From classical to quantum dynamics at Rokhsar–Kivelson points

2003/11/14 by Christopher L. Henley, C L Henley · 5 citations
Computer Science · Mathematics · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Spectral Theory in Mathematical Physics #cond-mat.str-el

paper · pdf · doi:10.1088/0953-8984/16/11/045

8pp (IOP) LaTex, no figures. Proc. Highly Frustrated Magnetism 2003 (to appear J. Phys. Condens. Matter)

arxiv created 2003/11/14 · openalex publication_date 2004/03/04 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31

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.

Citations

• On the ground state properties of the anisotropic triangular antiferromagnet

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