Invariant Neural Network Ansatz for weakly symmetric Open Quantum Lattices

• URL: http://arxiv.org/abs/2101.03511v2
• Date: Mon, 10 May 2021 09:32:21 GMT
• Title: Invariant Neural Network Ansatz for weakly symmetric Open Quantum Lattices
• Authors: Davide Nigro
• Abstract summary: We show that, whenever the steady state is unique, one can introduce a neural network representation for the system density operator. We demonstrate the validity of our approach by determining the steady state structure of the one dimensional dissipative XYZ model in the presence of a uniform magnetic field.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider $d$-dimensional open quantum lattices whose time evolution is governed by a master equation which is weakly symmetric under the action of a finite group $G$ that is a subgroup of all the possible permutations of the lattice sites. We show that, whenever the steady state is unique, one can introduce a neural network representation for the system density operator that explicitly accounts for the system symmetries and can be efficiently optimized by exploring only a relevant subspace of the parameter space. In particular, as a proof of principle, we demonstrate the validity of our approach by determining the steady state structure of the one dimensional dissipative XYZ model in the presence of a uniform magnetic field.

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