Condensed Matter Theory

Abstract:

Wave-like spatial statistics in walking-droplet systems are often associated with wave-mediated interactions and wave-memory effects. Here we explore how similar statistical structure can arise from the low-dimensional nonlinear dynamics of an inertial active particle with internal degrees of freedom. In this framework, steady propulsion corresponds to internal-state fixed points whose spiral or transiently chaotic relaxation organizes oscillatory ensemble densities. Local perturbations then generate wave-like statistics in both open and closed geometries, suggesting that wave-like ensemble behavior may emerge more generally from internal-state attractor dynamics in inertial active matter.

Abstract:

We prove an analog of the “bottleneck theorem,” well-known for classical Markov chains, for Markovian quantum channels. In particular, we show that if two regions (subspaces) of Hilbert space are separated by a region that has very low weight in the channel’s steady state, then states initialized on one side of this barrier will take a long time to relax, putting a lower bound on the mixing time in terms of an appropriately defined “quantum bottleneck ratio.” Importantly, this bottleneck ratio involves not only the probabilities of the relevant subspaces, but also the size of off-diagonal matrix elements between them. For low temperature quantum many-body systems, we use the bottleneck theorem to bound the performance of any quasilocal Gibbs sampler. This leads to a new perspective on thermally stable quantum phases in terms of a decomposition of the Gibbs state into multiple components separated by bottlenecks. As a concrete application, we show rigorously that weakly perturbed commuting projector models with extensive energy barriers (which include certain classical and quantum expander codes) have exponentially large mixing times.

Abstract:

We establish twisted SnSe₂ as a tunable platform for simulating dimension-dependent correlated physics, distinct from conventional K-valley moiré systems. By constructing interacting Wannier models, we show that the stacking configuration dictates the effective lattice geometry. In AAstacked bilayers, a momentum-space nonsymmorphic symmetry constrains the single-particle hopping within each valley to be effectively one-dimensional, while still allowing fully two-dimensional interactions, thereby giving rise to an effective quasi-one-dimensional system. This dimensional reduction stabilizes exotic phases including dimerized states with finite residual entropy, valence bond solids, and quantum paramagnetism. Conversely, AB-stacking maps to a frustrated Kagome lattice; here, strong interactions drive the emergence of a classical spin liquid. The high tunability of this moiré system, which allows control over both the filling and interaction strength (via twist angle), renders twisted SnSe₂ a versatile platform for realizing a wide range of exotic correlated quantum phases.

Abstract:

Many strongly correlated states, such as those arising in the fractional quantum Hall effect and spin liquids, are described by wavefunctions obtained by dividing particles into multiple clusters, constructing a readily evaluable wavefunction in each cluster, and (anti)symmetrizing across these clusters. We introduce a method to compute quantities such as energies and correlators, using Monte Carlo simulations for these states. Our framework overcomes the factorial scaling of explicit (anti)symmetrization, allowing for studies of systems beyond the reach of exact diagonalization.