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arXiv 2203.07451hep-thhep-lat
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手征Gross-Neveu模型的非均匀相

On the Inhomogeneous Phase of the Chiral Gross-Neveu Model

Riccardo Ciccone, Lorenzo Di Pietro, Marco Serone

备注：
6 pages, one figure; v2: several improvements, matches version accepted by PRL
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摘要：

有大量的证据表明，在存在$U(1)$费米子数化学势$μ$和大的$N$极限的情况下，2d手性Gross-Neveu模型的基态由{ \it手性螺旋}相给出，即具有空间周期性相的手性凝聚物的非均匀相。我们证明了对于任何$μ>0$，手性螺旋构型在有限$N$和$T=0$上都是存在的。我们的分析是基于非阿贝尔玻色化，涉及到一个$U(N)_1$ WZW模型变形的电流-电流相互作用的模型。在本说明书中，非均匀相的出现令人惊讶地简单。我们还重新推导了大的$N$手性Gross-Neveu模型的相图通过直接的图解计算，发现与以前的结果在文献中的协议。

英文摘要：

There is substantial evidence that the ground state of the 2d chiral Gross-Neveu model, in the presence of a $U(1)$ fermion number chemical potential $μ$ and in the large $N$ limit, is given by a {\it chiral spiral} phase, namely an inhomogeneous phase with a chiral condensate having a spatially periodic phase. We show that the chiral spiral configuration persists at finite $N$ and $T=0$ for any $μ>0$. Our analysis is based on non-abelian bosonization, that relates the model to a $U(N)_1$ WZW model deformed by current-current interactions. In this description the appearance of the inhomogeneous phase is surprisingly simple. We also rederive the phase diagram of the large $N$ chiral Gross-Neveu model via a direct diagrammatic computation, finding agreement with previous results in the literature.

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