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PT-symmetric, non-Hermitian quantum many-body physics-a methodological perspective.
V Meden1, L Grunwald1,2, D M Kennes1,2
1Institut fĂĽr Theorie der Statistischen Physik, RWTH Aachen University, 52056 Aachen, Germany.
Reports on Progress in Physics. Physical Society (Great Britain)
|October 23, 2023
Summary
This review advocates for the Hermitian approach to parity-time (PT)-symmetric, non-Hermitian quantum many-body systems. While PT-symmetric methods offer mathematical elegance, the Hermitian approach yields physically sensible results and aligns with experimental data.
Area of Science:
- Quantum Many-Body Physics
- Non-Hermitian Quantum Mechanics
- Condensed Matter Physics
Background:
- Parity-time (PT)-symmetric, non-Hermitian quantum systems exhibit unique properties distinct from generic open systems.
- Traditional studies of open quantum systems rely on Hermiticity, while mathematical physics introduced PT-symmetric and biorthogonal formalisms.
- Discrepancies exist regarding observables, expectation values, and statistical ensembles between Hermitian and PT-symmetric approaches.
Purpose of the Study:
- To review and reconcile methodologies for theoretically treating PT-symmetric, non-Hermitian quantum many-body systems.
- To advocate for the Hermitian perspective, particularly the ancilla approach, for analyzing these systems.
- To highlight the physical interpretability and experimental relevance of the Hermitian methodology.
Main Methods:
- Comprehensive review of existing theoretical approaches, including pseudo-Hermiticity.
- Detailed examination of the ancilla approach to embed non-Hermitian systems into larger Hermitian ones without approximations.
- Analysis of model Hamiltonians using both Hermitian and PT-symmetric/biorthogonal frameworks for comparison.
Main Results:
- The Hermitian approach, despite potential clumsiness, consistently yields physically sensible results.
- Hermitian methods show agreement with available experimental data for PT-symmetric systems.
- PT-symmetric and biorthogonal approaches, while mathematically elegant, can lead to results with unclear physical interpretations.
Conclusions:
- The Hermitian methodology is recommended for treating PT-symmetric, non-Hermitian quantum many-body systems due to its physical interpretability and experimental consistency.
- Awareness of PT-symmetric and biorthogonal concepts is crucial for a complete understanding of these systems.
- Established many-body methods like Green functions and functional integrals require re-evaluation for application to PT-symmetric, non-Hermitian systems.
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