Typicality at quantum-critical points

doi:10.1088/1674-1056/27/8/087501

中国物理B ›› 2018, Vol. 27 ›› Issue (8): 87501-087501.doi: 10.1088/1674-1056/27/8/087501

• CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES • 上一篇下一篇

Typicality at quantum-critical points

Lu Liu(刘录), Anders W Sandvik, Wenan Guo(郭文安)

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

收稿日期:2018-05-11 修回日期:2018-05-19 出版日期:2018-08-05 发布日期:2018-08-05
通讯作者: Anders W Sandvik, Wenan Guo E-mail:sandvik@bu.edu;waguo@bnu.edu.cn
基金资助:
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.

Typicality at quantum-critical points

Lu Liu(刘录)¹, Anders W Sandvik^2,3, 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

Received:2018-05-11 Revised:2018-05-19 Online:2018-08-05 Published:2018-08-05
Contact: Anders W Sandvik, Wenan Guo E-mail:sandvik@bu.edu;waguo@bnu.edu.cn
Supported by:
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.

摘要/Abstract

摘要：

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=aL^z, 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.

关键词: typicality, quantum criticality, bilayer Heisenberg antiferromagnet model, imaginary projecting time, projecting quantum Monte Carlo simulation

Abstract:

Key words: typicality, quantum criticality, bilayer Heisenberg antiferromagnet model, imaginary projecting time, projecting quantum Monte Carlo simulation

中图分类号: (Quantum spin liquids, valence bond phases and related phenomena)

75.10.Kt

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)

刘录, Anders W Sandvik, 郭文安. Typicality at quantum-critical points[J]. 中国物理B, 2018, 27(8): 87501-087501.

Lu Liu(刘录), Anders W Sandvik, Wenan Guo(郭文安). Typicality at quantum-critical points[J]. Chin. Phys. B, 2018, 27(8): 87501-087501.

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Typicality at quantum-critical points

Typicality at quantum-critical points

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