Ground states of quasi-two-dimensional correlated systems via energy expansion

We introduce a generic method for computing groundstates that is applicable to a wide range of spatially anisotropic 2D many-body quantum systems. By representing the 2D system using a low-energy 1D basis set, we obtain an effective 1D Hamiltonian that only has quasi-local interactions, at the price of a large local Hilbert space. We apply our new method to three specific 2D systems of weakly coupled chains: hardcore bosons, a spin-$1/2$ Heisenberg Hamiltonian, and spinful fermions with repulsive interactions. In particular, we showcase a non-trivial application of the energy expansion framework, to the anisotropic triangular Heisenberg lattice, a highly challenging model related to 2D spin liquids. Treating lattices of unprecedented size, we provide evidence for the existence of a quasi-1D gapless spin liquid state in this system. We also demonstrate the energy expansion-framework to perform well where external validation is possible. For the fermionic benchmark in particular, we showcase the energy expansion-framework's ability to provide results of comparable quality at a small fraction of the resources required for previous computational efforts.