Random walks near Rokhsar-Kivelson points

Abstract

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.

12 pages, 9 figures, RevTeX

References in corpus (3)

• Topological Order and Conformal Quantum Critical Points
• From classical to quantum dynamics at Rokhsar-Kivelson points
• Vison gap in the Rokhsar-Kivelson dimer model on the triangular lattice

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• Global scheme of sweeping cluster algorithm to sample among topological sectors
• Widely existing mixed phase structure of quantum dimer model on square lattice
• Resonating plaquette phase of a quantum six-vertex model
• Zero-temperature Kosterlitz-Thouless transition in a two-dimensional quantum system
• Fully packed quantum loop model on the square lattice: phase diagram and application for Rydberg atoms
• Accessing Excitation of Many-body Systems via Single-Mode Approximation within Quantum Monte Carlo Simulations