Typicality at quantum-critical points

作     者：Lu Liu Anders W Sandvik Wenan Guo 刘录;Anders W Sandvik;郭文安

作者机构：Department of PhysicsBeijing Normal UniversityBeijing 100875China Department of PhysicsBoston University590 Commonwealth AvenueBostonMassachusetts 02215USA Beijing National Laboratory for Condensed Matter Physics and Institute of PhysicsChinese Academy of SciencesBeijing 100190China 

出 版 物：《Chinese Physics B》 (中国物理B（英文版）)

年 卷 期：2018年第27卷第8期

页      面：517-528页

核心收录：

学科分类：07[理学] 0702[理学-物理学] 

基　　金：Project supported by the National Natural Science Foundation of China(Grant Nos.11734002 and 11775021) the National Science Foundation(Grant No.DMR-1710170) a Simons Investigator Award 

主　　题：typicality quantum criticality bilayer Heisenberg antiferromagnet model imaginary projectingtime, projecting quantum Monte Carlo simulation 

摘      要：We discuss the concept of typicality of quantum states at quantum-critical points, using projector Monte Carlo simu- lations of an S ---- 1/2 bilayer Heisenberg antiferromagnet as an illustration. With the projection （imaginary） time t scaled as t= aLz, L being the system length and z the dynamic critical exponent （which takes the value z = 1 in the bilayer model studied here）, a critical point can be identified which asymptotically flows to the correct location and universality class with increasing L, independently of the prefactor a and the initial state. Varying the proportionality factor a and the initial state only changes the cross-over behavior into the asymptotic large-L behavior. In some cases, choosing an optimal factor a may also lead to the vanishing of the leading finite-size corrections. The observation of typicality can be used to speed up simulations of quantum criticality, not only within the Monte Carlo approach but also with other numerical methods where imaginary-time evolution is employed, e.g., tensor network states, as it is not necessary to evolve fully to the ground state but only for sufficiently long times to reach the typicality regime.