From continuum neural quantum states to effective lattice models: Fluctuating Wigner molecules in moiré superlattices
Year: 2026
Type: preprint
Abstract: Effective descriptions of quantum materials rely on a separation of energy scales that identifies their low-energy degrees of freedom. When kinetic energy, lattice potential, and interactions compete, this hierarchy breaks down, and both the microscopic state and its effective description are unknown. Continuum neural quantum states (NQS) can find the ground state directly without projecting onto prescribed bands, orbitals, or spins, but their microscopic wavefunctions are difficult to interpret in terms of effective variables. Here, we introduce a wavefunction readout that maps the continuum NQS onto site-resolved charge and spin statistics, allowing effective degrees of freedom to emerge from the microscopic solution. Focusing on moiré transition metal dichalcogenides at filling $ν= 3$, the NQS reveals a low-spin ground state below the ferromagnetic crystal of spin-polarized Wigner molecules. Although the charge density retains triangular molecular motifs, our readout reveals significant charge fluctuations through bound nearest-neighbor doublon--hole pairs. Each molecular charge state has an inert spin-singlet core and rim electrons that carry the spin. Charge and spin fluctuations are therefore intertwined, with antiferromagnetic spin-correlations between sites, motivating an effective description by a spinful two-orbital Hubbard model. More generally, our results demonstrate a route from continuum wavefunctions to effective lattice models when competing scales preclude a controlled reduction.
Source: arXiv (Cornell University)
Authors: Khalifa, Ahmed, Chatterjee, Shubhayu
Institution: Carnegie Mellon University
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G1117273162, G1453181110, Track 4: Advanced CI Coordination Ecosystem: Monitoring and Measurement Services, G3062527969, G3562386289, G3778588758, Track 1: ACCESS Resource Allocations Marketplace and Platform Services (RAMPS), G4010157413, ACO: An Open CI Ecosystem to Advance Scientific Discovery (OpenCI), Track 3: COre National Ecosystem for CyberinfrasTructure (CONECT), G5367127336, G5464919783, G5483133893, G8054376542, Track 2: Customized Multi-tier Assistance, Training, and Computational Help (MATCH) for End User ACCESS to CI
OpenAlex ID: W7221005819