PT Symmetry in Classical and Quantum Statistical Mechanics

Abstract

PT-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside of the conventional equilibrium statistical mechanics of Hermitian systems. PT-symmetric models form a natural class where the partition function is necessarily real, but not necessarily positive. The correlation functions of these models display a much richer set of behaviors than Hermitian systems, displaying sinusoidally-modulated exponential decay, as in a dense fluid, or even sinusoidal modulation without decay. Classical spin models with PT symmetry include Z(N) models with a complex magnetic field, the chiral Potts model and the anisotropic next-nearest-neighbor Ising (ANNNI) model. Quantum many-body problems with a non-zero chemical potential have a natural PT-symmetric representation related to the sign problem. Two-dimensional QCD with heavy quarks at non-zero chemical potential can be solved by diagonalizing an appropriate PT-symmetric Hamiltonian.

36 pages, 6 figures

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Cited by in corpus (18)

• Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral
• Complex Saddle Points and Disorder Lines in QCD at finite temperature and density
• Complex saddle points in QCD at finite temperature and density
• Universality of Pattern Formation
• PT symmetric fermionic field theories with axions: Renormalization and dynamical mass generation
• Non-Hermitian effects of the intrinsic signs in topologically ordered wavefunctions
• Complex spectrum of finite-density lattice QCD with static quarks at strong coupling
• Nontrivial worldline winding in non-Hermitian quantum systems
• Physics of PT-Symmetric Quantum Systems at Finite Temperature
• Theory of charge-6e condensed phase in Kagome lattice superconductors
• Spatially oscillating correlation functions in $\left(2+1\right)$-dimensional four-fermion models: The mixing of scalar and vector modes at finite density
• Liquid-Gas Phase Transitions and $\mathcal{C}\mathcal{K}$ Symmetry in Quantum Field Theories
• Dilepton production from moaton quasiparticles
• PT-symmetry in quasi-integrable models
• The sign problem and Abelian lattice duality
• Lattice and PT symmetries in tensor-network renormalization group: Case study of a hard-square lattice gas model
• Simulation of Scalar Field Theories with Complex Actions
• Complex saddle points in finite-density QCD