Violation of the area law and long range correlations in infinite matrix product states

TL;DR

This paper introduces a new class of infinite matrix product states for 1D spin chains using bosonic operators, revealing violations of the area law and long-range correlations, with an experimental preparation method.

Contribution

It presents a novel construction of infinite-dimensional matrix product states that violate the area law and exhibit long-range correlations, along with an efficient experimental preparation scheme.

Findings

States violate the area law

States exhibit long-range correlations

Proposed sequential interaction preparation method

Abstract

We propose to construct a family of states of one-dimensional spin chains by replacing the finite dimensional matrices in matrix product states by infinite dimensional operators constructed from bosonic annihilation and creation operators. The resulting states are demonstrated to violate the area law and to exhibit long range correlations. In addition, we propose an efficient way to prepare the states experimentally, in which the spins interact sequentially with an ancilla system.