Quantum Entanglement In Inhomogeneous 1D Systems

TL;DR

This paper explores how inhomogeneity in 1D quantum systems affects entanglement entropy, revealing violations of the area law and connecting entanglement properties to curved space-time geometry.

Contribution

It provides a detailed analysis of entanglement in inhomogeneous 1D systems using renormalization group and conformal field theory approaches, linking entanglement to space-time curvature.

Findings

Inhomogeneity parameter tunes entanglement regimes.

Strong inhomogeneity leads to maximally entangled states described by RG.

Weak inhomogeneity relates to a thermo-field double state in curved space.

Abstract

The entanglement entropy of the ground state of a quantum lattice model with local interactions usually satisfies an area law. However, in 1D systems some violations may appear in inhomogeneous systems or in random systems. In our inhomogeneous system, the inhomogeneity parameter, $h$, allows us to tune different regimes where a volumetric violation of the area law appears. We apply the strong disorder renormalization group to describe the maximally entangled state of the system in a strong inhomogeneity regime. Moreover, in a weak inhomogeneity regime, we use a continuum approximation to describe the state as a thermo-field double in a conformal field theory with an effective temperature which is proportional to the inhomogeneity parameter of the system. The latter description also shows that the universal scaling features of this model are captured by a massless Dirac fermion in a curved space-time with constant negative curvature $R=-h^2$, providing another example of the relation between quantum entanglement and space-time geometry. The results we discuss here were already published before, but here we present a more didactic exposure of basic concepts of the rainbow system for the students attending the Latin American School of Physics Marcos Moshinsky 2017.