标题： 北极圈内的非均匀场论 显示英文标题

标题： Inhomogeneous field theory inside the arctic circle

摘要： 受自旋链中的量子淬火启发，求解了一个一维费米子粒子在虚时中从域墙初始状态演化的玩具模型。 该玩具模型的主要兴趣在于它表现出极地圆现象，即临界涨落区域和冻结区域之间的空间相分离。 临界区域内的大尺度关联被表示为（欧几里得）二维无质量狄拉克场理论中的关联函数。 观察到该理论是不均匀的：度规是位置相关的，因此实际上是弯曲空间中的狄拉克场理论。 然后将用于求解玩具模型的技术扩展到处理其他模型的转移矩阵：六边形晶格和正方形晶格上的二聚体，以及自由费米子点处的六顶点模型（$\Delta=0$）。 在所有情况下，都给出了临界区域内长程关联以及底层狄拉克作用量的显式表达式。 尽管此处开发的设置严重依赖于费米子可观测量，但可以通过玻色化将结果转化为高度配置和高斯自由场的语言。 附录中还简要回顾了接近相变边界的相关性以及所有这些模型中阿利过程的普遍出现。 显示英文摘要

摘要： Motivated by quantum quenches in spin chains, a one-dimensional toy-model of fermionic particles evolving in imaginary-time from a domain-wall initial state is solved. The main interest of this toy-model is that it exhibits the arctic circle phenomenon, namely a spatial phase separation between a critically fluctuating region and a frozen region. Large-scale correlations inside the critical region are expressed in terms of correlators in a (euclidean) two-dimensional massless Dirac field theory. It is observed that this theory is inhomogenous: the metric is position-dependent, so it is in fact a Dirac field theory in curved space. The technique used to solve the toy-model is then extended to deal with the transfer matrices of other models: dimers on the honeycomb and square lattice, and the six-vertex model at the free fermion point ($\Delta=0$). In all cases, explicit expressions are given for the long-range correlations in the critical region, as well as for the underlying Dirac action. Although the setup developed here is heavily based on fermionic observables, the results can be translated into the language of height configurations and of the gaussian free field, via bosonization. Correlations close to the phase boundary and the generic appearance of Airy processes in all these models are also briefly revisited in the appendix.