Continuous-Mixture Autoregressive Networks Learning the Kosterlitz–Thouless Transition  

作　　者：Lingxiao Wang Yin Jiang Lianyi He Kai Zhou 王凌霄;姜寅;何联毅;周凯(Frankfurt Institute for Advanced Studies,Ruth-Moufang-Str.1,60438 Frankfurt am Main,Germany;State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics,Tsinghua University,Beijing 100084,China;Department of Physics,Beihang University,Beijing 100191,China)

机构地区：[1]Frankfurt Institute for Advanced Studies,Ruth-Moufang-Str.1,60438 Frankfurt am Main,Germany [2]State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics,Tsinghua University,Beijing 100084,China [3]Department of Physics,Beihang University,Beijing 100191,China

出　　处：《Chinese Physics Letters》2022年第12期8-13,共6页中国物理快报（英文版）

基　　金：supported by the BMBF under the ErUM-Data project(K.Z.);the AI grant of SAMSON AG,Frankfurt(K.Z.);Xidian-FIAS International JRC support(L.W.);the National Natural Science Foundation of China[Grant No.11875002(Y.J.)and 11775123(L.H.and L.W.)];the Zhuobai Program of Beihang University(Y.J.);the National Key R&D Program of China[Grant No.2018YFA0306503(L.H.)]。

摘　　要：We develop deep autoregressive networks with multi channels to compute many-body systems with continuous spin degrees of freedom directly.As a concrete example,we demonstrate the two-dimensional XY model with the continuous-mixture networks and rediscover the Kosterlitz–Thouless(KT)phase transition on a periodic square lattice.Vortices characterizing the quasi-long range order are accurately detected by the generative model.By learning the microscopic probability distributions from the macroscopic thermal distribution,the networks are trained as an efficient physical sampler which can approximate the free energy and estimate thermodynamic observables unbiasedly with importance sampling.As a more precise evaluation,we compute the helicity modulus to determine the KT transition temperature.Although the training process becomes more time-consuming with larger lattice sizes,the training time remains unchanged around the KT transition temperature.The continuousmixture autoregressive networks we developed thus can be potentially used to study other many-body systems with continuous degrees of freedom.

关 键 词：TEMPERATURE TRANSITION unchanged 

分 类 号：O469[理学—凝聚态物理] TP183[理学—电子物理学]