A class of exactly solvable SO(n) symmetric spin chains

We introduce a class of exactly solvable $SO(n)$ symmetric Hamiltonians with matrix product ground states. For an odd $n\ensuremath{\ge}3$ case, the ground state is a translational invariant Haldane gap spin liquid state; while for an even $n\ensuremath{\ge}4$ case, the ground state is a spontaneously dimerized state with twofold degeneracy. In the matrix product ground states for both cases, we identify a hidden antiferromagnetic order, which is characterized by nonlocal string order parameters. The ground-state phase diagram of a generalized $SO(n)$ symmetric bilinear-biquadratic model is discussed.We introduce a class of exactly solvable $SO(n)$ symmetric Hamiltonians with matrix product ground states. For an odd $n\ensuremath{\ge}3$ case, the ground state is a translational invariant Haldane gap spin liquid state; while for an even $n\ensuremath{\ge}4$ case, the ground state is a spontaneously dimerized state with twofold degeneracy. In the matrix product ground states for both cases, we identify a hidden antiferromagnetic order, which is characterized by nonlocal string order parameters. The ground-state phase diagram of a generalized $SO(n)$ symmetric bilinear-biquadratic model is discussed.

arXiv:0806.1839Physical Review BSep 8, 200896 citations

The exactly solvable spin Sutherland model of BN type and its related spin chain

B. Basu-Mallick, Federico Finkel, Artemio González-López

arXiv:1207.5941Nuclear Physics BSep 17, 201211 citations

Phase transitions in coupled Ising chains and SO( N )-symmetric spin chains

Anonymous, Sylvain Capponi, Lukas Devos +1 more

We investigate the nature of quantum phase transitions in a (1+1)-dimensional field theory composed of $N$ copies of the Ising conformal field theory interacting via competing relevant perturbations. The field theory governs the competition between a mass term and an interaction involving the product of $N$ order-parameter fields, which is realized, e.g. in coupled Ising chains, two-leg spin ladders, and SO( $N$ )-symmetric spin chains. By combining a perturbative renormalization group analysis and large-scale matrix-product state simulations, we systematically determine the nature of the phase transition as a function of $N$ . For $N=2$ and $N=3$ , we confirm that the transition is continuous, belonging to the Ising and four-state Potts universality classes, respectively. In contrast, for $N \ge 4$ , our results provide compelling evidence that the transition becomes first order. We further apply these findings to specific lattice models with SO( $N$ ) symmetry, including spin- $1/2$ and spin- $1$ two-leg ladders, that realize a direct transition between an SO( $N$ ) symmetry-protected topological phase and a trivial phase. Our results refine a recent conjecture regarding the criticality of transitions between SPT phases.We investigate the nature of quantum phase transitions in a (1+1)-dimensional field theory composed of $N$ copies of the Ising conformal field theory interacting via competing relevant perturbations. The field theory governs the competition between a mass term and an interaction involving the product of $N$ order-parameter fields, which is realized, e.g. in coupled Ising chains, two-leg spin ladders, and SO($N$)-symmetric spin chains. By combining a perturbative renormalization group analysis and large-scale matrix-product state simulations, we systematically determine the nature of the phase transition as a function of $N$. For $N=2$ and $N=3$, we confirm that the transition is continuous, belonging to the Ising and four-state Potts universality classes, respectively. In contrast, for $N \ge 4$, our results provide compelling evidence that the transition becomes first order. We further apply these findings to specific lattice models with SO($N$) symmetry, including spin-$1/2$ and spin-$1$ two-leg ladders, that realize a direct transition between an SO($N$) symmetry-protected topological phase and a trivial phase. Our results refine a recent conjecture regarding the criticality of transitions between SPT phases.

arXiv:2602.17029Physical review. B./Physical review. BJul 13, 20260 citations

We introduce a class of exactly solvable

SO(n)

symmetric Hamiltonians with matrix product ground states. For an odd $n\ensuremath{\ge}3$ case, the ground state is a translational invariant Haldane gap spin liquid state; while for an even $n\ensuremath{\ge}4$ case, the ground state is a spontaneously dimerized state with twofold degeneracy. In the matrix product ground states for both cases, we identify a hidden antiferromagnetic order, which is characterized by nonlocal string order parameters. The ground-state phase diagram of a generalized

SO(n)

symmetric bilinear-biquadratic model is discussed.

We investigate the nature of quantum phase transitions in a (1+1)-dimensional field theory composed of

N

copies of the Ising conformal field theory interacting via competing relevant perturbations. The field theory governs the competition between a mass term and an interaction involving the product of

N

order-parameter fields, which is realized, e.g. in coupled Ising chains, two-leg spin ladders, and SO(

N

)-symmetric spin chains. By combining a perturbative renormalization group analysis and large-scale matrix-product state simulations, we systematically determine the nature of the phase transition as a function of

N

. For

N=2

and

N=3

, we confirm that the transition is continuous, belonging to the Ising and four-state Potts universality classes, respectively. In contrast, for

N \ge 4

, our results provide compelling evidence that the transition becomes first order. We further apply these findings to specific lattice models with SO(

N

) symmetry, including spin-

1/2

and spin-

1

two-leg ladders, that realize a direct transition between an SO(

N

) symmetry-protected topological phase and a trivial phase. Our results refine a recent conjecture regarding the criticality of transitions between SPT phases.