Continuum-extrapolated lattice QCD simulations with complex Langevin produce the equation of state at high baryon chemical potentials above the crossover temperature at the physical point.
Justification of the complex Langevin method with the gauge cooling procedure
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abstract
Recently there has been remarkable progress in the complex Langevin method, which aims at solving the complex action problem by complexifying the dynamical variables in the original path integral. In particular, a new technique called the gauge cooling was introduced and the full QCD simulation at finite density has been made possible in the high temperature (deconfined) phase or with heavy quarks. Here we provide a rigorous justification of the complex Langevin method including the gauge cooling procedure. We first show that the gauge cooling can be formulated as an extra term in the complex Langevin equation involving a gauge transformation parameter, which is chosen appropriately as a function of the configuration before cooling. The probability distribution of the complexified dynamical variables is modified by this extra term. However, this modification is shown not to affect the Fokker-Planck equation for the corresponding complex weight as far as observables are restricted to gauge invariant ones. Thus we demonstrate explicitly that the gauge cooling can be used as a viable technique to satisfy the convergence conditions for the complex Langevin method. We also discuss the "gauge cooling" in 0-dimensional systems such as vector models or matrix models.
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UNVERDICTED 4representative citing papers
Complex Langevin simulations of the deformed Lorentzian type IIB matrix model show emergence of smooth (3+1)-dimensional expanding spacetime with real space and time.
WV-HMC computes number and energy densities for the doped 2D Hubbard model on 6x6 and 8x8 lattices at U/t=8 and T/t≈0.156, showing effectiveness where standard DQMC fails.
A comparison of prominent correctness criteria for complex Langevin dynamics on four simple models shows differences in applicability, ease of use, and predictive power.
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Finite-density equation of state of hot QCD using the complex Langevin equation
Continuum-extrapolated lattice QCD simulations with complex Langevin produce the equation of state at high baryon chemical potentials above the crossover temperature at the physical point.
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The emergence of (3+1)-dimensional expanding spacetime from complex Langevin simulations of the Lorentzian type IIB matrix model with deformations
Complex Langevin simulations of the deformed Lorentzian type IIB matrix model show emergence of smooth (3+1)-dimensional expanding spacetime with real space and time.
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Applying the Worldvolume Hybrid Monte Carlo method to the Hubbard model away from half filling
WV-HMC computes number and energy densities for the doped 2D Hubbard model on 6x6 and 8x8 lattices at U/t=8 and T/t≈0.156, showing effectiveness where standard DQMC fails.
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Correctness criteria for complex Langevin
A comparison of prominent correctness criteria for complex Langevin dynamics on four simple models shows differences in applicability, ease of use, and predictive power.