Scalable implementations of mean-field and correlation methods based on Lie-algebraic similarity transformation of spin Hamiltonians in the Jordan-Wigner representation

TL;DR

This paper introduces scalable methods for simulating strongly correlated spin systems by combining Jordan-Wigner transformation with Lie-algebraic similarity transformations, enabling larger system analysis.

Contribution

It presents efficient implementations of mean-field and correlation methods based on LAST, allowing treatment of larger spin systems with improved accuracy.

Findings

Efficient gradient-based optimization for large clusters.

Size-extensive correlation energies achieved.

Applicable to systems with local spins s > 1/2.

Abstract

Recent work has highlighted that the strong correlation inherent in spin Hamiltonians can be effectively reduced by mapping spins to fermions via the Jordan-Wigner transformation (JW). The Hartree-Fock method is straightforward in the fermionic domain and may provide a reasonable approximation to the ground state. Correlation with respect to the fermionic mean-field can be recovered based on Lie-algebraic similarity transformation (LAST) with two-body correlators. Specifically, a unitary LAST variant eliminates the dependence on site ordering, while a non-unitary LAST yields size-extensive correlation energies. Whereas the first recent demonstration of such methods was restricted to small spin systems, we present efficient implementations using analytical gradients for the optimization with respect to the mean-field reference and the LAST parameters, thereby enabling the treatment of larger clusters, including systems with local spins s > 1/2.