Phase structure of matrix quantum mechanics at finite temperature

Abstract

We study matrix quantum mechanics at finite temperature by Monte Carlo simulation. The model is obtained by dimensionally reducing 10d U(N) pure Yang-Mills theory to 1d. Following Aharony et al., one can view the same model as describing the high temperature regime of (1+1)d U(N) super Yang-Mills theory on a circle. In this interpretation an analog of the deconfinement transition was conjectured to be a continuation of the black-hole/black-string transition in the dual gravity theory. Our detailed analysis in the critical regime up to N=32 suggests the existence of the non-uniform phase, in which the eigenvalue distribution of the holonomy matrix is non-uniform but gapless. The transition to the gapped phase is of second order. The internal energy is constant (giving the ground state energy) in the uniform phase, and rises quadratically in the non-uniform phase, which implies that the transition between these two phases is of third order.

17 pages, 9 figures, (v2) refined arguments in section 3 ; reference added

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Cited by in corpus (51)

• Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature
• Thermal phases of D1-branes on a circle from lattice super Yang-Mills
• The BFSS model on the lattice
• Phases of one dimensional large N gauge theory in a 1/D expansion
• Direct test of the gauge-gravity correspondence for Matrix theory correlation functions
• Lattice study of two-dimensional N=(2,2) super Yang-Mills at large-N
• Testing holography using lattice super-Yang--Mills on a 2-torus
• Emergent Cosmology from Matrix Theory
• A proposal of a fine tuning free formulation of 4d N=4 super Yang-Mills
• High temperature expansion in supersymmetric matrix quantum mechanics
• Comments on thermodynamics of supersymmetric matrix models
• Partial Deconfinement
• On the shape of a D-brane bound state and its topology change
• Hagedorn Instability in Dimensionally Reduced Large-N Gauge Theories as Gregory-Laflamme and Rayleigh-Plateau Instabilities
• Gauged And Ungauged: A Nonperturbative Test
• Gauge Invariant Target Space Entanglement in D-Brane Holography
• Quantum chaos, thermalization and entanglement generation in real-time simulations of the BFSS matrix model
• Numerical tests of the gauge/gravity duality conjecture for D0-branes at finite temperature and finite N
• Confinement/deconfinement transition in the D0-brane matrix model -- A signature of M-theory?
• Lattice Simulations of 10d Yang-Mills toroidally compactified to 1d, 2d and 4d
• Phases of a two dimensional large N gauge theory on a torus
• Thermal phase transition in Yang-Mills matrix model
• Monte Carlo Studies of the GWW Phase Transition in Large-N Gauge Theories
• Dynamical tachyons on fuzzy spheres
• Quantum chaos in supersymmetric quantum mechanics: an exact diagonalization study
• Partial Deconfinement at Strong Coupling on the Lattice
• Thermodynamics of black M-branes from SCFTs
• Gregory-Laflamme encounters Superradiance
• Nuclear states and spectra in holographic QCD
• Critical Dimension and Negative Specific Heat in One-dimensional Large-N Reduced Models
• Testing the holographic principle using lattice simulations
• Real-time dynamics of matrix quantum mechanics beyond the classical approximation
• Loop formulation of supersymmetric Yang-Mills quantum mechanics
• Black Hole Formation at the Correspondence Point
• Nonperturbative studies of supersymmetric matrix quantum mechanics with 4 and 8 supercharges at finite temperature
• The Flavoured BFSS Model at High Temperature
• Classical and quantum butterfly effect in nonlinear vector mechanics
• New States of Gauge Theories on a Circle
• Thermodynamics of Large N Gauge Theories with Chemical Potentials in a 1/D Expansion
• The Confining Transition in the Bosonic BMN Matrix Model
• Chaos in $SU(2)$ Yang-Mills Chern-Simons Matrix Model
• Real Time Quantum Gravity Dynamics from Classical Statistical Yang-Mills Simulations
• Chaotic Dynamics of the Mass Deformed ABJM Model
• Chaos from Massive Deformations of Yang-Mills Matrix Models
• Complex Langevin Method on Rotating Matrix Quantum Mechanics at Thermal Equilibrium
• Two approaches to quantum gravity and M-(atrix) theory at large number of dimensions
• A Scaling Relation, $Z_m$-type Deconfinement Phases and Imaginary Chemical Potentials in Finite Temperature Large-$N$ Gauge Theories
• D-dependence of gap between critical temperatures in one-dimensional gauge theories
• Phase Transitions of a (Super) Quantum Mechanical Matrix Model with a Chemical Potential
• High-Precision Bootstrap of Multimatrix Quantum Mechanics
• Non-perturbative phase structure of the bosonic BMN matrix model