Method for simulating O(N) lattice models at finite density

Abstract

We present a method for simulating relativistic and nonrelativistic scalar field theories at finite density, with matter transforming in the fundamental representation of the global symmetry group O(N). The method avoids the problem of complex probability weights which is present in conventional path integral Monte Carlo algorithms. To verify our approach, we simulate the free and interacting relativistic U(1)=O(2) theory in 2+1 dimensions. We compute the two-point correlation function and charge density as a function of chemical potential in the free theory. At weak phi^4 coupling and zero temperature we map the m^2-mu phase diagram and compare our numerical results with perturbative calculations. Finally, we compute properties of theT-mu phase diagram in the vicinity of the phase transition and at bare self-couplings large compared to the temperature and chemical potential.

27 pages, 14 figures

References in corpus (9)

• A new method to study lattice QCD at finite temperature and chemical potential
• Worm algorithms for classical statistical models
• Imaginary chemical potential and finite fermion density on the lattice
• Two-colour QCD at non-zero quark-number density
• A lattice theory for low energy fermions at finite chemical potential
• Numerical study of duality and universality in a frozen superconductor
• Magnetic permeability of near-critical 3d abelian Higgs model and duality
• Effective field theory of boson-fermion mixtures and bound fermion states on a vortex of boson superfluid
• Exact duality and dual Monte-Carlo simulation for the Bosonic Hubbard model

Cited by in corpus (45)

• High density QCD on a Lefschetz thimble?
• Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
• Monte Carlo simulations on the Lefschetz thimble: taming the sign problem
• Approaches to the sign problem in lattice field theory
• Adaptive stepsize and instabilities in complex Langevin dynamics
• The fermion bag approach to lattice field theories
• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Lattice study of the Silver Blaze phenomenon for a charged scalar phi-4 field
• Complex Langevin dynamics at finite chemical potential: mean field analysis in the relativistic Bose gas
• Finite size effects in the presence of a chemical potential: A study in the classical non-linear O(2) sigma-model
• The density of states approach to dense quantum systems
• Solving the sign problems of the massless lattice Schwinger model with a dual formulation
• Simulating the All-Order Strong Coupling Expansion I: Ising Model Demo
• Surface worm algorithm for abelian Gauge-Higgs systems on the lattice
• Dual lattice representations for O(N) and CP(N-1) models with a chemical potential
• 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
• Path integral contour deformations for noisy observables
• Anatomy of the sign-problem in heavy-dense QCD
• Solutions to sign problems in lattice Yukawa models
• Gauge and matter fields as surfaces and loops - an exploratory lattice study of the Z(3) Gauge-Higgs model
• Spectroscopy in finite density lattice field theory: An exploratory study in the relativistic Bose gas
• The sign problem and the Lefschetz thimble
• Phase Unwrapping and One-Dimensional Sign Problems
• Fermion bag approach to the sign problem in strongly coupled lattice QED with Wilson fermions
• Simulation strategies for the massless lattice Schwinger model in the dual formulation
• A study of symmetry breaking in a relativistic Bose gas using the contraction algorithm
• Free energy of the self-interacting relativistic lattice Bose gas at finite density
• Exponential reduction of the sign problem at finite density in the 2+1D XY model via contour deformations
• Lattice theory for nonrelativistic fermions in one spatial dimension
• Extended Mean Field study of complex ${\varphi }^4$-theory at finite density and temperature
• Sampling of General Correlators in Worm Algorithm-based Simulations
• Simulating the All-Order Strong Coupling Expansion V: Ising Gauge Theory
• Complex Langevin approach to interacting Bose gases
• Comparison of algorithms for solving the sign problem in the O(3) model in 1+1 dimensions at finite chemical potential
• Canonical simulations with worldlines: an exploratory study in ${\varphi }_2^4$ lattice field theory
• Finite density condensation and scattering data - a study in ${\varphi }^4$ lattice field theory
• Sign-problem-free effective models of triangular lattice quantum antiferromagnets
• Dual Methods for Lattice Field Theories at Finite Density
• Approximate dual representation for Yang-Mills SU(2) gauge theory
• A Geometric Monte Carlo Algorithm for the Antiferromagnetic Ising model with "Topological" Term at $\theta =\pi$
• The density of states approach to the sign problem
• Infinite-range correlations in 1D systems with continuous symmetry
• FRG analysis for a relativistic BEC in arbitrary spatial dimensions
• Complex path simulations of geometrically frustrated ladders