Green's Functions from Quantum Cluster Algorithms

TL;DR

This paper introduces a basis-independent method for measuring Green's functions in quantum models using cluster algorithms, demonstrated on the quantum XY model and applicable to quantum link models for improved estimators.

Contribution

It proposes a novel basis-independent approach to measure Green's functions from cluster algorithms, enhancing analysis of quantum models and related observables.

Findings

Equivalent Green's function measurements in the XY model.

Numerical evidence supporting the analytic approach.

Potential for precise glueball spectrum determination in quantum link models.

Abstract

We show that cluster algorithms for quantum models have a meaning independent of the basis chosen to construct them. Using this idea, we propose a new method for measuring with little effort a whole class of Green's functions, once a cluster algorithm for the partition function has been constructed. To explain the idea, we consider the quantum XY model and compute its two point Green's function in various ways, showing that all of them are equivalent. We also provide numerical evidence confirming the analytic arguments. Similar techniques are applicable to other models. In particular, in the recently constructed quantum link models, the new technique allows us to construct improved estimators for Wilson loops and may lead to a very precise determination of the glueball spectrum.