Sequentially generated states for the study of two dimensional systems

TL;DR

This paper introduces a new class of two-dimensional quantum states that extend Matrix Product States, enabling efficient evaluation of observables and suitable approximation of ground states in local Hamiltonians.

Contribution

It extends the concept of sequentially generated states from 1D to 2D, linking them to Projected Entangled Pair States and analyzing their properties.

Findings

Expectation values can be efficiently computed.

Correlation functions decay exponentially in translationally invariant systems.

States are suitable for approximating ground states of local Hamiltonians.

Abstract

Matrix Product States can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system. We introduce a new family of states which extends this definition to two dimensions. Like in Matrix Product States, expectation values of few body observables can be efficiently evaluated and, for the case of translationally invariant systems, the correlation functions decay exponentially with the distance. We show that such states are a subclass of Projected Entangled Pair States and investigate their suitability for approximating the ground states of local Hamiltonians.