# Long range interactions in antiferromagnetic quantum spin chains

## TL;DR

This paper investigates how long-range dipolar interactions influence antiferromagnetic spin chains across classical to quantum regimes, revealing phase transitions and the effects of fluctuations using various computational techniques.

## Contribution

It combines multiple methods to analyze the impact of long-range interactions on phase diagrams of antiferromagnetic chains from classical to quantum limits.

## Key findings

- Identifies a phase transition from dipolar ferromagnetic to antiferromagnetic regions.
- Shows thermal and quantum fluctuations destabilize classical order before saturation.
- Extensive DMRG confirms phases and shifts transition lines in the quantum limit.

## Abstract

We study the role of long range dipolar interactions on antiferromagnetic spin chains, from the classical $S\to \infty$ limit to the deep quantum case $S=1/2$, including a transverse magnetic field. To this end, we combine different techniques such as classical energy minima, classical Monte Carlo, linear spin waves, bosonization and DMRG. We find a phase transition from the already reported dipolar ferromagnetic region to an antiferromagnetic region for high enough antiferromagnetic exchange. Thermal and quantum fluctuations destabilize the classical order before reaching magnetic saturation in both phases, and also close to zero field in the antiferromagnetic phase. In the extreme quantum limit $S=1/2$, extensive DMRG computations show that the main phases remain present with transition lines to saturation significatively shifted to lower fields, in agreement with the bosonization analysis. The overall picture keeps close analogy with the phase diagram of the anisotropic XXZ spin chain in a transverse field.