Self-adapting method for the localization of quantum critical points using quantum Monte Carlo techniques

A generalization to the quantum case of a recently introduced algorithm [Tomita and Okabe, Phys. Rev. Lett. 86, 572 (2001)] for the determination of the critical temperature of classical spin models is proposed. We describe a simple method to automatically locate critical points in (Quantum) Monte Carlo simulations. The algorithm assumes the existence of a finite correlation length in at least one of the two phases surrounding the quantum critical point. We illustrate these ideas on the example of the critical interchain coupling for which coupled antiferromagnetic $S=1\mathrm{}$ spin chains order at $T=0.\mathrm{}$ Finite-size scaling relations are used to determine the exponents, $\nu =0.72\mathrm{}\left(2\right)\mathrm{}$ and $\eta =0.038\mathrm{}\left(3\right)\mathrm{}$ in agreement with previous estimates.