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arXiv:2609.40209

Designing Strongly Correlated Quantum Phases of Matter with Foundation Neural-Network Quantum States

Alessandro Sinibaldi, Luciano Loris Viteritti, Riccardo Rende, Federico Becca, Giuseppe Carleo

Published Sep 30, 2026• 0 citations
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Abstract

Materials design is an inverse problem: finding the couplings of a microscopic Hamiltonian whose ground state exhibits a desired property. For strongly correlated quantum systems, this remains largely out of reach, as each candidate Hamiltonian requires its own costly simulation. Here we show that Foundation Neural-Network Quantum States, single wave functions that encode the ground states of an entire family of Hamiltonians, make this search efficient. Because the Hamiltonian couplings enter as neural-network inputs, any ground-state property can be optimized by gradient descent directly in coupling space. We use this approach to search for nonmagnetic phases in two-dimensional spin models in coupling spaces of increasing dimensionality. Specifically, we focus on quantum spin liquids, exotic phases of matter in which quantum fluctuations prevent magnetic order at zero temperature. In the largest search space considered, spanned by eight superexchange couplings and containing many paradigmatic frustrated spin systems, the optimization converges to the $J_1$-$J_2$-$δ$ Heisenberg model when starting from a magnetic phase. We show that the ground state at the optimum set of couplings has neither magnetic nor valence-bond order in the thermodynamic limit, leading to a new quantum spin-liquid candidate. The approach is completely general and can be extended to other models and physical properties to optimize, demonstrating that Neural-Network Quantum States are tools not only for simulating quantum matter but also for designing it.

DOI
10.48550/arxiv.2609.40209

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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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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 (GCNNs) that allow us to impose space-group symmetries on our ansätze. We achieve state-of-the-art ground-state energies for the J1−J2J_1-J_2J1​−J2​ 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.
Simulating strongly correlated quantum materials often involves not a single Hamiltonian, but a family of Hamiltonians whose ground states evolve across experimentally tunable couplings. Foundation neural quantum states (FNQS) offer a promising route to amortizing many-body calculations across such families, but can lose accuracy near phase transitions and still incur non-negligible sampling costs that grow with the number of target couplings. We introduce the Foundation Neural Effective Hamiltonian (FNEH), which projects a Hamiltonian family onto a compact subspace spanned by FNQS sampled at selected couplings. By variationally combining FNQS across parameter space, FNEH systematically improves their ground-state approximation and can recover phase boundaries that the foundation model misidentifies. Once the required operator matrix elements are sampled, FNEH enables sweeps over couplings, observables, and phase boundaries at a cost governed by the small effective-Hamiltonian dimension, without repeated neural-network sampling at every target coupling. We demonstrate FNEH in strongly correlated moiré materials, where it accurately resolves competing phases, enables high-resolution multidimensional phase scans, and substantially reduces the computational cost of exploring many target Hamiltonians. The results open a new avenue for studying strongly correlated quantum materials with foundation models.
Many-body quantum mechanics is the fundamental theory behind many areas of modern science, such as condensed-matter physics, nuclear physics, and quantum chemistry. It is also notoriously hard: the classical picture of particles with well-defined positions and velocities is replaced by an intricate interference pattern between all their possible trajectories, captured by the quantum wave function. The exponentially large information content of wave functions makes direct simulation of large, strongly interacting quantum systems impossible, and necessitates strategies to manage the complexity in an analytically or computationally tractable manner. The bulk of this thesis explores two such strategies in the context of quantum spin liquids. In these materials, competition between incompatible interactions results in robust, massive entanglement, down to zero temperature. Such ground states give rise to a range of exotic behaviour, such as topological order and fractionalised excitations: understanding these is a central challenge in the physics of strongly correlated materials. Several quantum-spin-liquid phases are underpinned by strict local conservation laws, which give rise to lattice gauge theories with exotic quasiparticle excitations, such as emergent photons or magnetic monopoles. We developed a systematic approach, based on a large-S bosonisation formalism, to extract gauge-theoretic descriptions from such constrained Hamiltonians automatically, and thus make them amenable to the powerful techniques of quantum field theory. The same field theories also allow us to simulate quantum-spin-liquid systems semiclassically, that is, to replace spin-1/2 operators with classical ``compass needles,'' removing the computational complexity of quantum entanglement without losing the physical behaviour. We demonstrated this approach on quantum spin ice, a paradigmatic and experimentally relevant model of quantum spin liquids and, by simulating it on unprecedented large system sizes, obtained novel insights about its quasiparticles. The success of neural networks in a range of machine-learning problems makes them a natural candidate for representing highly entangled quantum states, allowing in principle an accurate simulation of large, challenging quantum systems with modest computational resources. However, most current approaches using such neural quantum states suffer from the infamous Monte-Carlo sign problem, making deep neural networks unable to learn ground states in antiferromagnetic and fermionic systems. We studied the possible origins of this sign problem and proposed a neural-network ansatz that is able to overcome the sign problem for unfrustrated antiferromagnets. In addition to this main theme, I have been part of an experiment--theory collaboration on understanding the unique magnetoresistance properties of the classical frustrated magnet Ho2Ir2O7. We discovered a mechanism by which antiferromagnetic domains can be coupled to an external magnetic field via an intercalated spin-ice system: such control is highly desirable for spintronics applications. We have also identified scattering channels through which magnetic monopoles give rise to a significant contribution to the resistivity of Ho2Ir2O7: this allows us to directly measure their density in a simple and flexible experiment. Finally, I report studies on the localisation properties of quasicrystals; namely, the discovery of thermodynamic universality not described by the usual power laws in one-dimensional quasiperiodic models, and of a two-dimensional quasicrystal in which localised and partially extended states coexist without a mobility edge.
Quantum simulation provides a powerful route for exploring many-body phenomena beyond the capabilities of classical computation. Existing approaches typically proceed in the forward direction: a model Hamiltonian is specified, implemented on a programmable quantum platform, and its phase diagram and properties are explored. Here we present a quantum algorithmic framework for inverse quantum simulation, enabling quantum material design with desired properties. Target material characteristics are encoded as a cost function, which is minimized on quantum hardware to prepare a many-body state with the desired properties in quantum memory. Hamiltonian learning is then used to reconstruct a low-energy Hamiltonian for which this state is an approximate ground state, yielding a physically interpretable model that can guide experimental synthesis. As illustrative applications, we outline how the method can be used to search for high-temperature superconductors within the fermionic Hubbard model, enhancing ddd-wave correlations over a broad range of dopings and temperatures, design quantum phases by stabilizing a topological order through continuous Hamiltonian modifications, and optimize dynamical properties relevant for photochemistry and frequency- and momentum-resolved condensed-matter data. These results extend the scope of quantum simulators from exploring quantum many-body systems to designing and discovering new quantum materials.