Emergent SU(3) symmetry in random spin-1 chains

We show that generic SU(2)-invariant random spin-1 chains have phases with an emergent SU(3) symmetry. We map out the full zero-temperature phase diagram and identify two different phases: (i) a conventional random singlet phase (RSP) of strongly bound spin pairs (SU(3) "mesons") and (ii) an unconventional RSP of bound SU(3) "baryons", which are formed, in the great majority, by spin trios located at random positions. The emergent SU(3) symmetry dictates that susceptibilities and correlation functions of both dipolar and quadrupolar spin operators have the same asymptotic behavior.Comment: 5 pages plus 3-page Supplemental Material, 5 figures; published versio

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

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.Comment: 5 pages, 2 figures, Contribution to the Topical Issue "Recent Advances in the Theory of Disordered Systems", edited by Ferenc Igl\'oi and Heiko Riege

Highly-symmetric random one-dimensional spin models

The interplay of disorder and interactions is a challenging topic of condensed matter physics, where correlations are crucial and exotic phases develop. In one spatial dimension, a particularly successful method to analyze such problems is the strong-disorder renormalization group (SDRG). This method, which is asymptotically exact in the limit of large disorder, has been successfully employed in the study of several phases of random magnetic chains. Here we develop an SDRG scheme capable to provide in-depth information on a large class of strongly disordered one-dimensional magnetic chains with a global invariance under a generic continuous group. Our methodology can be applied to any Lie-algebra valued spin Hamiltonian, in any representation. As examples, we focus on the physically relevant cases of SO(N) and Sp(N) magnetism, showing the existence of different randomness-dominated phases. These phases display emergent SU(N) symmetry at low energies and fall in two distinct classes, with meson-like or baryon-like characteristics. Our methodology is here explained in detail and helps to shed light on a general mechanism for symmetry emergence in disordered systems.Comment: 26 pages, 12 figure