes $L=5,6,7,8,9$. For $J_z<1$, larger values of $S_{\mathrm{avg}}$ indicate full Hilbert-space exploration in the chaotic phase, while for $J_z>1$, a marked decrease signals localization, consistent with a dynamical crossover near $J_z\simeq 1$. Slight differences between odd and even $L$ arise from the bipartition asymmetry in entropy calculations.
• Figure 5: (Color online) (Inset) Schematic representation of the procedure used to evaluate the measured entanglement entropy. (a) A projective measurement is performed on the $\sigma$ spins (upper leg) of a many-body eigenstate, resulting in the collapse of the wavefunction to a configuration-dependent post-measurement state $|\psi_p^{(m)}\rangle$ of the $\tau$ spins. (b) For each measurement outcome, the half-cut entanglement entropy associated with subsystem $A$ is computed as explained in the main text. (Main) Comparison of full and measured entanglement entropies in a spin ladder with strong inter-leg coupling $J_z = 10$. The total bipartite entropy $S_{L/2}$ (dark-red triangles) displays three characteristic regimes as mentioned in Fig. \ref{['fig:ent_dyn']}. Measured entropies after projective measurements on one leg, $S_A^{(\tau|\sigma)}$ (blue squares) and $S_A^{(\sigma|\tau)}$ (red diamonds), reveal the asymmetry in thermalization between legs. Notably, $S_A^{(\tau|\sigma)}$ saturates early, reflecting thermalization within the $\tau$, while $S_A^{(\sigma|\tau)}$ remains strongly suppressed, indicating localization of the $\sigma$s.