Quantum criticality in the SO(5) bilinear-biquadratic Heisenberg chain

TL;DR

This paper investigates the zero-temperature phases and quantum criticality of the SO(5) bilinear-biquadratic Heisenberg chain, revealing a dimerized phase, a hidden symmetry gapped phase with edge states, and a critical point in the SO(5)$_1$ universality class.

Contribution

It provides the first detailed analysis of the phase diagram and critical behavior of the SO(5) bilinear-biquadratic Heisenberg chain, including the identification of a new gapped phase and the critical point's universality class.

Findings

The chain exhibits a dimerized ground state with two-fold degeneracy.

A non-degenerate gapped phase with hidden symmetry and edge states exists.

The quantum critical point belongs to the SO(5)$_1$ universality class.

Abstract

The zero-temperature properties of the SO(5) bilinear-biquadratic Heisenberg spin chain are investigated by means of a low-energy approach and large scale numerical calculations. In sharp contrast to the spin-1 SO(3) Heisenberg chain, we show that the SO(5) Heisenberg spin chain is dimerized with a two-fold degenerate ground state. On top of this gapful phase, we find the emergence of a non-degenerate gapped phase with hidden (Z$_2$ $\times$ Z$_2$)$^2$ symmetry and spin-3/2 edge states that can be understood from a SO(5) AKLT wave function. We derive a low-energy theory describing the quantum critical point which separates these two gapped phases. It is shown and confirmed numerically that this quantum critical point belongs to the SO(5)$_1$ universality class.