Free energy of the self-interacting relativistic lattice Bose gas at finite density

Abstract

The density of state approach has recently been proposed as a potential route to circumvent the sign problem in systems at finite density. In this study, using the Linear Logarithmic Relaxation (LLR) algorithm, we extract the generalised density of states, which is defined in terms of the imaginary part of the action, for the self-interacting relativistic lattice Bose gas at finite density. After discussing the implementation and testing the reliability of our approach, we focus on the determination of the free energy difference between the full system and its phase-quenched counterpart. Using a set of lattices ranging from $4^4$ to $16^4$ , we show that in the low density phase, this overlap free energy can be reliably extrapolated to the thermodynamic limit. The numerical precision we obtain with the LLR method allows us to determine with sufficient accuracy the expectation value of the phase factor, which is used in the calculation of the overlap free energy, down to values of $\mathcal{O}(10^{-480})$. When phase factor measurements are extended to the dense phase, a change of behaviour of the overlap free energy is clearly visible as the chemical potential crosses a critical value. Using fits inspired by the approximate validity of mean-field theory, which is confirmed by our simulations, we extract the critical chemical potential as the non-analyticity point in the overlap free energy, obtaining a value that is in agreement with other determinations. Implications of our findings and potential improvements of our methodology are also discussed.

arXiv comment21 pages, 15 figures

References in corpus (18)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• 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
• The density of states method at non-zero chemical potential
• A new approach to the complex-action problem and its application to a nonperturbative study of superstring theory
• The density of states in gauge theories
• 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
• The density of states approach to dense quantum systems
• Method for simulating O(N) lattice models at finite density
• Anatomy of the sign-problem in heavy-dense QCD
• Controlling the Sign Problem in Finite Density Quantum Field Theory
• Density of States FFA analysis of SU(3) lattice gauge theory at a finite density of color sources
• Developing and testing the density of states FFA method in the SU(3) spin model
• A novel density of state method for complex action systems
• Ergodicity of the LLR method for the Density of States
• Anatomy of a strong residual sign problem on the thimbles

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• Reduced critical slowing down for statistical physics simulations
• New canonical and grand canonical DoS techniques for finite density lattice QCD
• Real Time Simulations of Quantum Spin Chains: Density-of-States and Reweighting approaches
• Efficient computations of continuous action densities of states for lattice models