平面Nambu-Jona-Lasino模型中磁场中的集体模和Kosterlitz-Lesser跃迁
Collective modes and Kosterlitz-Thouless transition in a magnetic field in the planar Nambu--Jona-Lasino model
摘要：
已知恒定的磁场是2+1维中动力学手征对称性破缺的强催化剂，导致即使在最弱吸引力下也产生动力学费米子质量。本文研究了具有连续U（1）手征对称性的（2+1）维Nambu-Jona-Lasinio模型在恒定磁场中与手征对称性动力学破缺相关的集体模.我们引入了一个自洽方案来计算1/N中首阶集体模的传播子。真空和磁场的贡献被分离，这样我们就可以对磁场消失的情况采用公认的正则化方案。同样的方法也可以应用于1/N中次首阶修正的研究。我们证明了在任意强度的磁场下，σ模总是轻束缚态，其质量是动力学费米子质量的两倍。由于集体模的动力学总是2+1维的，有限温度跃迁应该是Kosterlitz无（KT）型的。我们确定的KT转变温度$T_{\rm KT}$以及质量熔化温度$T^*$作为磁场的函数。研究发现，随着磁场强度的增加，赝能隙畴$T_{\rm KT}<T<T^*$增大。手性不平衡或轴向化学势$μ_5$的影响也进行了研究。我们发现，即使是一个恒定的轴向化学势$μ_5$可以导致反磁催化的KT转变温度在2+1维。这种逆磁催化行为实际上是由磁场与费米面相互作用引起的deHaas-van Alphen振荡。
英文摘要：
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 $T_{\rm KT}$ as well as the mass melting temperature $T^*$ as a function of the magnetic field. It is found that the pseudogap domain $T_{\rm KT}<T<T^*$ is enlarged with increasing strength of the magnetic field. The influence of a chiral imbalance or axial chemical potential $μ_5$ is also studied. We find that even a constant axial chemical potential $μ_5$ can lead to inverse magnetic catalysis of the KT transition temperature in 2+1 dimensions. 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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