Study of CP(N-1) \theta-Vacua by Cluster-Simulation of SU(N) Quantum Spin Ladders

TL;DR

This study uses cluster simulation of SU(N) quantum spin ladders within D-theory to explore CP(N-1) heta-vacua, revealing phase transitions and symmetry breaking at heta = \pi for N>2.

Contribution

It introduces an efficient cluster algorithm for D-theory simulations, enabling investigation of heta-vacua without sign problems, and demonstrates phase transitions at heta = \\pi.

Findings

No sign problem at heta = \\pi in D-theory.

First order phase transition at heta = \\pi for N>2.

Spontaneous charge conjugation symmetry breaking.

Abstract

D-theory provides an alternative lattice regularization of the (1+1)-d CP(N-1) quantum field theory. In this formulation the continuous classical CP(N-1) fields emerge from the dimensional reduction of discrete SU(N) quantum spins. In analogy to Haldane's conjecture, ladders consisting of an even number of transversely coupled spin chains lead to a CP(N-1) model with vacuum angle \theta = 0, while an odd number of chains yields \theta = \pi. In contrast to Wilson's formulation of lattice field theory, in D-theory no sign problem arises at \theta = \pi, and an efficient cluster algorithm is used to investigate the \theta-vacuum effects. At \theta = \pi there is a first order phase transition with spontaneous breaking of charge conjugation symmetry for CP(N-1) models with N>2.