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

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.