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arXiv 2004.00295hep-latcond-mat.str-elhep-th
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1+1维Gross-Neveu模型中有限味数下的非均匀相

Inhomogeneous phases in the Gross-Neveu model in 1+1 dimensions at finite number of flavors

Julian Lenz, Laurin Pannullo, Marc Wagner, Björn Wellegehausen, Andreas Wipf

备注：
32 pages + 4 pages appendix, text files with the data to reproduce the figures provided in source; version accepted for publication in PRD
发表信息：
Phys. Rev. D 101, 094512 (2020)
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摘要：

利用格点场论研究了有限费米子味数$N_f$、有限温度和有限化学势下1+1维Gross-Neveu（GN）模型的热力学性质.在极限$N_f \rightarrow \infty$中，该模型已在连续统中解析求解。在这个极限中存在三个相：一个大质量相，其中一个均匀的手征凝聚体自发地打破手征对称性，一个无质量的对称相与消失的凝聚体和最有趣的是一个非均匀相与凝聚体，它在空间方向上振荡。在本工作中，我们使用手征格点费米子（朴素费米子和SLAC费米子）来模拟具有2，8和16味道的GN模型。用两种离散化方法得到的结果一致。类似地，对于$N_f \rightarrow \infty$，我们在相图中发现三个不同的区域，其特征在于凝聚场的两点函数的性质不同的行为。对于$N_f = 8$，我们详细绘制了相图，并获得了一个小于极限$N_f \rightarrow \infty$的非均匀区域，其中量子涨落被抑制。我们还评论了Goldstone玻色子的存在与否与1+1维平移不变性的破缺有关。

英文摘要：

We explore the thermodynamics of the 1+1-dimensional Gross-Neveu (GN) model at finite number of fermion flavors $N_f$, finite temperature and finite chemical potential using lattice field theory. In the limit $N_f \rightarrow \infty$ the model has been solved analytically in the continuum. In this limit three phases exist: a massive phase, in which a homogeneous chiral condensate breaks chiral symmetry spontaneously, a massless symmetric phase with vanishing condensate and most interestingly an inhomogeneous phase with a condensate, which oscillates in the spatial direction. In the present work we use chiral lattice fermions (naive fermions and SLAC fermions) to simulate the GN model with 2, 8 and 16 flavors. The results obtained with both discretizations are in agreement. Similarly as for $N_f \rightarrow \infty$ we find three distinct regimes in the phase diagram, characterized by a qualitatively different behavior of the two-point function of the condensate field. For $N_f = 8$ we map out the phase diagram in detail and obtain an inhomogeneous region smaller as in the limit $N_f \rightarrow \infty$, where quantum fluctuations are suppressed. We also comment on the existence or absence of Goldstone bosons related to the breaking of translation invariance in 1+1 dimensions.

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