High-accuracy variational Monte Carlo for frustrated magnets with deep neural networks - INSPIRE

DataBETA

High-accuracy variational Monte Carlo for frustrated magnets with deep neural networks

Nov 14, 2022

12 pages

Published in:

Phys.Rev.B 108 (2023) 5, 054410

Published: Aug 1, 2023

e-Print:

2211.07749 [cond-mat.str-el]

DOI:

10.1103/PhysRevB.108.054410 (publication)

View in:

ADS Abstract Service

reference search41 citations

Citations per year

Abstract: (APS)

We show that neural quantum states based on very deep (4–16-layered) neural networks can outperform state-of-the-art variational approaches on highly frustrated quantum magnets, including quantum-spin-liquid candidates. We focus on group convolutional neural networks that allow us to efficiently impose space-group symmetries on our ansätze. We achieve state-of-the-art ground-state energies for the

J_{1} - J_{2}

Heisenberg models on the square and triangular lattices, in both ordered and spin-liquid phases, and discuss ways to access low-lying excited states in nontrivial symmetry sectors. We also compute spin and dimer correlation functions for the quantum paramagnetic phase on the triangular lattice, which do not indicate either conventional or valence-bond ordering.

Note:

12 pages, 8 figures

References(79)

Figures(8)

[1]

Spin liquids in frustrated magnets

Leon Balents

- Nature 464 (2010) 7286, 199-208
•
DOI:
- 10.1038/nature08917

[2]

Quantum spin liquids: a review

- Rept.Prog.Phys. 80 (2017) 1, 016502
•
e-Print:
- 1601.03742
•
DOI:
- 10.1088/0034-4885/80/1/016502

[3]

Fault tolerant quantum computation by anyons

A.Yu. Kitaev
(
- Landau Inst.
)

- Annals Phys. 303 (2003) 2-30
•
e-Print:
- quant-ph/9707021
•
DOI:
- 10.1016/S0003-4916(02)00018-0

[4]

Anyons in an exactly solved model and beyond

Alexei Kitaev
(
- Caltech, Pasadena (main)
)

- Annals Phys. 321 (2006) 1, 2-111
•
e-Print:
- cond-mat/0506438
•
DOI:
- 10.1016/j.aop.2005.10.005

[5]

Pyrochlore photons: The U (1) spin liquid in a S=12 three-dimensional frustrated magnet

Michael Hermele
(
- UC, Santa Barbara
)
,
Matthew P.A. Fisher
(
- UC, Santa Barbara
)
,
Leon Balents
(
- UC, Santa Barbara
)

- Phys.Rev.B 69 (2004) 064404
•
e-Print:
- cond-mat/0305401
•
DOI:
- 10.1103/PhysRevB.69.064404

[6]

Direct evidence for a gapless Z2 spin liquid by frustrating Néel antiferromagnetism

W.-J. Hu
,
F. Becca
,
A. Parola
,
S. Sorella

- Phys.Rev.B 88 (2013) 060402
•
DOI:
- 10.1103/PhysRevB.88.060402

[7]

Dirac-Type Nodal Spin Liquid Revealed by Refined Quantum Many-Body Solver Using Neural-Network Wave Function, Correlation Ratio, and Level Spectroscopy

- Phys.Rev.X 11 (2021) 3, 031034
•
e-Print:
- 2005.14142
•
DOI:
- 10.1103/PhysRevX.11.031034

[8]

Gapless quantum spin liquid and global phase diagram of the spin-1/2 $J_1$ - $J_2$ square antiferromagnetic Heisenberg model

Wen-Yuan Liu
(
- Hong Kong, Chinese U.
)
,
Shou-Shu Gong
(
- Beihang U.
)
,
Yu-Bin Li
(
- Hong Kong, Chinese U.
)
,
Didier Poilblanc
(
- LPT, Toulouse
)
,
Wei-Qiang Chen
(
- SUSTech, Shenzhen and
- SUSTech, SKLQSE, Shenzhen
)

et al.

- Sci.Bull. 67 (2022) 1034-1041,
- Science Bulletin (2022)
•
e-Print:
- 2009.01821
•
DOI:
- 10.1016/j.scib.2022.03.010

[9]

Emergence of Gapless Quantum Spin Liquid from Deconfined Quantum Critical Point

Wen-Yuan Liu
(
- Hong Kong, Chinese U.
)
,
Juraj Hasik
(
- LPT, Toulouse
)
,
Shou-Shu Gong
(
- Beihang U.
)
,
Didier Poilblanc
(
- LPT, Toulouse
)
,
Wei-Qiang Chen
(
- SUSTech, Shenzhen
)

et al.

