Data Accuracy Dependence on Number of Bins in Stochastic Series Expansion for Spin-1/2 Antiferromagnetic Heisenberg Chains

Abstract

Background:

Antiferromagnetic systems exhibit complex quantum behaviours that require accurate numerical methods to analyse. The Stochastic Series Expansion (SSE) is a quantum Monte Carlo technique that simulates these systems. This study examines the effect of the number of bins on the accuracy of physical property measurements using SSE.

Materials and Methods:

The SSE simulations were performed using Fortran 90 on a Ryzen 7 processor. The system was initialised with varying lattice sizes (64, 128, 256, and 1024) and dimensionless temperatures (1/32, 1/16, 1/2, and 4) to analyse different configurations. N_bins and Monte Carlo steps were adjusted systematically to investigate their impact on the results. Results were visualised in Origin Lab.

Results:

Increasing the number of bins (N_bins) reduced fluctuations, leading to reliable results, especially at low temperatures. Lower temperatures lead to higher fluctuations in susceptibility and specific heat of the system. The Neel temperatures were observed around dimensionless temperature.  Indicating phase transitions.

Conclusions:  

The study shows that N_bins are crucial for accurate results in SSE simulations. Although the method is effective for most properties, specific heat calculations require higher computational costs and present limitations in precision.