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Park, Chae-Yeun and Kastoryano, Michael J. (2022). Expressive power of complex-valued restricted Boltzmann machines for solving nonstoquastic Hamiltonians. Phys. Rev. B, 106 (13). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2469-9969

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Abstract

Variational Monte Carlo with neural network quantum states has proven to be a promising avenue for evaluating the ground-state energy of spin Hamiltonians. However, despite continuous efforts the performance of the method on frustrated Hamiltonians remains significantly worse than those on stoquastic Hamiltonians that are sign free. We present a detailed and systematic study of restricted Boltzmann machine (RBM) based variational Monte Carlo for quantum spin chains, resolving how relevant stoquasticity is in this setting. We show that in most cases, when the Hamiltonian is phase connected with a stoquastic point, the complex RBM state can faithfully represent the ground state, and local quantities can be evaluated efficiently by sampling. On the other hand, we identify several new phases that are challenging for the RBM Ansatz, including nontopological robust nonstoquastic phases as well as stoquastic phases where sampling is nevertheless inefficient. We further find that, in contrast to the common belief, an accurate neural network representation of ground states in nonstoquastic phases is hindered not only by the sign structure but also by their amplitudes.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Park, Chae-Yeun UNSPECIFIED UNSPECIFIED UNSPECIFIED Kastoryano, Michael J. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-668627
DOI:	10.1103/PhysRevB.106.134437
Journal or Publication Title:	Phys. Rev. B
Volume:	106
Number:	13
Date:	2022
Publisher:	AMER PHYSICAL SOC
Place of Publication:	COLLEGE PK
ISSN:	2469-9969
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language NETWORKS Multiple languages Materials Science, Multidisciplinary; Physics, Applied; Physics, Condensed Matter Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/66862