Finite size effects in the presence of a chemical potential: A study in the classical non-linear O(2) sigma-model

Abstract

In the presence of a chemical potential, the physics of level crossings leads to singularities at zero temperature, even when the spatial volume is finite. These singularities are smoothed out at a finite temperature but leave behind non-trivial finite size effects which must be understood in order to extract thermodynamic quantities using Monte Carlo methods, particularly close to critical points. We illustrate some of these issues using the classical non-linear O(2) sigma model with a coupling $\beta$ and chemical potential $\mu$ on a 2+1 dimensional Euclidean lattice. In the conventional formulation this model suffers from a sign problem at non-zero chemical potential and hence cannot be studied with the Wolff cluster algorithm. However, when formulated in terms of world-line of particles, the sign problem is absent and the model can be studied efficiently with the "worm algorithm". Using this method we study the finite size effects that arise due to the chemical potential and develop an effective quantum mechanical approach to capture the effects. As a side result we obtain energy levels of up to four particles as a function of the box size and uncover a part of the phase diagram in the $(\beta ,\mu )$ plane.

Published Version

References in corpus (16)

• Color superconductivity in dense quark matter
• New Critical Point Induced by the Axial Anomaly in Dense QCD
• Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
• Adaptive stepsize and instabilities in complex Langevin dynamics
• QCD Thermodynamics from the Lattice
• Nuclear Physics from lattice QCD at strong coupling
• n-Boson Energies at Finite Volume and Three-Boson Interactions
• Method for simulating O(N) lattice models at finite density
• Simulating the All-Order Strong Coupling Expansion I: Ising Model Demo
• Simulating the All-Order Strong Coupling Expansion III: O(N) sigma/loop models
• Efficient simulation of relativistic fermions via vertex models
• Phase-diagram of two-color lattice QCD in the chiral limit
• Effects of the anomaly on the two-flavor QCD chiral phase transition
• Simulating the All-Order Hopping Expansion II: Wilson Fermions
• Effective Potential for Complex Langevin Equations
• Geometric Algorithm for Abelian-Gauge Models

Cited by in corpus (50)

• Approaches to the sign problem in lattice field theory
• Controlling complex Langevin dynamics at finite density
• Exact blocking formulas for spin and gauge models
• Conformal dimensions via large charge expansion
• Complex Langevin dynamics in the SU(3) spin model at nonzero chemical potential revisited
• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Tensor lattice field theory with applications to the renormalization group and quantum computing
• Stability of complex Langevin dynamics in effective models
• Selected Topics in the Large Quantum Number Expansion
• Lattice study of the Silver Blaze phenomenon for a charged scalar phi-4 field
• Controlling sign problems in spin models using tensor renormalization
• Does the complex Langevin method give unbiased results?
• Controlling Complex Langevin simulations of lattice models by boundary term analysis
• O(3) nonlinear sigma model in 1+1 dimensions with matrix product states
• Dual lattice representations for O(N) and CP(N-1) models with a chemical potential
• Progress towards quantum simulating the classical O(2) model
• Dual lattice simulation of the U(1) gauge-Higgs model at finite density - an exploratory proof-of-concept study
• Complex Langevin simulations and the QCD phase diagram: Recent developments
• The fine structure of the entanglement entropy in the classical XY model
• Thirring model at finite density in 0+1 dimensions with stochastic quantization: Crosscheck with an exact solution
• Solutions to sign problems in lattice Yukawa models
• Tensor renormalization group study of the 3d $O(2)$ model
• Spectroscopy in finite density lattice field theory: An exploratory study in the relativistic Bose gas
• The two-dimensional O(3) model at nonzero density: from dual lattice simulations to repulsive bosons
• Thirring model at finite density in 2+1 dimensions with stochastic quantization
• Estimating the central charge from the Rényi entanglement entropy
• Examples of symmetry-preserving truncations in tensor field theory
• Discrete aspects of continuous symmetries in the tensorial formulation of Abelian gauge theories
• Grand canonical ensemble, multi-particle wave functions, scattering data, and lattice field theories
• Benchmark results in the 2D lattice Thirring model with a chemical potential
• Quantum Algorithms for Open Lattice Field Theory
• Phase diagram of the quantum O(2)-model in 2+1 dimensions
• Complex Langevin Dynamics in Large $N$ Unitary Matrix Models
• Numerical tests of the large charge expansion
• Exponential reduction of the sign problem at finite density in the 2+1D XY model via contour deformations
• Gibbs sampling of complex valued distributions
• Few-body physics on a space-time lattice in the worldline approach
• Sampling of General Correlators in Worm Algorithm-based Simulations
• Comparison of algorithms for solving the sign problem in the O(3) model in 1+1 dimensions at finite chemical potential
• Asymptotic Freedom at the Berezinskii-Kosterlitz-Thouless Transition without Fine-Tuning Using a Qubit Regularization
• Sampling versus Blocking
• Regularization of Complex Langevin Method
• Crystalline phases at finite winding densities in a quantum link ladder
• The density of states approach for the simulation of finite density quantum field theories
• Comparing Tensor Renormalization Group and Monte Carlo calculations for spin and gauge models
• Remarks on the construction of worm algorithms for lattice field theories in worldline representation
• Tensor RG calculations and quantum simulations near criticality
• Approaching conformality with the Tensor Renormalization Group method
• The XY model at finite chemical potential using complex Langevin dynamics
• Tensor-network study of the 3d $O(2)$ model at non-zero chemical potential and temperature