Optimization at the boundary of the tensor network variety

TL;DR

This paper introduces a new tensor network ansatz class that includes boundary states of the tensor network variety, enabling more efficient ground state optimization for quantum many-body systems.

Contribution

It defines and demonstrates how to optimize over a boundary-inclusive tensor network class, improving efficiency in finding ground states.

Findings

Favorable energies compared to standard methods

Reduced runtimes in simulations

Effective in various quantum models

Abstract

Tensor network states form a variational ansatz class widely used, both analytically and numerically, in the study of quantum many-body systems. It is known that if the underlying graph contains a cycle, e.g. as in projected entangled pair states (PEPS), then the set of tensor network states of given bond dimension is not closed. Its closure is the tensor network variety. Recent work has shown that states on the boundary of this variety can yield more efficient representations for states of physical interest, but it remained unclear how to systematically find and optimize over such representations. We address this issue by defining a new ansatz class of states that includes states at the boundary of the tensor network variety of given bond dimension. We show how to optimize over this class in order to find ground states of local Hamiltonians by only slightly modifying standard algorithms and code for tensor networks. We apply this new method to a different of models and observe favorable energies and runtimes when compared with standard tensor network methods.