Precise Determination of Quantum Critical Points by the Violation of the Entropic Area Law

Details Precise Determination of Quantum Critical Points by the Violation of the Entropic Area Law Precise Determination of Quantum Critical Points by the Violation of the Entropic Area Law

2011-06-22

arxiv.org/abs/1106.4527v3

Phys. Rev. B 84 094410 (2011)

Physics

Condensed Matter

Statistical Mechanics

to appear in PRB,8 pages, 2 figures, 3 tables

Scientific paper

Finite-size scaling analysis turns out to be a powerful tool to calculate the phase diagram as well as the critical properties of two dimensional classical statistical mechanics models and quantum Hamiltonians in one dimension. The most used method to locate quantum critical points is the so called crossing method, where the estimates are obtained by comparing the mass gaps of two distinct lattice sizes. The success of this method is due to its simplicity and the ability to provide accurate results even considering relatively small lattice sizes. In this paper, we introduce an estimator that locates quantum critical points by exploring the known distinct behavior of the entanglement entropy in critical and non critical systems. As a benchmark test, we use this new estimator to locate the critical point of the quantum Ising chain and the critical line of the spin-1 Blume-Capel quantum chain. The tricritical point of this last model is also obtained. Comparison with the standard crossing method is also presented. The method we propose is simple to implement in practice, particularly in density matrix renormalization group calculations, and provides us, like the crossing method, amazingly accurate results for quite small lattice sizes. Our applications show that the proposed method has several advantages, as compared with the standard crossing method, and we believe it will become popular in future numerical studies.

Affiliated with

Also associated with

No associations

Rating

Precise Determination of Quantum Critical Points by the Violation of the Entropic Area Law does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Precise Determination of Quantum Critical Points by the Violation of the Entropic Area Law, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Precise Determination of Quantum Critical Points by the Violation of the Entropic Area Law will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-207302