Efficient neural-network based variational Monte Carlo scheme for direct optimization of excited energy states in frustrated quantum systems

Scientific paper - Original scientific paper

• Author: Tanja Đurić
• Author: Tomislav Ševa
• Author's institution: University of Zagreb; Faculty of Science; (Department of Physics)
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract (english)

We examine applicability of the valence bond basis correlator product state ansatz, equivalent to the
restricted Boltzmann machine quantum artificial neural-network ansatz, and variational Monte Carlo method for
direct optimization of excited energy states to study properties of strongly correlated and frustrated quantum
systems. The energy eigenstates are found by stochastic minimization of the variational function for the
energy eigenstates, which allows direct optimization of particular energy state without knowledge of the lower
energy states. This approach combined with numerous tensor network or artificial neural-network ansatz wave
functions then allows further insight into quantum phases and phase transitions in various strongly correlated
models by considering properties of these systems beyond the ground-state properties. Also, the method is in
general applicable to any dimension and has no sign instability. An example that we consider is the square
lattice J1-J2 antiferromagnetic Heisenberg model. The model is one of the most studied models in frustrated
quantum magnetism since it is closely related to the disappearance of the antiferromagnetic order in the high-Tc
superconducting materials and there is still no agreement about the properties of the system in the highly
frustrated regime near J2/J1 = 0.5. For the J1-J2 model, we write the variational ansatz in terms of the two site
correlators and in the valence bond basis and calculate the lowest energy eigenstates in the highly frustrated
regime near J2/J1 = 0.5 where the system has a paramagnetic phase. We find that our results are in good
agreement with previously obtained results, which confirms applicability of the method to study frustrated spin
systems.

• Language: english
• Publication type: Scientific paper - Original scientific paper
• Publication status: Published
• Peer review: Peer review - international
• Publication version: Published version
• Journal title: Physical Review B
• Numbering: vol. 102, no. 8, 085104
• p-ISSN: 2469-9950
• e-ISSN: 2469-9969
• DOI: https://doi.org/10.1103/PhysRevB.102.085104
• URN:NBN: urn:nbn:hr:217:984917
• Publication: 2020
• Project: Number: KK.01.1.1.01.0004; Title (croatian): Provedba vrhunskih istraživanja u sklopu Znanstvenog centra izvrsnosti za kvantne i kompleksne sustave te reprezentacije Liejevih algebri; Acronym: ZCI QuantiXLie; Leader: Hrvoje Buljan; Jurisdiction: Croatia; Funding stream: ZC
• Document URL: https://link.aps.org/doi/10.1103/PhysRevB.102.085104
• Type of resource: Text
• Access conditions: Open access
• Public note: © 2020 American Physical Society. Received 24 February 2020; revised 9 June 2020; accepted 7 July 2020; published 3 August 2020.
• Created on: 2020-09-19 20:20:15