矩阵乘积态1+1维质量Thirring模型的相结构
Phase structure of the 1+1 dimensional massive Thirring model from matrix product states
摘要：
以矩阵乘积态为例，采用交错正则化方法研究了（1+1）维有质量Thirring模型在总费米子数为零的扇区内的非热相结构.在本文中，该项目的实施细节进行了说明。为了描述该模型的相图，我们考察了纠缠熵、费米子双线性凝聚和两种类型的关联函数。我们的调查表明，存在两个阶段，其中一个是关键的，另一个缺口。相结构的一个有趣的特点是费米子质量不为零的理论可以是共形的。我们还发现明确的数值证据表明，这些阶段分离的Berezinskiii-Kosterlitz-无齿型的过渡。本文给出的结果建立了在量子场论中使用矩阵乘积态探测这种相变的可能性。它们可以为进一步探索标度行为提供信息，并作为控制模式连续外推的重要成分。
英文摘要：
Employing matrix product states as an ansatz, we study the non-thermal phase structure of the (1+1)-dimensional massive Thirring model in the sector of vanishing total fermion number with staggered regularization. In this paper, details of the implementation for this project are described. To depict the phase diagram of the model, we examine the entanglement entropy, the fermion bilinear condensate and two types of correlation functions. Our investigation shows the existence of two phases, with one of them being critical and the other gapped. An interesting feature of the phase structure is that the theory with non-zero fermion mass can be conformal. We also find clear numerical evidence that these phases are separated by a transition of the Berezinskii-Kosterlitz-Thouless type. Results presented in this paper establish the possibility of using the matrix product states for probing this type of phase transition in quantum field theories. They can provide information for further exploration of scaling behaviour, and serve as an important ingredient for controlling the continuum extrapolation of the model.
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