Simulations of Discrete Quantum Systems in Continuous Euclidean Time

TL;DR

This paper introduces a continuous Euclidean time approach for simulating discrete quantum systems, enabling more efficient analysis of models like quantum spin systems and lattice fermions, and confirming theoretical predictions at low temperatures.

Contribution

It presents a novel continuous-time simulation method for discrete quantum systems, improving computational efficiency and accuracy over traditional Trotter-based approaches.

Findings

Confirmed chiral perturbation theory predictions at very low temperatures

Achieved excellent agreement with previous results and experiments

Demonstrated the method's applicability to quantum spin systems

Abstract

Path integrals are usually formulated in discrete Euclidean time using the Trotter formula. We propose a new method to study discrete quantum systems, in which we work directly in the Euclidean time continuum. The method is of general interest and can be applied to studies of quantum spin systems, lattice fermions, and in principle also lattice gauge theories. Here it is applied to the Heisenberg quantum antiferromagnet using a continuous-time version of a loop cluster algorithm. The computational advantage of this algorithm is exploited to confirm the predictions of chiral perturbation theory in the extreme low temperature regime, down to $T = 0.01 J$. A fit of the low-energy parameters of chiral perturbation theory gives excellent agreement with previous results and with experiments.