# Self-consistent theory of many-body localisation in a quantum spin chain with long-range interactions

## TL;DR

This paper develops a self-consistent mean-field theory to analyze many-body localisation in a disordered quantum spin chain with long-range interactions, revealing how interaction ranges affect localisation thresholds.

## Contribution

It introduces a novel self-consistent theoretical framework for many-body localisation in long-range interacting spin chains, supported by numerical diagnostics.

## Key findings

- Long-range transverse interactions hinder localisation.
- Long-range longitudinal interactions promote localisation.
- Critical disorder strength varies with interaction ranges.

## Abstract

Many-body localisation is studied in a disordered quantum spin-1/2 chain with long-ranged power-law interactions, and distinct power-law exponents for interactions between longitudinal and transverse spin components. Using a self-consistent mean-field theory centring on the local propagator in Fock space and its associated self-energy, a localisation phase diagram is obtained as a function of the power-law exponents and the disorder strength of the random fields acting on longitudinal spin-components. Analytical results are corroborated using the well-studied and complementary numerical diagnostics of level statistics, entanglement entropy, and participation entropy, obtained via exact diagonalisation. We find that increasing the range of interactions between transverse spin components hinders localisation and enhances the critical disorder strength. In marked contrast, increasing the interaction range between longitudinal spin components is found to enhance localisation and lower the critical disorder.