Volume 104, Number 2, October 2013
|Number of page(s)||6|
|Published online||20 November 2013|
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.