Multilayer wave functions: A recursive coupling of local excitations

TL;DR

This paper introduces a recursive multilayer wave function ansatz for disordered quantum systems, enabling efficient energy estimation and phase transition detection using message-passing algorithms.

Contribution

It presents a novel multilayer wave function construction that simplifies Hamiltonian expectation calculations and applies message-passing for variational optimization.

Findings

Accurate ground-state energy estimations for the transverse Ising model.

Effective detection of quantum phase transition points.

First application of message-passing algorithms in structured variational problems.

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.