3d fermion-boson map with imaginary chemical potential

G., Filothodoros, Evangelos; Petkou, Anastasios C.; Vlachos, N.D.

doi:10.1103/physrevd.95.065029

Cited by 16 publications

(44 citation statements)

References 47 publications

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“…Another relation between the CP N −1 model and the GN model in 2 + 1 dimensions has recently been found in ref. [91] in which the large-N free energy densities for the both theories are found to be remarkably similar. Though it would be important to see whether the similar structure also appears in the 1 + 1 dimensions, we leave it as a future problem.…”

Section: Discussionmentioning

confidence: 86%

Self-consistent large-N analytical solutions of inhomogeneous condensates in quantum ℂPN − 1 model

Nitta

Yoshii

2017

J. High Energ. Phys.

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We give, for the first time, self-consistent large-N analytical solutions of inhomogeneous condensates in the quantum CP N −1 model in the large-N limit. We find a map from a set of gap equations of the CP N −1 model to those of the Gross-Neveu (GN) model (or the gap equation and the Bogoliubov-de Gennes equation), which enables us to find the self-consistent solutions. We find that the Higgs field of the CP N −1 model is given as a zero mode of solutions of the GN model, and consequently only topologically nontrivial solutions of the GN model yield nontrivial solutions of the CP N −1 model. A stable single soliton is constructed from an anti-kink of the GN model and has a broken (Higgs) phase inside its core, in which CP N −1 modes are localized, with a symmetric (confining) phase outside. We further find a stable periodic soliton lattice constructed from a real kink crystal in the GN model, while the Ablowitz-Kaup-Newell-Segur hierarchy yields multiple solitons at arbitrary separations.

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Section: Discussionmentioning

confidence: 86%

Self-consistent large-N analytical solutions of inhomogeneous condensates in quantum ℂPN − 1 model

Nitta

Yoshii

2017

J. High Energ. Phys.

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“…It is well known that in the absence of a chemical potential the two models above exhibit very different patterns of symmetry breaking at finite temperature T . We nevertheless we have shown in [11] that the situation changes in the presence of the imaginary chemical potential, and the corresponding phase structures of the two models can be mapped into each other. We have further observed in [11] the relevance of the celebrated Bloch-Wigner function [13] in our calculations of the gap equations and free energies.…”

Section: Introductionmentioning

confidence: 86%

“…We nevertheless we have shown in [11] that the situation changes in the presence of the imaginary chemical potential, and the corresponding phase structures of the two models can be mapped into each other. We have further observed in [11] the relevance of the celebrated Bloch-Wigner function [13] in our calculations of the gap equations and free energies. This mathematical curiosity, together with the aim to shed more light into the physics of bosonisation, prompted us to study in the present work the fermion-boson map in higher dimensions.…”

Section: Introductionmentioning

confidence: 86%

“…If fermion-boson duality is a fundamental property of three-dimensional quantum physics one may think that it is not necessary to invoke non-abelian gauge fields to make it manifest. Having this idea in mind we revisited in [11] the finite temperature phase structure of two 3d systems; the fermionic U (N ) Gross-Neveu model and the bosonic CP N −1 model. We have studied those systems in the canonical formalism by introducing an imaginary chemical potential for the U (1) charge.…”

Section: Introductionmentioning

confidence: 99%

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The fermion–boson map for large d

Petkou

Vlachos

2019

Nuclear Physics B

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We show that the three-dimensional map between fermions and bosons at finite temperature generalises for all odd dimensions d > 3. We further argue that such a map has a nontrivial large d limit. Evidence comes from studying the gap equations, the free energies and the partition functions of the U (N ) Gross-Neveu and CP N −1 models for odd d ≥ 3 in the presence of imaginary chemical potential. We find that the gap equations and the free energies can be written in terms of the Bloch-Wigner-Ramakrishnan D d (z) functions analysed by Zagier. Since D 2 (z) gives the volume of ideal tetrahedra in 3d hyperbolic space our three-dimensional results are related to resent studies of complex Chern-Simons theories, while for d > 3 they yield corresponding higher dimensional generalizations. As a spinoff, we observe that particular complex saddles of the partition functions correspond to the zeros and the extrema of the Clausen functions Cl d (θ) with odd and even index d respectively. These saddles lie on the unit circle at positions remarkably well approximated by a sequence of rational multiples of π.

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“…In this subsection, we briefly review the other approach to a NJL/CP N −1 correspondence in higher dimensions [30]. The main idea is as follows.…”

Section: Njl/cp N−1 Correspondence In 2+1 Dimensionmentioning

confidence: 99%

Nambu-Jona Lasinio and Nonlinear Sigma Models in Condensed Matter Systems

Yoshii

Nitta

2019

Symmetry

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We review various connections between condensed matter systems with the Nambu-Jona Lasinio model and nonlinear sigma models. The field theoretical description of interacting systems offers a systematic framework to describe the dynamical generation of condensates. Resent findings of a duality between the Nambu-Jona Lasinio model and the nonlinear sigma model enables us to investigate various properties underlying both theories. In this review we mainly focus on inhomogeneous condensations in static situations. The various methods developed in the Nambu-Jona Lasinio model reveal the inhomogeneous phase structures and also yield new inhomogeneous solutions in the nonlinear sigma model owing to the duality. The recent progress on interacting systems in finite systems is also reviewed.PACS numbers:

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3d fermion-boson map with imaginary chemical potential

Cited by 16 publications

References 47 publications

Self-consistent large-N analytical solutions of inhomogeneous condensates in quantum ℂPN − 1 model

Self-consistent large-N analytical solutions of inhomogeneous condensates in quantum ℂPN − 1 model

The fermion–boson map for large d

Nambu-Jona Lasinio and Nonlinear Sigma Models in Condensed Matter Systems

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