Entanglement entropy bounds for pure states of rapid decorrelation

TL;DR

This paper establishes area-law bounds for entanglement entropy in pure quantum states with rapid decorrelation, demonstrating exponential decay of mutual information and applying results to the quantum Ising model.

Contribution

It provides a new method to approximate states with low complexity and proves area-law bounds for entanglement entropy in a broad class of quantum systems.

Findings

High fidelity low-complexity approximations are constructed for decorrelated states.

Exponential decay of mutual information and clustering of local observables are demonstrated.

Area-law bounds on entanglement are established for the quantum Ising model's ground states.

Abstract

For pure states of multi-dimensional quantum lattice systems, which in a convenient computational basis have amplitude and phase structure of sufficiently rapid decorrelation, we construct high fidelity approximations of relatively low complexity. These are used for a conditional proof of area-law bounds for the states' entanglement entropy. The condition is also shown to imply exponential decay of the state's mutual information between disjoint regions, and hence exponential clustering of local observables. The applicability of the general results is demonstrated on the quantum Ising model in transverse field. Combined with available model-specific information on spin-spin correlations, we establish an area-law type bound on the entanglement in the model's subcritical ground states, valid in all dimensions and up to the model's quantum phase transition.