Quantum simulation of general spin-1/2 Hamiltonians with parity-violating fermionic Gaussian states

• URL: http://arxiv.org/abs/2601.13811v1
• Date: Tue, 20 Jan 2026 10:09:29 GMT
• Title: Quantum simulation of general spin-1/2 Hamiltonians with parity-violating fermionic Gaussian states
• Authors: Michael Kaicher, Joseph Vovrosh, Alexandre Dauphin, Simon B. Jäger,
• Abstract summary: We introduce equations of motion for a parity-violating fermionic mean-field theory (PV-FMFT)<n>PV-FMFT is a numerically efficient fermionic mean-field theory based on parity-violating fermionic states (PV-FGS)<n>We demonstrate that PV-FMFT can exactly capture the imaginary- and real-time dynamics of non-interacting spin-1/2 Hamiltonians.
• Score: 39.146761527401424
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce equations of motion for a parity-violating fermionic mean-field theory (PV-FMFT): a numerically efficient fermionic mean-field theory based on parity-violating fermionic Gaussian states (PV-FGS). This work provides explicit equations of motion for studying the real- and imaginary-time evolution of spin-1/2 Hamiltonians with arbitrary geometries and interactions. We extend previous formulations of parity-preserving fermionic mean-field theory (PP-FMFT) by including fermionic displacement operators in the variational Ansatz. Unlike PP-FMFT, PV-FMFT can be applied to general spin-1/2 Hamiltonians, describe quenches from arbitrary initial spin-1/2 product states, and compute local and non-local observables in a straight-forward manner at the same modest computational cost as PP-FMFT -- scaling as $O(N^3)$ in the worst case for a system of $N$ spins or fermionic modes. We demonstrate that PV-FMFT can exactly capture the imaginary- and real-time dynamics of non-interacting spin-1/2 Hamiltonians. We then study the post quench-dynamics of the one- and two-dimensional Ising model in presence of longitudinal and transversal fields with PV-FMFT and compute the single site magnetization and correlation functions, and compare them against results from other state-of-the-art numerical approaches. In two-dimensional spin systems, we show that the employed spin-to-fermion mapping can break rotational symmetry within the PV-FMFT description, and we discuss the resulting consequences for the calculated correlation functions. Our work introduces PV-FMFT as a benchmark for other numerical techniques and quantum simulators, and it outlines both its capabilities and its limitations.

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