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 nonlocal observables in a straightforward manner at the same modest computational cost as PP-FMFT—scaling as $O\left(N^3\right)$ 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 noninteracting spin-1/2 Hamiltonians. We then study the postquench dynamics of the one- and two-dimensional Ising model in the 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.

Close

PrevNext

View figure in article

• Spin dynamics
• Parity
• Mean field theory