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 quasilocal 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- <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mn>1</a:mn> <a:mo>/</a:mo> <a:mn>2</a:mn> </a:mrow> </a:math> Heisenberg, and spinful fermions with repulsive interactions. In particular, we showcase a nontrivial 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.