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Rotating systems in thermal equilibrium are ubiquitous in our world. In thecontext of high energy physics, rotations would affect the phase structure ofQCD. However, the standard Monte-Carlo methods in rotating systems areproblematic because the chemical potentials for the angular momenta (angularvelocities) cause sign problems even for bosonic variables. In this article, wedemonstrate that the complex Langevin method (CLM) may overcome this issue. Weapply the CLM to the Yang-Mills (YM) type one-dimensional matrix model (matrixquantum mechanics) that is a large-$N$ reduction (or dimensional reduction) ofthe $(D+1)$-dimensional U$(N)$ pure YM theory (bosonic BFSS model). This modelshows a large-$N$ phase transition at finite temperature, which is analogous tothe confinement/deconfinement transition of the original YM theory, and our CLMpredicts that the transition temperature decreases as the angular momentumchemical potential increases. In order to verify our results, we computeseveral quantities via the minimum sensitivity method and find goodquantitative agreements. Hence, the CLM properly works in this rotating system.We also argue that our results are qualitatively consistent with a holographyand the recent studies of the imaginary angular velocity in QCD. As abyproduct, we develop an analytic approximation to treat the so-called ``smallblack hole" phase in the matrix model.

Complex Langevin Method on Rotating Matrix Quantum Mechanics at Thermal Equilibrium