title: Markov entropy decomposition: a variational dual for quantum belief propagation.
abstract: We present a lower bound for the free energy of a quantum many-body system at finite temperature. This lower bound is expressed as a convex optimization problem with linear constraints, and is derived using strong subadditivity of von Neumann entropy and a relaxation of the consistency condition of local density operators. The dual to this minimization problem leads to a set of quantum belief propagation equations, thus providing a firm theoretical foundation to that approach. The minimization problem is numerically tractable, and we find good agreement with quantum Monte Carlo calculations for spin-1/2 Heisenberg antiferromagnet in two dimensions. This lower bound complements other variational upper bounds. We discuss applications to Hamiltonian complexity theory and give a generalization of the structure theorem of [P. Hayden et al., Commun. Math. Phys. 246, 359 (2004).] to trees in an appendix.
authors.affiliation: Département de Physique, Université de Sherbrooke, Québec, J1K 2R1, Canada.
authors.forename: David
authors.initials: D
authors.lastname: Poulin
authors.forename: Matthew B
authors.initials: MB
authors.lastname: Hastings