Complex Langevin Method on Rotating Matrix Quantum Mechanics at Thermal Equilibrium

Hiroki Yoshida; Takehiro Azuma; Takeshi Morita

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Complex Langevin Method on Rotating Matrix Quantum Mechanics at Thermal Equilibrium

Takehiro Azuma, Takeshi Morita, Hiroki Yoshida

High Energy Physics - Theory · Submitted 28 Feb 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Hence, the CLM properly works in this rotating system.

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arXiv ID2302.14259 (version 4)

Pith IDQEONDK7I, Pith's permanent record of this paper and its review

CitationHiroki Yoshida, Takehiro Azuma, Takeshi Morita. "Complex Langevin Method on Rotating Matrix Quantum Mechanics at Thermal Equilibrium." arXiv:2302.14259 (2023). https://pith.science/paper/QEONDK7I

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Rotating systems in thermal equilibrium are ubiquitous in our world. In the context of high energy physics, rotations would affect the phase structure of QCD. However, the standard Monte-Carlo methods in rotating systems are problematic because the chemical potentials for the angular momenta (angular velocities) cause sign problems even for bosonic variables. In this article, we demonstrate that the complex Langevin method (CLM) may overcome this issue. We apply the CLM to the Yang-Mills (YM) type one-dimensional matrix model (matrix quantum mechanics) that is a large-$N$ reduction (or dimensional reduction) of the $(D+1)$-dimensional U$(N)$ pure YM theory (bosonic BFSS model). This model shows a large-$N$ phase transition at finite temperature, which is analogous to the confinement/deconfinement transition of the original YM theory, and our CLM predicts that the transition temperature decreases as the angular momentum chemical potential increases. In order to verify our results, we compute several quantities via the minimum sensitivity method and find good quantitative agreements. Hence, the CLM properly works in this rotating system. We also argue that our results are qualitatively consistent with a holography and the recent studies of the imaginary angular velocity in QCD. As a byproduct, we develop an analytic approximation to treat the so-called ``small black hole" phase in the matrix model.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Rotating systems in thermal equilibrium are ubiquitous in our world.	background 1.00	0.03	0.01	asserted 1.00
s1	In the context of high energy physics, rotations would affect the phase structure of QCD.	background 1.00	0.04	0.02	hedged possibility 0.50
s2	However, the standard Monte-Carlo methods in rotating systems are problematic because the chemical potentials for the angular momenta (angular velocities) cause sign problems even for bosonic variables.	background 0.80	0.07	0.02	asserted 1.00
s3	In this article, we demonstrate that the complex Langevin method (CLM) may overcome this issue.	contribution 0.98	0.63	0.41	hedged possibility 0.87
s4	We apply the CLM to the Yang-Mills (YM) type one-dimensional matrix model (matrix quantum mechanics) that is a large-$N$ reduction (or dimensional reduction) of the $(D+1)$-dimensional U$(N)$ pure YM theory (bosonic BFSS model).	method 0.83	0.88	0.04	asserted 0.98
s5	This model shows a large-$N$ phase transition at finite temperature, which is analogous to the confinement/deconfinement transition of the original YM theory, and our CLM predicts that the transition temperature decreases as the angular momentum chemical potential increases.	result 0.98	0.93	0.35	asserted 0.94
s6	In order to verify our results, we compute several quantities via the minimum sensitivity method and find good quantitative agreements.	method 0.70	0.96	0.06	asserted 1.00
s7	Hence, the CLM properly works in this rotating system.	interpretation 0.83	0.80	0.61	asserted 1.00
s8	We also argue that our results are qualitatively consistent with a holography and the recent studies of the imaginary angular velocity in QCD.	interpretation 1.00	0.53	0.06	hedged possibility 0.99
s9	As a byproduct, we develop an analytic approximation to treat the so-called ``small black hole" phase in the matrix model.	contribution 0.89	0.96	0.03	asserted 1.00

What kind of paper the classifier reports this is: simulation study 0.93 · evidence from simulation or computation 1.00.

