Gauge and matter fields as surfaces and loops - an exploratory lattice study of the Z(3) Gauge-Higgs model

Abstract

We discuss a representation of the Z(3) Gauge-Higgs lattice field theory at finite density in terms of dual variables, i.e., loops of flux and surfaces. In the dual representation the complex action problem of the conventional formulation is resolved and Monte Carlo simulations at arbitrary chemical potential become possible. A suitable algorithm based on plaquette occupation numbers and link-fluxes is introduced and we analyze the model at zero temperature and finite density both in the weak and strong coupling phases. We show that at zero temperature the model has different first order phase transitions as a function of the chemical potential both for the weak and strong coupling phases. The exploratory study demonstrates that alternative degrees of freedom may successfully be used for Monte Carlo simulations in several systems with gauge and matter fields.

Typos corrected and some statements refined. Final version to appear in Phys. Rev. D

References in corpus (13)

• Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
• Flux representation of an effective Polyakov loop model for QCD thermodynamics
• Method for simulating O(N) lattice models at finite density
• The QCD phase diagram according to the center group
• Efficient simulation of relativistic fermions via vertex models
• Cluster simulation of relativistic fermions in two space-time dimensions
• Worm algorithms for the 3-state Potts model with magnetic field and chemical potential
• Triviality of ${\varphi }_4^4$ theory: small volume expansion and new data
• Simulating the All-Order Hopping Expansion II: Wilson Fermions
• Fermion bag approach to the sign problem in strongly coupled lattice QED with Wilson fermions
• Fermion loop simulation of the lattice Gross-Neveu model
• Anomalous discrete chiral symmetry in the Gross-Neveu model and loop gas simulations
• Lattice theory for nonrelativistic fermions in one spatial dimension

Cited by in corpus (21)

• Approaches to the sign problem in lattice field theory
• Finite-Density Monte Carlo Calculations on Sign-Optimized Manifolds
• Solving the sign problems of the massless lattice Schwinger model with a dual formulation
• Surface worm algorithm for abelian Gauge-Higgs systems on the lattice
• Dual simulation of the 2d U(1) gauge Higgs model at topological angle $\theta =\pi$: Critical endpoint behavior
• Dual lattice simulation of the U(1) gauge-Higgs model at finite density - an exploratory proof-of-concept study
• Tensor renormalization group study of (3+1)-dimensional $Z_2$ gauge-Higgs model at finite density
• New developments for dual methods in lattice field theory at non-zero density
• Critical endpoint of (3+1)-dimensional finite density $Z_3$ gauge-Higgs model with tensor renormalization group
• Simulation strategies for the massless lattice Schwinger model in the dual formulation
• Phase diagram of the quantum O(2)-model in 2+1 dimensions
• Simulating the All-Order Strong Coupling Expansion V: Ising Gauge Theory
• 't Hooft surface in lattice gauge theory
• Monte Carlo simulation of abelian gauge-Higgs lattice models using dual representation
• Solving the sign problem of two flavor scalar electrodynamics at finite chemical potential
• Dual Methods for Lattice Field Theories at Finite Density
• Exploring the worldline formulation of the Potts model
• ${\mathbb{Z}}_3$ lattice gauge theory as a toy model for dense QCD
• Quantum circuit for ${\mathbb{Z}}_3$ lattice gauge theory at nonzero baryon density
• A Geometric Monte Carlo Algorithm for the Antiferromagnetic Ising model with "Topological" Term at $\theta =\pi$
• The sign problem and Abelian lattice duality