- Phys.Rev.X 12 (2022) 3, 031039,
- PhysRevX.12.031039 (2022)
•
e-Print:
- 2110.11138
•
DOI:
- 10.1103/PhysRevX.12.031039

[10]

Spin liquid nature in the Heisenberg

Y. Iqbal
,
W.-J. Hu
,
R. Thomale
,
D. Poilblanc
,
F. Becca

- Phys.Rev.B 93 (2016) 144411
•
DOI:
- 10.1103/PhysRevB.93.144411

[11]

Dirac Spin Liquid on the Spin-1/2 Triangular Heisenberg Antiferromagnet

S. Hu
,
W. Zhu
,
S. Eggert
,
Y.-C. He

- Phys.Rev.Lett. 123 (2019) 207203
•
DOI:
- 10.1103/PhysRevLett.123.207203

[12]

Chiral spin liquid and quantum criticality in extended S=12 Heisenberg models on the triangular lattice

- Phys.Rev.B 95 (2017) 3, 035141
•
e-Print:
- 1604.07829
•
DOI:
- 10.1103/PhysRevB.95.035141

[13]

Spin-Liquid Ground State of the S = 1/2 Kagome Heisenberg Antiferromagnet

S. Yan
(
- UC, Irvine
)
,
D.A. Huse
(
- Princeton U. and
- Princeton, Inst. Advanced Study
)
,
S.R. White
(
- UC, Irvine
)

- Science 332 (2011) 6034, 1173-1176
•
e-Print:
- 1011.6114
•
DOI:
- 10.1126/science.1201080

[14]

Nature of the Spin-Liquid Ground State of the S = 1/2 Heisenberg Model on the Kagome Lattice

S. Depenbrock
,
I.P. McCulloch
,
U. Schollwöck

- Phys.Rev.Lett. 109 (2012) 067201
•
DOI:
- 10.1103/PhysRevLett.109.067201

[15]

Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet

Y. Iqbal
,
F. Becca
,
S. Sorella
,
D. Poilblanc

- Phys.Rev.B 87 (2013) 060405
•
DOI:
- 10.1103/PhysRevB.87.060405

[16]

Signatures of Dirac Cones in a DMRG Study of the Kagome Heisenberg Model

- Phys.Rev.X 7 (2017) 3, 031020
•
e-Print:
- 1611.06238
•
DOI:
- 10.1103/PhysRevX.7.031020

[17]

The S = 1/2 kagome Heisenberg antiferromagnet revisited

A.M. Läuchli
,
J. Sudan
,
R. Moessner

- Phys.Rev.B 100 (2019) 155142
•
DOI:
- 10.1103/PhysRevB.100.155142

[18]

Pinch-points to half-moons and up in the stars: The kagome skymap

D. Kiese
,
F. Ferrari
,
N. Astrakhantsev
,
N. Niggemann
,
P. Ghosh

et al.

- Phys.Rev.Res. 5 (2023) L012025
•
DOI:
- 10.1103/PhysRevResearch.5.L012025

[19]

Chiral Spin Liquid Phase of the Triangular Lattice Hubbard Model: A Density Matrix Renormalization Group Study

- Phys.Rev.X 10 (2020) 2, 021042
•
e-Print:
- 1808.00463
•
DOI:
- 10.1103/PhysRevX.10.021042

[20]

Ground-state phase diagram of the quantum J_{1}-J_{2} model on the square lattice

Fabio Mezzacapo
(
- Munich, Max Planck Inst. Quantenopt.
)

- Phys.Rev.B 86 (2012) 4, 045115
•
e-Print:
- 1203.6381
•
DOI:
- 10.1103/PhysRevB.86.045115

[21]

Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations

Matthias Troyer
(
- Zurich, ETH
)
,
Uwe-Jens Wiese
(
- Bern U.
)

- Phys.Rev.Lett. 94 (2005) 170201
•
e-Print:
- cond-mat/0408370
•
DOI:
- 10.1103/PhysRevLett.94.170201

[22]

A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States

Roman Orus
(
- Mainz U., Inst. Phys.
)

- Annals Phys. 349 (2014) 117-158
•
e-Print:
- 1306.2164
•
DOI:
- 10.1016/j.aop.2014.06.013

[23]

Studying two-dimensional systems with the density matrix renormalization group

E.M. Stoudenmire
,
S.R. White

- Ann.Rev.Condensed Matter Phys. 3 (2012) 111
•
DOI:
- 10.1146/annurev-conmatphys-020911-125018

[24]

Solving the quantum many-body problem with artificial neural networks

Giuseppe Carleo
(
- Zurich, ETH
)
,
Matthias Troyer
(
- Zurich, ETH and
- Microsoft, Redmond
)

- Science 355 (2017) 6325, 602-606
•
DOI:
- 10.1126/science.aag2302

[25]

Multilayer feedforward networks are universal approximators

- Neural Networks 2 359-366,
- Neural Networks 2 (1989) 5, 359-366
•
DOI:
- 10.1016/0893-6080(89)90020-8

1-25 of 79
1
2
3
4
25 / page