Speaker
Description
Despite the exact solvability of the spectrum in interacting quantum integrable models, the computation of (dynamical) correlation functions remains a major open challenge analytically and numerically. A fundamental bottleneck is that the Lehmann representation for the correlators involves a summation over a number of form factors that scales exponentially with system size, rendering exact summations prohibitive for any classical computational resources. I will present recent progress based on Markov Chain Monte Carlo sampling of form factors and overlaps that enables the accurate reconstruction of correlation functions in (generalized) Gibbs ensembles [1], as well as out-of-equilibrium following global quantum quenches [2], for generic energy densities, particle densities, and interaction strengths. To demonstrate the efficacy of the approach I will focus on the transverse-field Ising chain and the repulsive Lieb-Liniger gas, where a few benchmarks are available. Finally, I will address the origin of the absence of a Monte Carlo “sign problem”, and discuss scenarios in which it persists.
[1] R. Senese, F.H.L. Essler; https://doi.org/10.1103/8qtr-dm7g
[2] R. Senese, F.H.L. Essler; in preparation