Complex Langevin calculations in finite density QCD at large $\mu /T$ with the deformation technique

Abstract

It is well known that investigating QCD at finite density by standard Monte Carlo methods is extremely difficult due to the sign problem. Some years ago, the complex Langevin method with gauge cooling was shown to work at high temperature, i.e., in the deconfined phase. The same method was also applied to QCD in the so-called heavy dense limit in the whole temperature region. In this paper we attempt to apply this method to the large $\mu /T$ regime with moderate quark mass using four-flavor staggered fermions on a $4^3\times 8$ lattice. While a straightforward application faces with the singular-drift problem, which spoils the validity of the method, we overcome this problem by the deformation technique proposed earlier. Explicit results for the quark number density and the chiral condensate obtained in this way for $3.2\le \mu /T\le 5.6$ are compared with the results for the phase-quenched model obtained by the standard rational hybrid Monte Carlo calculation. This reveals a clear difference, which is qualitatively consistent with the Silver Blaze phenomenon.

arXiv comment14 pages, 5 figures; (v2) a typo for the lattice size in the abstract was corrected; (v3) detailed discussions on the interpretation of the results added; version published in PRD

References in corpus (30)

• The Complex Langevin method: When can it be trusted?
• Complex Langevin: Etiology and Diagnostics of its Main Problem
• Simulating full QCD at nonzero density using the complex Langevin equation
• Gauge cooling in complex Langevin for QCD with heavy quarks
• Controlling complex Langevin dynamics at finite density
• The argument for justification of the complex Langevin method and the condition for correct convergence
• New insights into the problem with a singular drift term in the complex Langevin method
• Complex Langevin Dynamics for chiral Random Matrix Theory
• Complex Langevin dynamics and zeroes of the fermion determinant
• Complex Langevin dynamics for dynamical QCD at nonzero chemical potential: a comparison with multi-parameter reweighting
• The QCD phase diagram in the limit of heavy quarks using complex Langevin dynamics
• Justification of the complex Langevin method with the gauge cooling procedure
• Does the complex Langevin method give unbiased results?
• Complex Langevin Simulation of a Random Matrix Model at Nonzero Chemical Potential
• Complex saddle points and the sign problem in complex Langevin simulation
• Complex Langevin analysis of the spontaneous symmetry breaking in dimensionally reduced super Yang-Mills models
• Gauge cooling for the singular-drift problem in the complex Langevin method --a test in Random Matrix Theory for finite density QCD
• An improvement in complex Langevin dynamics from a view point of Lefschetz thimbles
• Combining the complex Langevin method and the generalized Lefschetz-thimble method
• The complex Langevin analysis of spontaneous symmetry breaking induced by complex fermion determinant
• Testing the criterion for correct convergence in the complex Langevin method
• Reweighting complex Langevin trajectories
• Complex Langevin method applied to the 2D $SU(2)$ Yang-Mills theory
• Modifying partition functions: a way to solve the sign problem
• Complex Langevin Dynamics in Large $N$ Unitary Matrix Models
• Analytical studies of the complex Langevin equation with a Gaussian Ansatz and multiple solutions in the unstable region
• Complex Langevin Simulations of QCD at Finite Density -- Progress Report
• Test for a universal behavior of Dirac eigenvalues in the complex Langevin method
• Complex Langevin simulation of QCD at finite density and low temperature using the deformation technique
• Performance of Complex Langevin Simulation in 0+1 dimensional massive Thirring model at finite density

Cited by in corpus (21)

• Review on novel methods for lattice gauge theories
• Finite-density lattice QCD and sign problem: current status and open problems
• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Calculating the EoS of the dense quark-gluon plasma using the Complex Langevin equation
• Applying Complex Langevin Simulations to Lattice QCD at Finite Density
• Complex Langevin simulations and the QCD phase diagram: Recent developments
• Complex Langevin calculations in QCD at finite density
• Gauge invariant input to neural network for path optimization method
• Improving efficiency of the path optimization method for a gauge theory
• Density-Induced Hadron-Quark Crossover via the Formation of Cooper Triples
• Color superconductivity on the lattice -- analytic predictions from QCD in a small box
• Regularization of Complex Langevin Method
• Complex Langevin analysis of 2D U(1) gauge theory on a torus with a $\theta$ term
• Exploring the phase diagram of finite density QCD at low temperature by the complex Langevin method
• Exploring the QCD phase diagram at finite density by the complex Langevin method on a $16^3\times 32$ lattice
• On the validity of the complex Langevin method near the deconfining phase transition in QCD at finite density
• A projected complex Langevin sampling method for bosons in the canonical and microcanonical ensembles
• Classical Statistical simulation of Quantum Field Theory
• Dynamical Compactification of Extra Dimensions in the Euclidean IKKT Matrix Model via Spontaneous Symmetry Breaking
• Can the complex Langevin method see the deconfinement phase transition in QCD at finite density?
• Complex Langevin for Lattice QCD