# 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.

## Key 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.