Exact results for nonequilibrium ultracold matter

Quantum many-body dynamics raise fertile scientific questions, for example about thermalization, entanglement generation, and classical simulability. These questions are explored in a variety of experiments with ultracold matter, but they resist theory: semi-analytic methods can fail to capture the essential physics, and numerical methods are often impossible to convincingly converge. Exact results are jewels: illuminating and beautiful, but rare.

I will describe our research on exact results for nonequilibrium quantum matter. Mostly, I will focus on a new method [1] that improves the bound on the speed at which correlations can spread, and its applications [2]. These improvements are sometimes qualitative: as a dramatic example, the method proves a finite speed of information spreading in special nonlocally interacting systems. Even when the improvement is “merely quantitative,” the implications are surprisingly important, opening up new applications. As an example, I will discuss how one can obtain mathematically rigorous, and reasonably tight, bounds on the finite-size error of numerical simulations on classical computers, quantum computers, and quantum simulators [2]. I will discuss how this applies to numerous experiments with ultracold atoms and molecules. I will also briefly discuss our results on exactly solvable models [3], which allow one to study exotic features in dynamics, including topological phenomena.

[1] Tightening the Lieb-Robinson bound in locally interacting systems, Z Wang and KRAH, Phys. Rev. X Quantum 1, 010303 (2020)

[2] Bounding the finite-size error of quantum many-body dynamics simulations, Z Wang, M Foss-Feig, KRAH, Phys. Rev. Research 3, L032047 (2021)

[3] Topological correlations in three dimensional classical Ising models: an exact solution with a continuous phase transition, Z Wang and KRAH, arxiv:2202.11303