A New Approach to Stochastic State selections in Quantum Spin Systems

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.

10 pages, 2 figures, 8 tables

References in corpus (5)

• Correlated Electrons in High Temperature Superconductors
• Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model
• Exact dimer ground state of the two dimensional Heisenberg spin system SrCu_2(BO_3)_2
• Finite size and temperature effects in the AF Heisenberg model
• Numerical Study of Excited States in the Shastry-Sutherland Model

Cited by in corpus (5)

• The Stochastic State Selection Method for Energy Eigenvalues in the Shastry-Sutherland Model
• A Recursive Method of the Stochastic State Selection for Quantum Spin Systems
• An Equilibrium for Frustrated Quantum Spin Systems in the Stochastic State Selection Method
• The Stochastic State Selection Method Combined with the Lanczos Approach to Eigenvalues in Quantum Spin Systems
• A constrained stochastic state selection method applied to quantum spin systems