# Ensemble Quasi-Newton HMC

## TL;DR

This paper introduces an enhanced Hybrid Monte Carlo algorithm that incorporates an approximate inverse Hessian to improve sampling efficiency in lattice gauge theories, demonstrated on 2D U(1) models.

## Contribution

It proposes a novel method to exchange information within Markov chain ensembles and integrates a quasi-Newton inspired Hessian into HMC to mitigate critical slowing down.

## Key findings

- Improved sampling efficiency in 2D U(1) gauge theory
- Effective exchange of information within Markov chain ensembles
- Potential for application to more complex gauge theories

## Abstract

We present a modification of the Hybrid Monte Carlo algorithm for tackling the critical slowing down of generating Markov chains of lattice gauge configurations towards the continuum limit. We propose a new method to exchange information within an ensemble of Markov chains, and use it to construct an approximate inverse Hessian matrix of the action inspired from quasi-Newton algorithms for optimization. The kinetic term of the molecular dynamics evolution includes the approximate Hessian for long distance couplings among the momenta. We show the result of applying the new algorithm to the $U(1)$ gauge theory in two dimensions, and discuss our future plans.