QMC and Scaling

This letter addresses the case without a sign problem. I think eqn. 3 can be trivially applied to a DMC calculation. I should look at it further though.

Quantum Monte Carlo Simulations of Fidelity at Magnetic Quantum Phase Transitions

Authors:
David Schwandt,1,2 Fabien Alet,1,2 and Sylvain Capponi1,2
1Laboratoire de Physique Théorique, Université de Toulouse, UPS, (IRSAMC), F-31062 Toulouse, France
2CNRS, LPT (IRSAMC), F-31062 Toulouse, France

Abstract:
When a system undergoes a quantum phase transition, the ground-state wave function shows a change of nature, which can be monitored using the fidelity concept. We introduce two quantum Monte Carlo schemes that allow the computation of fidelity and its susceptibility for large interacting many-body systems. These methods are illustrated on a two-dimensional Heisenberg model, where fidelity estimators show marked behavior at two successive quantum phase transitions. We also develop a scaling theory which relates the divergence of the fidelity susceptibility to the critical exponent of the correlation length. A good agreement is found with the numerical results.

http://link.aps.org/doi/10.1103/PhysRevLett.103.170501