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Chin. Phys. B, 2018, Vol. 27(8): 087501    DOI: 10.1088/1674-1056/27/8/087501
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES Prev   Next  

Typicality at quantum-critical points

Lu Liu(刘录)1, Anders W Sandvik2,3, Wenan Guo(郭文安)1
1 Department of Physics, Beijing Normal University, Beijing 100875, China;
2 Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA;
3 Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
Abstract  

We discuss the concept of typicality of quantum states at quantum-critical points, using projector Monte Carlo simulations of an S=1/2 bilayer Heisenberg antiferromagnet as an illustration. With the projection (imaginary) time τ scaled as τ=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.

Keywords:  typicality      quantum criticality      bilayer Heisenberg antiferromagnet model      imaginary projecting time      projecting quantum Monte Carlo simulation  
Received:  11 May 2018      Revised:  19 May 2018      Published:  05 August 2018
PACS:  75.10.Kt (Quantum spin liquids, valence bond phases and related phenomena)  
  75.10.Jm (Quantized spin models, including quantum spin frustration)  
  75.40.Mg (Numerical simulation studies)  
  75.40.-s (Critical-point effects, specific heats, short-range order)  
Fund: 

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

Corresponding Authors:  Anders W Sandvik, Wenan Guo     E-mail:  sandvik@bu.edu;waguo@bnu.edu.cn

Cite this article: 

Lu Liu(刘录), Anders W Sandvik, Wenan Guo(郭文安) Typicality at quantum-critical points 2018 Chin. Phys. B 27 087501

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