Topological phases with long-range interactions

TL;DR

This paper investigates the stability of topological phases in quantum spin chains with long-range interactions, revealing that frustration plays a crucial role in preserving topological order under such conditions.

Contribution

It demonstrates how frustration in long-range interactions can protect topological phases, extending understanding beyond short-range interaction models.

Findings

Non-frustrated long-range interactions can destroy topological phases for $\,\alpha\lesssim3$

Frustrated long-range interactions preserve topological phases for all $\,\alpha>0$

Results are supported by large-scale simulations and effective-field-theory calculations

Abstract

Topological phases of matter are primarily studied in systems with short-range interactions. In nature, however, non-relativistic quantum systems often exhibit long-range interactions. Under what conditions topological phases survive such interactions, and how they are modified when they do, is largely unknown. By studying the symmetry-protected topological phase of an antiferromagnetic spin-1 chain with $1/r^{\alpha}$ interactions, we show that two very different outcomes are possible, depending on whether or not the interactions are frustrated. While non-frustrated long-range interactions can destroy the topological phase for $\alpha\lesssim3$, the topological phase survives frustrated interactions for all $\alpha>0$. Our conclusions are based on strikingly consistent results from large-scale matrix-product-state simulations and effective-field-theory calculations, and we expect them to hold for more general interacting spin systems. The models we study can be naturally realized in trapped-ion quantum simulators, opening the prospect for experimental investigation of the issues confronted here.