From Spin Ladders to the 2-d O(3) Model at Non-Zero Density

TL;DR

This paper introduces a method to simulate the 2-d O(3) model at non-zero density by mapping it to a quantum spin ladder system, solving the sign problem with a meron-cluster algorithm, thus enabling studies of complex action systems.

Contribution

It presents a novel approach to address the complex action problem in the 2-d O(3) model by using dimensional reduction from a quantum spin ladder and applying a meron-cluster algorithm.

Findings

Successfully maps the 2-d O(3) model to a quantum spin ladder.

Solves the sign problem using a meron-cluster algorithm.

Enables numerical simulations of the model at non-zero density.

Abstract

The numerical simulation of various field theories at non-zero chemical potential suffers from severe complex action problems. In particular, QCD at non-zero quark density can presently not be simulated for that reason. A similar complex action problem arises in the 2-d O(3) model -- a toy model for QCD. Here we construct the 2-d O(3) model at non-zero density via dimensional reduction of an antiferromagnetic quantum spin ladder in a magnetic field. The complex action problem of the 2-d O(3) model manifests itself as a sign problem of the ladder system. This sign problem is solved completely with a meron-cluster algorithm.