Condensed Matter Theory

Abstract:

The theory of generalized symmetries has recently clarified how twisted sectors resolve the Callan–Rubakov paradox, where scattering of a charged particle by a magnetic monopole appeared to violate conservation laws. Here we study a more general setting of wavepackets that propagate across topological interfaces in quantum spin systems exhibiting non-invertible symmetries and across duality defects coupling dual theories. In these scenarios, we find that the transmission is always perfect and a particle traversing the interface is converted into a non-local string-like excitation. We give a systematic way of constructing such a defect by identifying its Hilbert space with the virtual bond dimension of the matrix product operator representing defect lines. Our work provides a precise characterization of topological interfaces in perfect transmission phenomena and yields a lattice analogue of the solution to the monopole paradox in quantum field 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.