Generating Generalised Ground-State Ansatzes from Few-Body Examples

• URL: http://arxiv.org/abs/2503.00497v2
• Date: Thu, 24 Apr 2025 11:56:14 GMT
• Title: Generating Generalised Ground-State Ansatzes from Few-Body Examples
• Authors: Matt Lourens, Ilya Sinayskiy, Johannes N. Kriel, Francesco Petruccione,
• Abstract summary: We introduce a method that generates ground-state ansatzes for quantum many-body systems.<n>The ansatzes are analytically tractable and accurate over wide parameter regimes.<n>We demonstrate this method on the Lipkin-Meshkov-Glick model (LMG) and the quantum transverse-field Ising model (TFIM)
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a method that generates ground-state ansatzes for quantum many-body systems which are both analytically tractable and accurate over wide parameter regimes. Our approach leverages a custom symbolic language to construct tensor network states (TNS) via an evolutionary algorithm. This language provides operations that allow the generated TNS to automatically scale with system size. Consequently, we can evaluate ansatz fitness for small systems, which is computationally efficient, while favouring structures that continue to perform well with increasing system size. This ensures that the ansatz captures robust features of the ground state structure. Remarkably, we find analytically tractable ansatzes with a degree of universality, which encode correlations, capture finite-size effects, accurately predict ground-state energies, and offer a good description of critical phenomena. We demonstrate this method on the Lipkin-Meshkov-Glick model (LMG) and the quantum transverse-field Ising model (TFIM), where the same ansatz was independently generated for both. The simple structure of the ansatz allows us to restore broken symmetries and obtain exact expressions for the expectation values of local observables and correlation functions.

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