Variational Tensor Network Operator

TL;DR

This paper introduces a versatile variational tensor network operator framework for efficiently studying quantum spin systems, capable of capturing complex phases and phase transitions with minimal parameters.

Contribution

It presents a new, simple construction of tensor network operators that can accurately approximate ground states and identify quantum phases without gauge fixing.

Findings

Achieves accurate ground states with few parameters

Can identify symmetry breaking and topological phases

Detects quantum phase transitions universally

Abstract

We propose a simple and generic construction of the variational tensor network operators to study the quantum spin systems by the synergy of ideas from the imaginary-time evolution and variational optimization of trial wave functions. By applying these operators to simple initial states, accurate variational ground state wave functions with extremely few parameters can be obtained. Furthermore, the framework can be applied to study spontaneously symmetry breaking, symmetry protected topological, and intrinsic topologically ordered phases, and we show that symmetries of the local tensors associated with these phases can emerge directly after the optimization without any gauge fixing. This provides a universal way to identify quantum phase transitions without prior knowledge of the system.