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arXiv · 1307.3871

Multilayer wave functions: A recursive coupling of local excitations

A. Ramezanpour
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Abstract

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.

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A. Ramezanpour. 2013-11-18. Multilayer wave functions: A recursive coupling of local excitations. https://doi.org/10.1209/0295-5075%2F104%2F20003

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