Continuum Neural Momentum Eigenstate for Variationally Solving Quasiparticles

• URL: http://arxiv.org/abs/2606.12928v2
• Date: Sun, 14 Jun 2026 17:19:40 GMT
• Title: Continuum Neural Momentum Eigenstate for Variationally Solving Quasiparticles
• Abstract summary: Our architecture, EVE, enables off-the-shelf VMC to solve for momentum-sector ground states.<n>We test EVE on 2D bosons with mutual $1/r$ interactions, finding that a single unified ansatz is capable of describing four qualitatively different states.<n>We analyze the roton's phase texture and find unexpected multi-particle phase strings.
• Score: 1.2891210250935148
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We design the first neural quantum state for continuum particles that, for any chosen allowed momentum $\mathbf{k}$, is by construction an exact eigenstate of total momentum with eigenvalue $\mathbf{k}$. Our architecture, EVE, enables off-the-shelf VMC to solve for momentum-sector ground states. We test EVE on 2D bosons with mutual $1/r$ interactions, finding that a single unified ansatz is capable of describing four qualitatively different states: superfluid, roton, crystal, and phonon. At different densities, we extract the underlying phase of matter from the dispersion's shape. At $r_s = 20.0$, we see the roton minimum at finite $k$ expected of a superfluid. At $r_s = 100.0$, we see striking zone folding indicative of crystalline order, with periodically spaced minima representing floating crystals connected by phonon arcs in between. Using density-density correlation functions, we confirm the phase diagnoses and probe the excitations' correlation structures. Finally, we analyze the roton's phase texture and find unexpected multi-particle phase strings, formed when several vortex dipoles merge, leaving two vortices connected by a phase slip.

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