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PT symmetry in classical and quantum statistical mechanics
Peter N Meisinger1, Michael C Ogilvie
1Department of Physics, Washington University, St Louis, MO 63130, USA.
Summary
Parity-time (PT)-symmetric models in statistical mechanics offer new insights beyond Hermitian systems. These models exhibit unique correlation functions and can solve complex quantum problems, including quantum chromodynamics.
Area of Science:
- Statistical Mechanics
- Quantum Mechanics
- Condensed Matter Physics
Background:
- Conventional equilibrium statistical mechanics typically deals with Hermitian systems.
- Parity-time (PT)-symmetric models involve complex or negative weights, extending beyond Hermitian frameworks.
- These PT-symmetric models are crucial for understanding phenomena outside standard equilibrium statistical mechanics.
Purpose of the Study:
- To explore the properties and applications of PT-symmetric Hamiltonians and transfer matrices in statistical mechanics.
- To demonstrate how PT-symmetry provides a framework for addressing systems with complex weights and the sign problem.
- To highlight the potential of PT-symmetric models in solving challenging quantum many-body problems.
Main Methods:
- Analysis of PT-symmetric Hamiltonians and transfer matrices in classical and quantum models.
- Investigation of partition functions and correlation functions in PT-symmetric systems.
- Application of PT-symmetric Hamiltonians to solve quantum many-body problems, such as two-dimensional quantum chromodynamics.
Main Results:
- PT-symmetric models yield real partition functions, though not necessarily positive.
- Correlation functions exhibit rich behaviors like sinusoidally modulated exponential decay or pure sinusoidal modulation.
- PT-symmetry offers a natural representation for quantum many-body problems with non-zero chemical potential, circumventing the sign problem.
Conclusions:
- PT-symmetric models represent a significant extension of statistical mechanics, encompassing systems with complex weights.
- These models reveal novel correlation function behaviors not observed in Hermitian systems.
- PT-symmetric Hamiltonians provide a viable approach for solving previously intractable quantum problems, including those in quantum chromodynamics.
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