Multilayer wave functions: A recursive coupling of local excitations
DISAT and Center for Computational Sciences, Politecnico di Torino - Corso Duca degli Abruzzi 24, 10129 Torino, Italy
Received: 23 July 2013
Accepted: 25 October 2013
Finding a succinct representation to describe the ground state of a disordered interacting system could be very helpful in understanding the interplay between the interactions that is manifested in a quantum phase transition. In this work we use some elementary states to construct recursively an ansatz of multilayer wave functions, where in each step the higher-level wave function is represented by a superposition of the locally “excited states” obtained from the lower-level wave function. This allows us to write the Hamiltonian expectation in terms of some local functions of the variational parameters, and employ an efficient message-passing algorithm to find the optimal parameters. We obtain good estimations of the ground-state energy and the phase transition point for the transverse Ising model with a few layers of mean-field and symmetric tree states. The work is the first step towards the application of local and distributed message-passing algorithms in the study of structured variational problems in finite dimensions.
PACS: 05.30.-d – Quantum statistical mechanics / 64.60.De – Statistical mechanics of model systems (Ising model, Potts model, field-theory models, Monte Carlo techniques, etc.) / 75.10.Nr – Spin-glass and other random models
© EPLA, 2013