A New Approach to Stochastic State selections in Quantum Spin Systems

TL;DR

This paper introduces a novel Monte Carlo method for quantum spin systems that avoids the negative sign problem by selectively sampling states, enabling efficient calculations of expectation values and energy estimates with limited resources.

Contribution

The paper presents a new stochastic state selection technique that bypasses the negative sign problem in quantum Monte Carlo simulations.

Findings

Effective evaluation of expectation values for small quantum systems.

Successful estimation of the lowest energy eigenvalue.

Method performs well with limited computational resources.

Abstract

We propose a new type of Monte Carlo approach in numerical studies of quantum systems. Introducing a probability function which determines whether a state in the vector space survives or not, we can evaluate expectation values of powers of the Hamiltonian from a small portion of the full vector space. This method is free from the negative sign problem because it is not based on importance sampling techniques. In this paper we describe our method and, in order to examine how effective it is, present numerical results on the 4x4, 6x6 and 8x8 Heisenberg spin one-half model. The results indicate that we can perform useful evaluations with limited computer resources. An attempt to estimate the lowest energy eigenvalue is also stated.