Novel Quantum Monte Carlo Algorithms for Fermions

TL;DR

This paper introduces new quantum Monte Carlo algorithms based on a positive definite cluster representation for fermionic models, enabling efficient simulations of complex fermionic systems and confirming superfluid phase transitions.

Contribution

The authors develop novel quantum Monte Carlo algorithms leveraging a positive cluster representation for fermions, expanding computational capabilities for fermionic models.

Findings

Validated the new algorithms on Hubbard-type models

Confirmed superfluid phase transition in 2D attractive fermion model

Demonstrated tractability of models with both attractive and repulsive interactions

Abstract

Recent research shows that the partition function for a class of models involving fermions can be written as a statistical mechanics of clusters with positive definite weights. This new representation of the model allows one to construct novel algorithms. We illustrate this through models consisting of fermions with and without spin. A Hubbard type model with both attractive and repulsive interactions becomes tractable using the new approach. Precision results in the two dimensional attractive model confirm a superfluid phase transition in the Kosterlitz-Thouless universality class.