Collective modes and Kosterlitz-Thouless transition in a magnetic field in the planar Nambu–Jona-Lasinio model

Cao, Gaoqing; He, Lianyi; Zhuang, Pengfei

doi:10.1103/PhysRevD.90.056005

Title: Collective modes and Kosterlitz-Thouless transition in a magnetic field in the planar Nambu–Jona-Lasinio model

Journal Article · Mon Sep 15 00:00:00 EDT 2014 · Physical Review. D, Particles, Fields, Gravitation and Cosmology

DOI:https://doi.org/10.1103/PhysRevD.90.056005· OSTI ID:1246920

Cao, Gaoqing ^[1]; He, Lianyi ^[2]; Zhuang, Pengfei ^[1]

Tsinghua Univ. and Collaborative Innovation Center of Quantum Matter, Beijing (China)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Frankfurt Institute for Advanced Studies, Frankfurt am Main (Germany)

It is known that a constant magnetic field is a strong catalyst of dynamical chiral symmetry breaking in 2+1 dimensions, leading to generating dynamical fermion mass even at weakest attraction. In this work we investigate the collective modes associated with the dynamical chiral symmetry breaking in a constant magnetic field in the (2+1)-dimensional Nambu–Jona-Lasinio model with continuous U(1) chiral symmetry. We introduce a self-consistent scheme to evaluate the propagators of the collective modes at the leading order in 1/N. The contributions from the vacuum and from the magnetic field are separated such that we can employ the well-established regularization scheme for the case of vanishing magnetic field. The same scheme can be applied to the study of the next-to-leading order correction in 1/N. We show that the sigma mode is always a lightly bound state with its mass being twice the dynamical fermion mass for arbitrary strength of the magnetic field. Since the dynamics of the collective modes is always 2+1 dimensional, the finite temperature transition should be of the Kosterlitz-Thouless (KT) type. We determine the KT transition temperature T_KT as well as the mass melting temperature T* as a function of the magnetic field. It is found that the pseudogap domain T_KT < T < T* is enlarged with increasing strength of the magnetic field. The influence of a chiral imbalance or axial chemical potential μ₅ is also studied. We find that even a constant axial chemical potential μ5 can lead to inverse magnetic catalysis of the KT transition temperature in 2+1 dimensions. As a result, the inverse magnetic catalysis behavior is actually the de Haas–van Alphen oscillation induced by the interplay between the magnetic field and the Fermi surface.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: 11335005; 2013CB922000; 2014CB845400; AC52-06NA25396

OSTI ID:: 1246920

Alternate ID(s):: OSTI ID: 1181465

Report Number(s):: LA-UR-14-26175; PRVDAQ

Journal Information:: Physical Review. D, Particles, Fields, Gravitation and Cosmology, Vol. 90, Issue 5; ISSN 1550-7998

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 29 works

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Title: Collective modes and Kosterlitz-Thouless transition in a magnetic field in the planar Nambu–Jona-Lasinio model

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