Fate of a Fractional Chern Insulator under Nonlocal Interactions in Synthetic Dimensions

TL;DR

This paper explores how nonlocal interactions in synthetic dimensions affect fractional Chern insulators, revealing an adiabatic transition to a charge-ordered state without gap closure, challenging traditional topological diagnostics.

Contribution

It demonstrates an adiabatic evolution between topologically distinct states in a synthetic dimension system with nonlocal interactions, highlighting the role of nonlocality in topological phases.

Findings

Adiabatic transition from fractional Chern insulator to charge-ordered state without gap closing.

Topological invariants remain unchanged despite entanglement spectrum restructuring.

Nonlocal interactions can interpolate between topological and charge-ordered regimes.

Abstract

Synthetic dimensions provide a powerful route to engineer topological lattice models in ultracold atomic systems, but they contain intrinsic nonlocal interactions along the synthetic direction. We investigate an extended Harper-Hofstadter model subject to infinite-range column interactions that mimic this synthetic nonlocality. By tuning this interaction strength, we demonstrate an adiabatic evolution from a Laughlin-type bosonic fractional Chern insulator to a charge-ordered Tao-Thouless-like state without closing the many-body gap. Along this path, the many-body Chern number and the topological entanglement entropy remain unchanged, despite a pronounced restructuring of the entanglement spectrum and the loss of robustness against local perturbations. This adiabatic connectivity establishes a controlled bridge between topologically ordered and effect- ively one-dimensional charge-ordered regimes, opening potential new avenues for state preparation. Our results also show that conventional topological markers may fail to diagnose the breakdown of locality-protected topological order in synthetic dimensions, and identify nonlocal interactions as a powerful knob to coherently interpolate between distinct many-body regimes.