Équipe de Recherche en Physique de l'Information Quantique


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 for the spin-1/2 Heisenberg anti-ferromagnet 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 to trees in an appendix.},
Author = {David Poulin and Matthew B. Hastings},
Eprint = {arXiv:1012.2050},
Journal = {Phys. Rev. Lett},
Pages = {080403},
Title = {Markov entropy decomposition: a variational dual for quantum belief propagation},
Volume = {106},
Year = {2011},
local-url = {PH11b1.pdf}}