PT
	    
	   symmetry, pattern formation, and finite-density QCD

Schindler, Moses A.; Schindler, Stella T.; Ogilvie, Michael C.

doi:10.1088/1742-6596/2038/1/012022

Cited by 8 publications

(11 citation statements)

References 52 publications

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“…Finite-density QCD belongs to the class of so-called non-Hermitian PT -symmetric systems due to its invariance under the PT -type operator CK, the simultaneous action of charge and complex conjugation [1,2]. Since its inception in 1998 [3], the field of PT symmetry has had a wide impact on physics, generating thousands of experiments and applications across such diverse areas as optics, condensed matter, and quantum computing [4][5][6][7][8].…”

Section: Motivationmentioning

confidence: 99%

“…Since its inception in 1998 [3], the field of PT symmetry has had a wide impact on physics, generating thousands of experiments and applications across such diverse areas as optics, condensed matter, and quantum computing [4][5][6][7][8]. We bring knowledge of PT symmetry to bear on lattice gauge theory, inspiring novel analytic and simulation techniques for finite-density models [2,9,10]. Our findings indicate that finite-density QCD may have complicated phase behavior associated with the Polyakov loop, including inhomogeneous phases and sinusoidally-modulated Polyakov loop correlators near the critical endpoint.…”

Section: Motivationmentioning

confidence: 99%

“…( 2) is the source of the lattice QCD sign problem. It is also manifestly symmetric under the simultaneous action of the linear charge operator C and antilinear complex conjugation K, a symmetry of the PT type [2]. Finite-density QCD is thus amenable to study using PT methods.…”

Section: Pos(lattice2021)555mentioning

confidence: 99%

“…We can determine the phase structure of a complex QFT by doing a conventional stability analysis of the propagator [2,10]. Let us consider a generic theory with multiple scalar fields…”

Section: Phase Structure Of Complex Qftsmentioning

confidence: 99%

“…Let us now apply these methods to a simple effective model of finite-density QCD, a heavy quark theory [2]. Consider the action…”

Section: Phase Structure Of a Qcd-like Modelmentioning

confidence: 99%

See 4 more Smart Citations

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: Motivationmentioning

confidence: 99%

Section: Motivationmentioning

confidence: 99%

Section: Pos(lattice2021)555mentioning

confidence: 99%

“…We can determine the phase structure of a complex QFT by doing a conventional stability analysis of the propagator [2,10]. Let us consider a generic theory with multiple scalar fields…”

Section: Phase Structure Of Complex Qftsmentioning

confidence: 99%

“…Let us now apply these methods to a simple effective model of finite-density QCD, a heavy quark theory [2]. Consider the action…”

Section: Phase Structure Of a Qcd-like Modelmentioning

confidence: 99%

See 3 more Smart Citations

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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Detecting inhomogeneous chiral condensation from the bosonic two-point function in the (1 + 1)-dimensional Gross–Neveu model in the mean-field approximation*

Koenigstein¹,

Pannullo²,

Rechenberger³

et al. 2022

J. Phys. A: Math. Theor.

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The phase diagram of the (1 + 1)-dimensional Gross-Neveu model is reanalyzed for (non-)zero chemical potential and (non-)zero temperature within the mean-ﬁeld approximation. By investigating the momentum dependence of the bosonic two-point function, the well-known second-order phase transition from the ℤ2 symmetric phase to the so-called inhomogeneous phase is detected. In the latter phase the chiral condensate is periodically varying in space and translational invariance is broken. This work is a proof of concept study that conﬁrms that it is possible to correctly localize second-order phase transition lines between phases without condensation and phases of spatially inhomogeneous condensation via a stability analysis of the homogeneous phase. To complement other works relying on this technique, the stability analysis is explained in detail and its limitations and successes are discussed in context of the Gross-Neveu model. Additionally, we present explicit results for the bosonic wave-function renormalization in the mean-ﬁeld approximation, which is extracted analytically from the bosonic two-point function. We ﬁnd regions – a so-called moat regime – where the wave function renormalization is negative accompanying the inhomogeneous phase as expected.

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Revisiting the spatially inhomogeneous condensates in the ( 1 + 1 ) -dimensional chiral Gross–Neveu model via the bosonic two-point function in

Koenigstein,

Winstel

2024

J. Phys. A: Math. Theor.

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This work shows that the known phase boundary between the phase with chiral symmetry and the phase of spatially inhomogeneous chiral symmetry breaking in the phase diagram of the (1 + 1)-dimensional chiral Gross-Neveu model can be detected from the bosonic two-point function alone and thereby confirms and extends previous results. The analysis is referred to as the stability analysis of the symmetric phase and does not require knowledge about spatial modulations of condensates. We perform this analysis in the infinite-N limit at nonzero temperature and nonzero quark and chiral chemical potentials also inside the inhomogeneous phase. Thereby we observe an interesting relation between the bosonic $1$-particle irreducible two-point vertex function of the chiral Gross-Neveu model and the spinodal line of the Gross-Neveu model.

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PT symmetry, pattern formation, and finite-density QCD

Cited by 8 publications

References 52 publications

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

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

Detecting inhomogeneous chiral condensation from the bosonic two-point function in the (1 + 1)-dimensional Gross–Neveu model in the mean-field approximation*

Revisiting the spatially inhomogeneous condensates in the ( 1 + 1 ) -dimensional chiral Gross–Neveu model via the bosonic two-point function in

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