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Transformer Wave Function for two dimensional frustrated magnets: emergence of a Spin-Liquid Phase in the Shastry-Sutherland Model

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arxiv 2311.16889 v4 pith:QVRFUJ4R submitted 2023-11-28 cond-mat.str-el cond-mat.dis-nn

Luciano Loris Viteritti , Riccardo Rende , Alberto Parola , Sebastian Goldt , Federico Becca This is my paper
classification cond-mat.str-elcond-mat.dis-nn
keywords propertiesfrustratedansatzcompetingevidenceground-statehighlymagnets
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abstract

Understanding quantum magnetism in two-dimensional systems represents a lively branch in modern condensed-matter physics. In the presence of competing super-exchange couplings, magnetic order is frustrated and can be suppressed down to zero temperature. Still, capturing the correct nature of the exact ground state is a highly complicated task, since energy gaps in the spectrum may be very small and states with different physical properties may have competing energies. Here, we introduce a variational Ansatz for two-dimensional frustrated magnets by leveraging the power of representation learning. The key idea is to use a particular deep neural network with real-valued parameters, a so-called Transformer, to map physical spin configurations into a high-dimensional feature space. Within this abstract space, the determination of the ground-state properties is simplified and requires only a shallow output layer with complex-valued parameters. We illustrate the efficacy of this variational Ansatz by studying the ground-state phase diagram of the Shastry-Sutherland model, which captures the low-temperature behavior of SrCu$_2$(BO$_3$)$_2$ with its intriguing properties. With highly accurate numerical simulations, we provide strong evidence for the stabilization of a spin-liquid between the plaquette and antiferromagnetic phases. In addition, a direct calculation of the triplet excitation at the $\Gamma$ point provides compelling evidence for a gapless spin liquid. Our findings underscore the potential of Neural-Network Quantum States as a valuable tool for probing uncharted phases of matter, and open up new possibilities for establishing the properties of many-body systems.

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Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. New non-Euclidean neural quantum states from hyperbolic Lorentz recurrent architectures

    quant-ph 2026-04 unverdicted novelty 7.0 of 10

    Hyperbolic RNN and GRU neural quantum states outperform Euclidean versions on Heisenberg J1J2 and J1J2J3 models with 100 spins.

  2. Quantum spin liquid phase in the Shastry-Sutherland model revealed by high-precision infinite projected entangled-pair states

    cond-mat.str-el 2025-02 conditional novelty 7.0 of 10

    iPEPS simulations with bond-dimension extrapolation locate a quantum spin liquid phase in the Shastry-Sutherland model for 0.785(5) ≤ J'/J ≤ 0.82(1).

  3. Graph-Theoretic Analysis of Phase Optimization Complexity in Variational Wave Functions for Heisenberg Antiferromagnets

    cond-mat.str-el 2026-02 accept novelty 6.0 of 10

    Ground-state phase reconstruction for Heisenberg antiferromagnets with fixed amplitudes is equivalent to weighted Max-Cut on the Hilbert-space graph, establishing worst-case NP-hardness.

  4. Exact ground state on the 3D analogue of the Shastry-Sutherland model

    cond-mat.str-el 2025-07 conditional novelty 6.0 of 10

    A 3D deformation of the pyrochlore lattice is shown to have an exact dimer-singlet ground state for J2 >= 2 in the quantum spin-1/2 model, with classical phase diagrams matching the 2D Shastry-Sutherland results.

  5. New non-Euclidean neural quantum states from hyperbolic Lorentz recurrent architectures

    quant-ph 2026-04 conditional novelty 5.0 of 10

    On 100-site Heisenberg J1-J2 and J1-J2-J3 chains, hyperbolic Poincaré/Lorentz RNN and GRU neural quantum states mostly beat Euclidean counterparts; Lorentz RNN wins four of eight settings despite about three times few...

  6. New non-Euclidean neural quantum states from hyperbolic Lorentz recurrent architectures

    quant-ph 2026-04 conditional novelty 5.0 of 10

    Hyperbolic recurrent networks, especially a Lorentz-model RNN, reach lower variational ground-state energies than Euclidean RNN/GRU wavefunctions on 100-spin Heisenberg chains, with up to three times fewer parameters.

  7. Time-dependent Neural Galerkin Method for Quantum Dynamics

    quant-ph 2024-12 unverdicted novelty 5.0 of 10

    Presents a Neural Galerkin method that solves quantum dynamics globally via variational minimization of a Schrödinger loss, demonstrated on 1D/2D transverse-field Ising quenches showing non-thermalization in 2D.

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