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arXiv listing abstract v4

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Original abstract

Rotating systems in thermal equilibrium are ubiquitous in our world. In the context of high energy physics, rotations would affect the phase structure of QCD. However, the standard Monte-Carlo methods in rotating systems are problematic because the chemical potentials for the angular momenta (angular velocities) cause sign problems even for bosonic variables. In this article, we demonstrate that the complex Langevin method (CLM) may overcome this issue. We apply the CLM to the Yang-Mills (YM) type one-dimensional matrix model (matrix quantum mechanics) that is a large-$N$ reduction (or dimensional reduction) of the $(D+1)$-dimensional U$(N)$ pure YM theory (bosonic BFSS model). This model shows a large-$N$ phase transition at finite temperature, which is analogous to the confinement/deconfinement transition of the original YM theory, and our CLM predicts that the transition temperature decreases as the angular momentum chemical potential increases. In order to verify our results, we compute several quantities via the minimum sensitivity method and find good quantitative agreements. Hence, the CLM properly works in this rotating system. We also argue that our results are qualitatively consistent with a holography and the recent studies of the imaginary angular velocity in QCD. As a byproduct, we develop an analytic approximation to treat the so-called ``small black hole" phase in the matrix model.

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Papers citing it

Cites it as background 1 paper

Various effective models and perturbative approaches predict that rotation promotes chiral symmetry restoration [ref] and deconfinement [ref] .

Deconfinement transition in the revolving bag model · Introduction · 0.84

What it cites · 109 sentences without a confident label

Builds on 1 paper

We can formally extend this correspondence to a general $D$ by taking $d=D-1$ [ref] .

Hagedorn Instability in Dimensionally Reduced Large-N Gauge Theories as Gregory-Laflamme and Rayleigh-Plateau Instabilities · Review of the previous results on the non-rotating model · 0.98

Uses the method or tool of 11 papers

(The advantage of this approximation is that the analysis in Ref. [ref] is available.)

Fine structure of Hagedorn transitions · The derivation of the effective action [ref] · 0.82
For this purpose, we introduce trial masses $m_Z$ and $m_X$ for $Z^I$ and $X^I$, respectively, and deform the action [ref] as [ref] [equation] Here $κ$ is a formal expansion parameter.

Critical Dimension and Negative Specific Heat in One-dimensional Large-N Reduced Models · Derivation of Free energy · 0.87
* By using the minimum sensitivity, we study the properties of the model with an imaginary angular momentum chemical potential, which has been employed to evade the sign problem in the MC computations [ref] .

Influence of relativistic rotation on the confinement/deconfinement transition in gluodynamics · Summary of this work · 0.87

Compares with 11 papers

In the uniform phase, $|u_n|$ has a finite-$N$ effect of order O$( 1/N )$ [ref] , and we compare the CLM results of $|u_n|$ with the minimum sensitivity result with the $1/N$ correction [ref], which also agree with each other.

Hagedorn Instability in Dimensionally Reduced Large-N Gauge Theories as Gregory-Laflamme and Rayleigh-Plateau Instabilities · Polyakov loop $|u_1|$ and $|u_2|$ · 0.80
We also found that the increasing transition temperature consistent with Refs. [ref] .

Inhomogeneity of rotating gluon plasma and Tolman-Ehrenfest law in imaginary time: lattice results for fast imaginary rotation · Discussions · 0.83
We also found that the increasing transition temperature consistent with Refs. [ref] .

Perturbative confinement in thermal Yang-Mills theories induced by imaginary angular velocity · Discussions · 0.83

Cites as background 16 papers

Recent studies [ref] have clarified the conditions that the CLM results converge to the correct result equivalent to the path integral.

Gauge cooling for the singular-drift problem in the complex Langevin method --a test in Random Matrix Theory for finite density QCD · Introduction and Summary · 0.81
Recent studies [ref] have clarified the conditions that the CLM results converge to the correct result equivalent to the path integral.

Complex Langevin: Etiology and Diagnostics of its Main Problem · Introduction and Summary · 0.81
Recent studies [ref] have clarified the conditions that the CLM results converge to the correct result equivalent to the path integral.

Gauge cooling in complex Langevin for QCD with heavy quarks · Introduction and Summary · 0.81

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