Kaleidoscope of quantum phases in a long-range interacting spin-1 chain

TL;DR

This study explores how long-range interactions in a spin-1 chain influence its quantum phases, revealing the destruction of the Haldane phase and emergence of new phases, with potential experimental observation.

Contribution

It provides a comprehensive analysis of the phase diagram of a long-range interacting spin-1 chain, highlighting qualitative changes due to ferromagnetic long-range interactions.

Findings

Long-range interactions destroy the Haldane phase for $\alpha extless3$.

New phase spontaneously breaks a $U(1)$ symmetry.

Presence of an exotic tricritical point not seen in short-range chains.

Abstract

Motivated by recent trapped-ion quantum simulation experiments, we carry out a comprehensive study of the phase diagram of a spin-1 chain with XXZ-type interactions that decay as $1/r^{\alpha}$, using a combination of finite and infinite-size DMRG calculations, spin-wave analysis, and field theory. In the absence of long-range interactions, varying the spin-coupling anisotropy leads to four distinct phases: a ferromagnetic Ising phase, a disordered XY phase, a topological Haldane phase, and an antiferromagnetic Ising phase. If long-range interactions are antiferromagnetic and thus frustrated, we find primarily a quantitative change of the phase boundaries. On the other hand, ferromagnetic (non-frustrated) long-range interactions qualitatively impact the entire phase diagram. Importantly, for $\alpha\lesssim3$, long-range interactions destroy the Haldane phase, break the conformal symmetry of the XY phase, give rise to a new phase that spontaneously breaks a $U(1)$ continuous symmetry, and introduce an exotic tricritical point with no direct parallel in short-range interacting spin chains. We show that the main signatures of all five phases found could be observed experimentally in the near future.