Duality and ground-state phase diagram for the quantum XYZ model with arbitrary spin $s$ in one spatial dimension

TL;DR

This paper uncovers five duality transformations in the quantum XYZ model with arbitrary spin in one dimension, simplifying the ground-state phase diagram and identifying critical points with specific conformal charges.

Contribution

It introduces a set of five duality transformations that reduce the complexity of the phase diagram for the quantum XYZ model with arbitrary spin.

Findings

Phase diagram reduces to two principal regimes via dualities.

Critical points with central charge c=1 are self-dual.

Presence of Haldane phase leads to additional critical lines with c=1/2.

Abstract

Five duality transformations are unveiled for the quantum XYZ model with arbitrary spin $s$ in one spatial dimension. The presence of these duality transformations drastically reduces the entire ground-state phase diagram to two {\it finite} regimes - the principal regimes, with all the other ten regimes dual to them. Combining with the determination of critical points from the conventional order parameter approach and/or the fidelity approach to quantum phase transitions, we are able to map out the ground-state phase diagram for the quantum XYZ model with arbitrary spin $s$. This is explicitly demonstrated for $s=1/2,1,3/2$ and 2. As it turns out, all the critical points, with central charge $c=1$, are self-dual under a respective duality transformation for half-integer as well as integer spin $s$. However, in the latter case, the presence of the so-called symmetry protected topological phase, i.e., the Haldane phase, results in extra lines of critical points with central charge $c=1/2$, which is not self-dual under any duality transformation.