Anomalous finite size spectrum in the S=1/2 two dimensional Heisenberg model

TL;DR

This study investigates the low energy spectrum of the 2D S=1/2 Heisenberg model, revealing slow crossover to expected scaling and an anomalous finite size effect, with implications for experimental detection.

Contribution

It provides the first detailed quantum Monte Carlo analysis of the finite size spectrum across different spins, highlighting anomalies specific to the S=1/2 case.

Findings

Nonlinear sigma model predictions hold for large systems.

Slow crossover to the scaling regime in S=1/2 models.

Finite temperature experiments may detect the anomalous spectrum.

Abstract

We study the low energy spectrum of the nearest neighbor Heisenberg model on a square lattice as a function of the total spin S. By quantum Monte Carlo simulation we compute this spectrum for the s=1/2, s=1 and s=3/2 Heisenberg models. We conclude that the nonlinear sigma model prediction for the low energy spectrum is always verified for large enough system size. However the crossover to the correct scaling regime is particularly slow just for the s=1/2 Heisenberg model. The possibility to detect this unexpected anomaly with finite temperature experiments on s=1/2 isotropic quantum antiferromagnets is also discussed.