Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2005-04-08
Int. Jour. Mod. Phys. B 19, 1973-1993 (2005)
Physics
Condensed Matter
Strongly Correlated Electrons
12 pages, 9 figures, RevTeX
Scientific paper
10.1142/S021797920502964X
There is a class of quantum Hamiltonians known as Rokhsar-Kivelson(RK)-Hamiltonians for which static ground state properties can be obtained by evaluating thermal expectation values for classical models. The ground state of an RK-Hamiltonian is known explicitly, and its dynamical properties can be obtained by performing a classical Monte Carlo simulation. We discuss the details of a Diffusion Monte Carlo method that is a good tool for studying statics and dynamics of perturbed RK-Hamiltonians without time discretization errors. As a general result we point out that the relation between the quantum dynamics and classical Monte Carlo simulations for RK-Hamiltonians follows from the known fact that the imaginary-time evolution operator that describes optimal importance sampling, in which the exact ground state is used as guiding function, is Markovian. Thus quantum dynamics can be studied by a classical Monte Carlo simulation for any Hamiltonian that is free of the sign problem provided its ground state is known explicitly.
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