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

Yoshii, Ryosuke; Nitta, Muneto

doi:10.3390/sym11050636

Cited by 12 publications

(8 citation statements)

References 132 publications

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“…This feature has been investigated in the (1+1) dimensional Nambu-Jona-Lasinio model or the chiral Gross-Neveu model [41][42][43][44][45]. Recently, the connection between the Nambu-Jona-Lasinio model and the non-linear sigma model is also of particular interest to the inhomogeneous condensate [46]. Moreover, the generalized Ginzburg-Landau approach with higher derivatives of the order parameter has been developed and it has been revealed that the LOFF phase of the chiral condensate is energetically preferred in Ref.…”

Section: Introductionmentioning

confidence: 99%

Kink Crystalline Condensate and Multi-kink Solution in Holographic Superconductor

Matsumoto,

Nakamura,

Yoshii

2019

Preprint

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We explore inhomogeneous solutions of a holographic superconductor. At lower T /µ, we find kink crystalline condensates in which condensates are well-fitted by the Jacobi elliptic functions. We present the relation between T /µ and the elliptic modulus ν, which determines the profile of the functions. We also find multi-kink solutions, which is not realized as a solution within the conventional Ginzburg-Landau theory with secondorder derivative and φ 4 potential. This shows that the holographic superconductor model captures the physics beyond the conventional Ginzburg-Landau theory.

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Section: Introductionmentioning

confidence: 99%

Kink Crystalline Condensate and Multi-kink Solution in Holographic Superconductor

Matsumoto,

Nakamura,

Yoshii

2019

Preprint

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“…Such similarities can be explained by several physical setups, in which the two-dimensional CP N −1 sigma model effectively describes various physical properties of four-dimensional gauge theories; non-Abelian vortices in the non-Abelian gauge-Higgs models [5-10, 10, 11] and dense QCD [12][13][14][15], long strings in Yang-Mills theories [16], and an appropriately compactified Yang-Mills theory [17]. Non-perturbative properties of the CP N −1 model have long been studied analytically by the gap equations with the large-N approximation [2][3][4][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] and by lattice simulations [36][37][38][39][40][41][42][43][44][45][46][47][48][49]. In the previous work [47,48] of the present authors, they have studied the CP N −1 model on S 1 s (large) × S 1 τ (small) by lattice Monte Carlo simulations.…”

Section: Introductionmentioning

confidence: 99%

Lattice ℂPN−1 model with ℤN twisted boundary condition: bions, adiabatic continuity and pseudo-entropy

Fujimori

Itou

Misumi

et al. 2020

J. High Energ. Phys.

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We investigate the lattice CP N −1 sigma model on S 1 s (large) × S 1 τ (small) with the Z N symmetric twisted boundary condition, where a sufficiently large ratio of the circumferences (L s L τ) is taken to approximate R × S 1. We find that the expectation value of the Polyakov loop, which is an order parameter of the Z N symmetry, remains consistent with zero (| P | ∼ 0) from small to relatively large inverse coupling β (from large to small L τ). As β increases, the distribution of the Polyakov loop on the complex plane, which concentrates around the origin for small β, isotropically spreads and forms a regular N-sided-polygon shape (e.g. pentagon for N = 5), leading to | P | ∼ 0. By investigating the dependence of the Polyakov loop on S 1 s direction, we also verify the existence of fractional instantons and bions, which cause tunneling transition between the classical N vacua and stabilize the Z N symmetry. Even for quite high β, we find that a regular-polygon shape of the Polyakov-loop distribution, even if it is broken, tends to be restored and | P | gets smaller as the number of samples increases. To discuss the adiabatic continuity of the vacuum structure from another viewpoint, we calculate the β dependence of "pseudo-entropy" density ∝ T xx − T τ τ. The result is consistent with the absence of a phase transition between large and small β regions.

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Section: Introductionmentioning

confidence: 99%

Kink crystalline condensate and multi-kink solution in holographic superconductor

Matsumoto

Nakamura

Yoshii

2020

J. High Energ. Phys.

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The theory of superconductivity can be divided into two groups depending on whether it has multi-kink solutions. For example, the BCS theory and the Gross-Neveu model have metastable multi-kink solutions whereas the conventional Ginzburg-Landau theory without higher-derivative interactions does not have any multi-kink solutions. In this paper, we systematically examine the solutions of the holographic superconductor model to find out which group the model falls into. We show that the holographic superconductor model has metastable multi-kink solutions. In this sense, we find that the holographic superconductor model falls into the category of the BCS theory and the Gross-Neveu model. We also find that the holographic superconductor model has kink crystalline condensates which are well-fitted by the Jacobi elliptic functions.

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

Cited by 12 publications

References 132 publications

Kink Crystalline Condensate and Multi-kink Solution in Holographic Superconductor

Kink Crystalline Condensate and Multi-kink Solution in Holographic Superconductor

Lattice ℂPN−1 model with ℤN twisted boundary condition: bions, adiabatic continuity and pseudo-entropy

Kink crystalline condensate and multi-kink solution in holographic superconductor

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