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

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 θ= 0, while an odd number of chains yields θ= π. In contrast to Wilson's formulation of lattice field theory, in D-theory no sign problem arises at θ= π, and an efficient cluster algorithm is used to investigate the θ-vacuum effects. At θ= πthere is a first order phase transition with spontaneous breaking of charge conjugation symmetry for CP(N-1) models with N>2.