# Class of exactly solvable SO(n) symmetric spin chains with matrix product ground states

@article{Tu2008ClassOE, title={Class of exactly solvable SO(n) symmetric spin chains with matrix product ground states}, author={Hong-Hao Tu and Guang-ming Zhang and Tao Xiang}, journal={Physical Review B}, year={2008}, volume={78}, pages={094404} }

We introduce a class of exactly solvable SO(n) symmetric Hamiltonians with matrix product ground states. For an odd n >= 3 case, the ground state is a translational invariant Haldane gap spin liquid state; while for an even n >= 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… Expand

#### 37 Citations

Lowest-energy states in parity-transformation eigenspaces of SO (N) spin chain

- Physics, Mathematics
- 2015

Abstract We expand the symmetry of the open finite-size SO ( N ) symmetric spin chain to O ( N ) . We partition its space of states into the eigenspaces of the parity transformations in the flavor… Expand

Product Vacua with Boundary States and the Classification of Gapped Phases

- Physics, Mathematics
- 2014

We address the question of the classification of gapped ground states in one dimension that cannot be distinguished by a local order parameter. We introduce a family of quantum spin systems on the… Expand

Discriminating string order parameter for topological phases of gapped SU(N) spin chains

- Physics, Mathematics
- 2012

One-dimensional gapped spin chains with symmetry PSU(N) = SU(N)/Z_N are known to possess N different topological phases. In this paper, we introduce a non-local string order parameter which… Expand

Hierarchy of exactly solvable spin-1/2 chains with so (N)_I critical points

- Physics
- 2014

We construct a hierarchy of exactly solvable spin-1/2 chains with so(N)1 critical points. Our construction is based on the framework of condensate-induced transitions between topological phases. We… Expand

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

- Physics
- 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)… Expand

On Gapped Phases with a Continuous Symmetry and Boundary Operators

- Mathematics, Physics
- 2014

We discuss the role of compact symmetry groups, G, in the classification of gapped ground state phases of quantum spin systems. We consider two representations of G on infinite subsystems. First, in… Expand

Spontaneous parity violation in a quantum spin chain

- Physics
- 2010

We report on a spontaneous breakdown of parity in the ground state of a spin Hamiltonian involving nearest-neighbor interactions. This occurs for a one-dimensional model where spins transform under… Expand

Topologically distinct classes of valence-bond solid states with their parent Hamiltonians

- Physics
- 2009

We present a general method to construct one-dimensional translationally invariant valence-bond solid states with a built-in Lie group G and derive their matrix product representations. The general… Expand

Entanglement spectra of q-deformed higher spin VBS states

- Physics, Mathematics
- 2012

We calculate the reduced density matrix of a block of integer spin-S’s in a q-deformed valence-bond-solid (VBS) state. This matrix is diagonalized exactly for an infinitely long block in an… Expand

PEPS as ground states: Degeneracy and topology

- Physics
- 2010

We introduce a framework for characterizing Matrix Product States (MPS) and Projected Entangled Pair States (PEPS) in terms of symmetries. This allows us to understand how PEPS appear as ground… Expand