3 papers
cs.DS2020
Efficient Algorithms for Approximating Quantum Partition Functions
Ryan L. Mann, Tyler Helmuth
We establish a polynomial-time approximation algorithm for partition functions of quantum spin models at high temperature. Our algorithm is based on the quantum cluster expansion o…
math.PR2020
Loop-erased random walk as a spin system observable
Tyler Helmuth, Assaf Shapira
The determination of the Hausdorff dimension of the scaling limit of loop-erased random walk is closely related to the study of the one-point function of loop-erased random walk, i…
math-ph2018
Dynkin isomorphism and Mermin--Wagner theorems for hyperbolic sigma models and recurrence of the two-dimensional vertex-reinforced jump process
Roland Bauerschmidt, Tyler Helmuth, Andrew Swan
We prove the vertex-reinforced jump process (VRJP) is recurrent in two dimensions for any translation invariant finite range initial rates. Our proof has two main ingredients. The…