New Approaches to Tensor Network Simulation of 2D Quantum Systems

Accessing generic many-body quantum ground states in two full dimensions remains an outstanding problem in numerical condensed matter physics. Quantum Monte Carlo suffers from the sign problem, exact diagonalization cannot access large systems, DMRG struggles to reach beyond quasi-1D ladders, and many existing 2D tensor network approaches still have much room for improvement in terms of computational costs and numerical stability. We develop a PEPS approach, inspired by successful DMRG methods in one spatial dimension, which has much better performance than DMRG while retaining many of its advantages. We discuss the benefits and some drawbacks of the method, and we present some preliminary successes in fully two dimensional simulations with an eye to working towards simulating models on the frontier of numerical and analytical understanding.