Dual simulation of the two-dimensional lattice U(1) gauge-Higgs model with a topological term

Abstract

The 2-dimensional U(1) gauge-Higgs model with a topological term is a simple example of a lattice field theory where the complex action problem comes from the topological term. We show that the model can be exactly rewritten in terms of dual variables, such that the dual partition sum has only real and positive contributions. Using suitable algorithms the dual formulation allows for Monte Carlo simulations at arbitrary values of the vacuum angle. We demonstrate the feasibility of the dual simulation and study the continuum limit, as well as the phase diagram of the system.While working on the reply to the referee report the sad news reached us that our friend and co-author Michael Müller-Preussker has passed away on 12th of October 2015. Michael has devoted 50 years of his life to physics as a very successful researcher, but also was a colleague for whom service to the community was an important duty. Michael was an inspiration for many and his untimely early death is a big loss for all of us.

Comparison of algorithms for solving the sign problem in the O(3) model in 1+1 dimensions at finite chemical potential

“…The worm algorithm, also called the dual variables approach [30], however, completely eliminates the sign problem of the model by introducing new, dual variables. The difficulty in this case is the rewriting of the model to these dual variables, but after it has been accomplished, effective simulations using the worm algorithm can be performed, and in fact many interesting models have been studied throughout the years [31][32][33][34][35][36][37][38][39][40]. Here, using the worm algorithm we study the thermodynamic properties of the O(3) model.…”

Density of states techniques for lattice field theories using the functional fit approach (FFA)

“…On the lattice the gauge action S G [U] and the topological charge Q[U] in the field theoretical definition can be written as (see [10] for our conventions for Q[U]):…”

“…becomes 2π-periodic [10]. We remark that U(1) lattice gauge theory in 2 dimensions with a geometric definition of the topological charge Q[U] was studied in [12], using a Monte Carlo approach that includes a trial distribution for the topological charges and Metropolis updates connecting neighboring charge sectors.…”

“…An important aspect for the choice of the model (6.1) as a test case for systems with a vacuum angle is the fact that, based on a dual variable approach, one can write the partition sum Z as [10] 2) where the I n are the modified Bessel functions and we define η ≡…”

Topology and index theorem with a generalized Villain lattice action – a test in 2d

“…For many cases the complex action problem can be solved in this formulation by exactly mapping the system to dual variables such that worm algorithms [3] and their generalization to gauge surfaces [4] can be used for numerical simulations. In an application of this new formulation the 2-d U(1) gauge Higgs model at topological angle θ = π was studied in [5,6] (for earlier related studies see [7,8,9]). With the solution of the complex action problem by dualization and the correct implementation of charge conjugation symmetry at θ = π it was possible to study the spontaneous breaking of the charge conjugation symmetry and show [5,6] that the transition is in the 2-d Ising universality class as expected [10,11,12] In this paper we further explore the formulation of topological terms based on [1], now focussing on the index theorem [13].…”