Collective modes and KosterlitzThouless transition in a magnetic field in the planar Nambu–JonaLasinio model
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–JonaLasinio model with continuous U(1) chiral symmetry. We introduce a selfconsistent 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 wellestablished regularization scheme for the case of vanishing magnetic field. The same scheme can be applied to the study of the nexttoleading 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 KosterlitzThouless (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 thatmore »
 Authors:

^{[1]};
^{[2]};
^{[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)
 Publication Date:
 Report Number(s):
 LAUR1426175
Journal ID: ISSN 15507998; PRVDAQ
 Grant/Contract Number:
 11335005; 2013CB922000; 2014CB845400; AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review. D, Particles, Fields, Gravitation and Cosmology
 Additional Journal Information:
 Journal Volume: 90; Journal Issue: 5; Journal ID: ISSN 15507998
 Publisher:
 American Physical Society (APS)
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; dynamical chiral symmetry breaking; magnetic catalysis; KosterlitzThouless transition; Nambu–JonaLasino model
 OSTI Identifier:
 1246920
 Alternate Identifier(s):
 OSTI ID: 1181465
Cao, Gaoqing, He, Lianyi, and Zhuang, Pengfei. Collective modes and KosterlitzThouless transition in a magnetic field in the planar Nambu–JonaLasinio model. United States: N. p.,
Web. doi:10.1103/PhysRevD.90.056005.
Cao, Gaoqing, He, Lianyi, & Zhuang, Pengfei. Collective modes and KosterlitzThouless transition in a magnetic field in the planar Nambu–JonaLasinio model. United States. doi:10.1103/PhysRevD.90.056005.
Cao, Gaoqing, He, Lianyi, and Zhuang, Pengfei. 2014.
"Collective modes and KosterlitzThouless transition in a magnetic field in the planar Nambu–JonaLasinio model". United States.
doi:10.1103/PhysRevD.90.056005. https://www.osti.gov/servlets/purl/1246920.
@article{osti_1246920,
title = {Collective modes and KosterlitzThouless transition in a magnetic field in the planar Nambu–JonaLasinio model},
author = {Cao, Gaoqing and He, Lianyi and Zhuang, Pengfei},
abstractNote = {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–JonaLasinio model with continuous U(1) chiral symmetry. We introduce a selfconsistent 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 wellestablished regularization scheme for the case of vanishing magnetic field. The same scheme can be applied to the study of the nexttoleading 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 KosterlitzThouless (KT) type. We determine the KT transition temperature TKT as well as the mass melting temperature T* as a function of the magnetic field. It is found that the pseudogap domain TKT < 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.},
doi = {10.1103/PhysRevD.90.056005},
journal = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},
number = 5,
volume = 90,
place = {United States},
year = {2014},
month = {9}
}