From classical to quantum dynamics at Rokhsar-Kivelson points

TL;DR

This paper generalizes the Rokhsar-Kivelson point from classical statistical models with detailed balance to quantum Hamiltonians, linking classical relaxation modes to quantum excitations and correlators.

Contribution

It introduces a method to construct quantum Hamiltonians from classical models at Rokhsar-Kivelson points, connecting classical and quantum dynamics on the same state space.

Findings

Quantum Hamiltonians can be derived from classical models with detailed balance.

Excited states correspond to classical relaxation modes.

Classical and quantum correlations are related via analytic continuation.

Abstract

For any classical statistical-mechanics model with a discrete state space, and endowed with a dynamics satisfying detailed balance, it is possible to generalize the Rokhsar-Kivelson point for the quantum dimer model. That is, a quantum Hamiltonian can be constructed (on the same state space), such that the ground state wavefunction coincides with the classical equilibrium distribution. Furthermore the excited eigenstates correspond to classical relaxation modes, which (in cases with a symmetry or conserved quantity) permits extraction of the dispersion law of long-wavelength excitations. The mapping is natural mainly when the states have equal weight, as is typical of a highly frustrated model. Quantum and classical correlation functions are related by analytic continuation to the imaginary time axis.