Emergent SU(N) symmetry in disordered SO(N) spin chains

TL;DR

This paper demonstrates that disordered SO(N) spin chains can exhibit emergent SU(N) symmetry with distinct ground states, universal scaling, and critical behavior, relevant for experimental systems.

Contribution

It reveals the emergence of SU(N) symmetry in disordered SO(N) spin chains and characterizes two distinct phases with universal properties.

Findings

Emergent SU(N) symmetry in disordered SO(N) chains

Identification of mesonic and baryonic phases

Universal temperature scaling and critical exponents

Abstract

Strongly disordered spin chains invariant under the SO(N) group are shown to display random-singlet phases with emergent SU(N) symmetry without fine tuning. The phases with emergent SU(N) symmetry are of two kinds: one has a ground state formed of randomly distributed singlets of strongly bound pairs of SO(N) spins (a `mesonic' phase), while the other has a ground state composed of singlets made out of strongly bound integer multiples of N SO(N) spins (a `baryonic' phase). The established mechanism is general and we put forward the cases of $\mathrm{N}=2,3,4$ and $6$ as prime candidates for experimental realizations in material compounds and cold-atoms systems. We display universal temperature scaling and critical exponents for susceptibilities distinguishing these phases and characterizing the enlarging of the microscopic symmetries at low energies.