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arXiv:2507.05073

Quantum Spin Glass in the Two-Dimensional Disordered Heisenberg Model via Foundation Neural-Network Quantum States

Luciano Loris Viteritti, Riccardo Rende, Giacomo Bracci-Testasecca, Jacopo Niedda, Roderich Moessner, Giuseppe Carleo, Antonello Scardicchio

Published Jul 7, 2025• 0 citations
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Abstract

We investigate the two-dimensional frustrated quantum Heisenberg model with bond disorder on nearest-neighbor couplings using the recently introduced Foundation Neural-Network Quantum States framework, which enables accurate and efficient computation of disorder-averaged observables with a single variational optimization. Simulations on large lattices reveal an extended region of the phase diagram where conventional magnetic long-range order vanishes in the thermodynamic limit, while the Edwards-Anderson order parameter remains finite, signaling the emergence of a quantum spin-glass phase. These findings, supported by a semiclassical analysis based on a large-spin expansion, provide compelling evidence that the spin glass-order is stable against quantum fluctuations, unlike the classical case where it disappears at any finite temperature.

DOI
10.48550/arxiv.2507.05073

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We investigate the two-dimensional frustrated quantum Heisenberg model with bond disorder on nearest-neighbor couplings using the recently introduced Foundation Neural-Network Quantum States framework, which enables accurate and efficient computation of disorder-averaged observables with a single variational optimization. Simulations on large lattices reveal an extended region of the phase diagram where conventional magnetic long-range order vanishes in the thermodynamic limit, while the Edwards-Anderson order parameter remains finite, signaling the emergence of a quantum spin-glass phase. These findings, supported by a semiclassical analysis based on a large-spin expansion, provide compelling evidence that the spin glass-order is stable against quantum fluctuations, unlike the classical case where it disappears at any finite temperature.
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The spin-1=2 Heisenberg model on the pyrochlore lattice is an iconic frustrated three-dimensional spin system with a rich phase diagram.Besides hosting several ordered phases, the model is debated to possess a spin-liquid ground state when only nearest-neighbor antiferromagnetic interactions are present.Here, we contest this hypothesis with an extensive numerical investigation using both exact diagonalization and complementary variational techniques.Specifically, we employ a resonating-valence-bond-like, manyvariable, Monte Carlo ansatz and convolutional neural network quantum states for (variational) calculations with up to 4 × 4 3 and 4 × 3 3 spins, respectively.We demonstrate that these techniques yield consistent results, allowing for reliable extrapolations to the thermodynamic limit.We consider the ðλ; j 2 =j 1 Þ parameter space, with j 2 , j 1 being nearest and next-to-nearest neighbor interactions and λ the XXZ interaction anisotropy.Our main results are (1) the determination of the phase transition between the putative spin-liquid phase and the neighboring magnetically ordered phase and (2) a careful characterization of the ground state in terms of symmetry-breaking tendencies.We find clear indications of a dimer order with spontaneously broken inversion and rotational symmetry, calling the scenario of a featureless quantum spin liquid into question.Our work showcases how many-variable variational techniques can be used to make progress in answering challenging questions about three-dimensional frustrated quantum magnets.
We uncover a new kind of entropic long range order in finite dimensional spin glasses. We study the link-diluted version of the Edwards–Anderson spin glass model with bimodal couplings ( J = ± 1) on a 3D lattice. By using exact reduction algorithms, we prove that there exists a region of the phase diagram (at zero temperature and low enough link density), where spins are long range correlated, even if the ground state energy stiffness is null. In other words, in this region twisting the boundary conditions costs no energy, but spins are long range correlated by means of pure entropic effects.
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