Typicality at quantum-critical points

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

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=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.

Keywords: typicality quantum criticality bilayer Heisenberg antiferromagnet model imaginary projecting time projecting quantum Monte Carlo simulation

Received: 11 May 2018
Revised: 19 May 2018
Accepted manuscript online:

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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