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 of providing 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 into 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.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 of providing 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 into 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.

arXiv:1711.04783Physical review. B./Physical review. BDec 6, 20199 citations

Emergent symmetries in disordered quantum spin systems

Victor L. Quito, Pedro L. S. Lopes, José A. Hoyos +1 more

Bulletin of the American Physical SocietyMar 15, 20170 citations

SO( $n$ ) Affleck-Kennedy-Lieb-Tasaki states as conformal boundary states of integrable SU( $n$ ) spin chainsSO($n$) Affleck-Kennedy-Lieb-Tasaki states as conformal boundary states of integrable SU($n$) spin chains

Yueshui Zhang, Ying-Hai Wu, Meng Cheng +1 more

We construct a class of conformal boundary states in the \mathrm{SU}(n)_1 S U ( n ) 1 Wess-Zumino-Witten (WZW) conformal field theory (CFT) using the symmetry embedding \mathrm{Spin}(n)_2 \subset \mathrm{SU}(n)_1 S p i n ( n ) 2 ⊂ S U ( n ) 1 . These boundary states are beyond the standard Cardy construction and possess \mathrm{SO}(n) S O ( n ) symmetry. The \mathrm{SU}(n) S U ( n ) Uimin-Lai-Sutherland (ULS) spin chains, which realize the \mathrm{SU}(n)_1 S U ( n ) 1 WZW model on the lattice, allow us to identify these boundary states as the ground states of the \mathrm{SO}(n) S O ( n ) Affleck-Kennedy-Lieb-Tasaki spin chains. Using the integrability of the \mathrm{SU}(n) S U ( n ) ULS model, we analytically compute the corresponding Affleck-Ludwig boundary entropy using exact overlap formulas. Our results unveil intriguing connections between exotic boundary states in CFT and integrable lattice models, thus providing deep insights into the interplay of symmetry, integrability, and boundary critical phenomena.We construct a class of conformal boundary states in the \mathrm{SU}(n)_1 S U ( n ) 1 Wess-Zumino-Witten (WZW) conformal field theory (CFT) using the symmetry embedding \mathrm{Spin}(n)_2 \subset \mathrm{SU}(n)_1 S p i n ( n ) 2 ⊂ S U ( n ) 1 . These boundary states are beyond the standard Cardy construction and possess \mathrm{SO}(n) S O ( n ) symmetry. The \mathrm{SU}(n) S U ( n ) Uimin-Lai-Sutherland (ULS) spin chains, which realize the \mathrm{SU}(n)_1 S U ( n ) 1 WZW model on the lattice, allow us to identify these boundary states as the ground states of the \mathrm{SO}(n) S O ( n ) Affleck-Kennedy-Lieb-Tasaki spin chains. Using the integrability of the \mathrm{SU}(n) S U ( n ) ULS model, we analytically compute the corresponding Affleck-Ludwig boundary entropy using exact overlap formulas. Our results unveil intriguing connections between exotic boundary states in CFT and integrable lattice models, thus providing deep insights into the interplay of symmetry, integrability, and boundary critical phenomena.

arXiv:2508.13114SciPost PhysicsMar 2, 20261 citation

The ordering of energy levels for su(n) symmetric antiferromagnetic chains

Tigran Hakobyan

arXiv:cond-mat/0403587Nuclear Physics BAug 14, 200413 citations

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 into 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.

SO(

n

) Affleck-Kennedy-Lieb-Tasaki states as conformal boundary states of integrable SU(

n

) spin chains