Complex Langevin simulation of a random matrix model at nonzero chemical potential

Bloch, Jacques; Glesaaen, Jonas; Verbaarschot, J. J. M.; Zafeiropoulos, Savvas

doi:10.1007/jhep03(2018)015

Cited by 42 publications

(31 citation statements)

References 51 publications

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“…One alternative in this scenario is the complex Langevin technique, which has been used to study theories with sign problems such as those with repulsive interactions [24] as well as polarized [25,26] and massimbalanced fermions [27] (see Ref. [28] for a review), finite density QCD with staggered quarks [29][30][31][32], random matrix models [33,34], rotating bosons [35,36], superstringinspired matrix models [37], among others.…”

Section: Many-body Methodsmentioning

confidence: 99%

Thermodynamics of spin-orbit-coupled bosons in two dimensions from the complex Langevin method

Attanasio

Drut

2020

Phys. Rev. A

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We investigate the thermal properties of interacting spin-orbit coupled bosons with contact interactions in two spatial dimensions. To that end, we implement the complex Langevin method, motivated by the appearance of a sign problem, on a square lattice with periodic boundary conditions. We calculate the density equation of state non-perturbatively in a range of spin-orbit couplings and chemical potentials. Our results show that mean-field solutions tend to underestimate the average density, especially for stronger values of the spin-orbit coupling. Additionally, the finite nature of the simulation volume induces the formation of pseudo-condensates. These have been observed to be destroyed by the spin-orbit interactions.

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Section: Many-body Methodsmentioning

confidence: 99%

Thermodynamics of spin-orbit-coupled bosons in two dimensions from the complex Langevin method

Attanasio

Drut

2020

Phys. Rev. A

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“…In addition to usage of CL as remedy for the sign problem related to non-zero chemical potential (see, e.g., [76][77][78][79] for early attempts), the method was tested for real-time simulations, see, e.g., [80][81][82]. The problems, along with general features of CL simulations, have been investigated, e.g., in the framework of random matrix theory [69,[83][84][85][86][87] 4 . Significant progress has been achieved employing the method of gauge cooling [106], see, e.g., Refs.…”

Section: B Overcoming the Sign Problem In Lqcdmentioning

confidence: 99%

Review on novel methods for lattice gauge theories

2020

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Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying quantum field theories, and has led to impressive achievements. In particular, it significantly deepened our understanding of quantum chromodynamics. Yet, some very relevant problems remain inherently challenging, such as real time evolution, or the presence of a chemical potential, cases in which Monte Carlo simulations are hindered by a sign problem.In the last few years, a number of possible alternatives have been put forward, based on quantum information ideas, which could potentially open the access to areas of research that have so far eluded more standard methods. They include tensor network calculations, quantum simulations with different physical platforms and quantum computations, and constitute nowadays a vibrant research area. Experts from different fields, including experimental and theoretical high energy physics, condensed matter, and quantum information, are turning their attention to these interdisciplinary possibilities, and driving the progress of the field. The aim of this article is to review the status and perspectives of these new avenues for the exploration of lattice gauge theories.

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“…This result in different Langevin forces [22]. To analyze the dynamics of the shifted representation we analyze the matrix elements of A and A during a typical CL simulation; these are shown in figure 7.…”

Section: Shifted Representationmentioning

confidence: 99%

Progress on Complex Langevin simulations of a finite density matrix model for QCD

et al. 2018

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Abstract. We study the Stephanov model, which is an RMT model for QCD at finite density, using the Complex Langevin algorithm. Naive implementation of the algorithm shows convergence towards the phase quenched or quenched theory rather than to intended theory with dynamical quarks. A detailed analysis of this issue and a potential resolution of the failure of this algorithm are discussed. We study the effect of gauge cooling on the Dirac eigenvalue distribution and time evolution of the norm for various cooling norms, which were specifically designed to remove the pathologies of the complex Langevin evolution. The cooling is further supplemented with a shifted representation for the random matrices. Unfortunately, none of these modifications generate a substantial improvement on the complex Langevin evolution and the final results still do not agree with the analytical predictions.

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Complex Langevin simulation of a random matrix model at nonzero chemical potential

Cited by 42 publications

References 51 publications

Thermodynamics of spin-orbit-coupled bosons in two dimensions from the complex Langevin method

Thermodynamics of spin-orbit-coupled bosons in two dimensions from the complex Langevin method

Review on novel methods for lattice gauge theories

Progress on Complex Langevin simulations of a finite density matrix model for QCD

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