Winding in non-Hermitian systems

Schindler, Stella T.; Bender, Carl M.

doi:10.1088/1751-8121/aa9faf

Cited by 12 publications

(5 citation statements)

References 29 publications

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“…Finite-density QCD, PT symmetry, and exotic phases Stella T. Schindler such as unitary time evolution, orthogonality [21], completeness [22], and interlacing eigenfunctions [23,24]. These properties break down in a characteristic manner when symmetry is broken and one or more eigenvalue pairs becomes complex.…”

Section: Pos(lattice2021)555mentioning

confidence: 99%

Finite-density QCD, $\mathcal{PT}$ symmetry, and exotic phases

Schindler¹,

Schindler²,

Ogilvie³

2022

Proceedings of the 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021)

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We study the phase structure of effective models of finite-density QCD using analytic and lattice simulation techniques developed for the study of non-Hermitian and PT -symmetric QFTs. Finitedensity QCD is symmetric under the combined operation of the charge and complex conjugation operators CK, which falls into the class of so-called generalized PT symmetries. We show that PT -symmetric quantum field theories can support patterned ground-state field configurations in the vicinity of a critical endpoint. We apply our methods to a lattice heavy quark model at nonzero chemical potential that displays patterning behavior for a range of parameters. We derive a simple approximate criterion for the formation of these patterns, which can be used with lattice results.

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Section: Pos(lattice2021)555mentioning

confidence: 99%

Finite-density QCD, $\mathcal{PT}$ symmetry, and exotic phases

Schindler¹,

Schindler²,

Ogilvie³

2022

Proceedings of the 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021)

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“…If one or more tuples of eigenvalues are coalesced at the same value, the operator is said to be at an exceptional point [17]. PT -unbroken Hamiltonians exhibit many of the properties of Hermitian systems: unitarity, a positive norm under a (CPT ) inner product [17], eigenfunctions that possess analogs of interlacing zeros [18,19], orthogonality, and completeness [20,21]. These behaviors break down in a characteristic manner when moving a parameter like in H past an exceptional point and into the broken symmetry regime.…”

Section: Pt Symmetry and Quantum Field Theorymentioning

confidence: 99%

$\mathcal PT$ symmetry, pattern formation, and finite-density QCD

Schindler,

Ogilvie

2021

Preprint

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A longstanding issue in the study of quantum chromodynamics (QCD) is its behavior at nonzero baryon density, which has implications for many areas of physics. The path integral has a complex integrand when the quark chemical potential is nonzero and therefore has a sign problem, but it also has a generalized PT symmetry. We review some new approaches to PT -symmetric field theories, including both analytical techniques and methods for lattice simulation. We show that PT -symmetric field theories with more than one field generally have a much richer phase structure than their Hermitian counterparts, including stable phases with patterning behavior. The case of a PT -symmetric extension of a φ 4 model is explained in detail. The relevance of these results to finite density QCD is explained, and we show that a simple model of finite density QCD exhibits a patterned phase in its critical region.

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“…This terminology has no direct connection to spontaneous symmetry breaking. such as unitary time evolution, orthogonality [21], completeness [22], and interlacing eigenfunctions [23,24]. These properties break down in a characteristic manner when symmetry is broken and one or more eigenvalue pairs becomes complex.…”

Section: Brief Introduction To Pt Symmetrymentioning

confidence: 99%