Spontaneous Parity Violation in a Quantum Spin Chain

Abstract

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 the gauge field representation of QCD, the eight-dimensional adjoint representation of SU(3). The ground state spontaneously violates parity and is two-fold degenerate. In addition, the model possesses a non-vanishing topological string order parameter which we explicate analytically.

4 pages, 2 figures; Conference contribution to ICM 2009

References in corpus (6)

• Valence bond solids for SU(n) spin chains: exact models, spinon confinement, and the Haldane gap
• Class of exactly solvable SO(n) symmetric spin chains with matrix product ground states
• Exact results for SU(3) spin chains: trimer states, valence bond solids, and their parent Hamiltonians
• Simplex solid states of SU(N) quantum antiferromagnets
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• Valence bond solid states with symplectic symmetry

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• Entanglement entropy in quantum spin chains with broken reflection symmetry
• Entanglement in Valence-Bond-Solid States
• Novel families of $\mathrm{SU}(N)$ AKLT states with arbitrary self-conjugate edge states
• Symmetry-protected topological phases in two-leg SU(N) spin ladder with unequal spins
• Topological qubits from valence bond solids
• "Haldane" phases with ultracold fermionic atoms in double-well optical lattices
• SU(3) quantum critical model emerging from a spin-1 topological phase
• Correlation-Assisted Quantized Charge Pumping
• Symmetry protected topological phases in two-orbital SU(4) fermionic atoms
• Symmetry-protected topological phases in the SU(N) Heisenberg spin chain: a Majorana-fermion approach
• Lieb-Schultz-Mattis constraints for the insulating phases of the one-dimensional SU($N$) Kondo lattice model
• Non-Landau quantum phase transition in modulated SU(N) Heisenberg spin chains
• A brief note on the G${}_2$ Affleck-Kennedy-Lieb-Tasaki chain
• Bosonic realization of SU(3) chiral Haldane phases