Random transverse-field Ising chain with long-range interactions

TL;DR

This paper investigates the critical behavior of a long-range disordered quantum spin chain, revealing a fixed point with a finite dynamical exponent and universal scaling properties, using strong-disorder renormalization group methods.

Contribution

It introduces a detailed analysis of the critical properties of the long-range random transverse-field Ising chain, highlighting the role of long-range interactions in quantum phase transitions.

Findings

Critical behavior governed by a fixed point with z_c=alpha

Correlation length diverges exponentially near criticality

Entanglement entropy obeys an area law at criticality

Abstract

We study the low-energy properties of the long-range random transverse-field Ising chain with ferromagnetic interactions decaying as a power alpha of the distance. Using variants of the strong-disorder renormalization group method, the critical behavior is found to be controlled by a strong-disorder fixed point with a finite dynamical exponent z_c=alpha. Approaching the critical point, the correlation length diverges exponentially. In the critical point, the magnetization shows an alpha-independent logarithmic finite-size scaling and the entanglement entropy satisfies the area law. These observations are argued to hold for other systems with long-range interactions, even in higher dimensions.