Dual lattice representations for O(N) and CP(N-1) models with a chemical potential

TL;DR

The paper tackles the sign problem of finite-density lattice theories by constructing dual representations for O(N) and CP(N-1) models. It derives exact dual forms with integer flux variables whose weights remain real and positive for arbitrary chemical potential, enabling sign-problem-free Monte Carlo simulations. For O(N) the dual formulation uses flux loops with auxiliary variables; for CP(N-1) it uses multiple current-type flux sets, both subject to local conservation constraints and link-sum constraints. The chemical potential translates into winding-number couplings of the dual fluxes, and the work provides a practical framework potentially extendable to non-abelian gauge theories and other finite-density systems.

Abstract

We derive dual representations for O(N) and CP(N-1) models on the lattice. In terms of the dual variables the partition sums have only real and positive contributions also at finite chemical potential. Thus the complex action problem of the conventional formulation is overcome and using the dual variables Monte Carlo simulations are possible at arbitrary chemical potential.