Dynamics of defects and interfaces for interacting quantum hard disks

Abstract

Defects and interfaces are essential to understand the properties of matter. However, studying their dynamics in the quantum regime remains a challenge in particular concerning the regime of two spatial dimensions. Recently, it has been shown that a quantum counterpart of the hard-disk problem on a lattice yields defects and interfaces, which are stable just due to quantum effects while they delocalize and dissolve in an analogous classical stochastic process. Here, we study in more detail the properties of defects and interfaces in this quantum hard-disk problem with a particular emphasis on the stability of these quantum effects upon including perturbations. Specifically, we introduce short-range soft-core interactions between the hard disks. From both analytical arguments and numerical simulations we find that large classes of defects and interfaces remain stable even under such perturbations suggesting that the quantum nature of the dynamics exhibits a large range of robustness. Our findings demonstrate the stability and non-classical behavior of quantum interface dynamics, offering insights into the dynamics of two-dimensional quantum matter and establishing the quantum hard-disk model as a platform for studying unconventional constrained quantum dynamics.

Figures (7)

• Figure 1: Defect dynamics on the square lattice with interactions. (A) Schematic representation of the interacting quantum hard disk model on a square lattice. The interactions are of next-to-nearest-neighbor type, acting only between particles located diagonally. There are no interactions between particles that are separated by two sites in the same row or column. (B) The Hilbert space fragmentation as a function of particle density $\eta$. Here, $\eta_1 = 1/L$, $\eta_2 = \frac{1}{2} - \frac{\lceil L/2 \rceil }{ L^2}$, and $\eta_{\textrm{max}} = \frac{1}{2} - \frac{L(\textrm{mod} 2)}{2L^2}$. $\eta^*$ denotes the threshold density for the weak-to-strong crossover region. (C) Long-time dynamics of on-site occupations at $Jt = 10^{2}$, showing memory of the initial state even in the presence of interactions.
• Figure 2: Memory of the initial condition measured through the autocorrelation function $G(t)$ as a function of the interaction strength $\lambda$ for different initial configurations. The three initial configurations correspond to removing particles in (A) the second row, showing fast relaxation; (B) the first row exhibiting a long plateau; and (C) along half of the diagonal, leading to indefinite memory retention.
• Figure 3: Finite-size dependence of the autocorrelation function $G(t)$ in the interacting and free hard disks corresponding to the initial configurations: (A) particles removed in the second row, (B) particles removed in the first row, and (C) particles removed along half of the diagonal.
• Figure 4: Long-time average of the autocorrelation function $G(t)$ as a function of the interaction strength $\lambda$ corresponding to the initial configurations: (A) particles removed in the second row, (B) particles removed in the first row, and (C) particles removed along half of the diagonal. The time-window considered here is $Jt=10^4 - 10^5.$
• Figure 5: Quantum Many-Body Cages in the presence of interactions. The entanglement entropy of the eigenstates of the largest fragment is shown for different interaction strengths in a $6\times6$ lattice: (A) $\lambda = 0.01$, showing weak interactions; (B) $\lambda = 0.1$, illustrating moderate interactions; and (C) $\lambda = 0.8$, highlighting strong interaction effects. The green line marks the maximal entropy, and the gray line marks the Page entropy. Both are computed using the effective subsystem dimension $\dim \mathcal{H}_A \approx \sqrt{\dim \mathcal{N}_{\max}}$, with the Page value obtained from the standard approximation $S_{\mathrm{Page}} \simeq \ln(\dim \mathcal{H}_A) - \tfrac{1}{2}$.