Regular Article

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

¹ Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA
² Department of Physics and National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32306, USA
³ Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
⁴ Département de Physique, Institut Quantique and Regroupement Québécois sur les Matériaux de Pointe, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada
⁵ Instituto de Física de São Carlos, Universidade de São Paulo, C.P. 369, São Carlos, SP 13560-970, Brazil
⁶ Instituto de Física Gleb Wataghin, Unicamp, Rua Sérgio Buarque de Holanda, 777, CEP 13083-859 Campinas, SP, Brazil

^a e-mail: hoyos@ifsc.usp.br

Received: 27 November 2019
Received in final form: 17 December 2019
Published online: 28 January 2020

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 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.