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

Abstract

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 characterizes each of these N phases unambiguously. Numerics confirm that our order parameter allows to extract a quantized topological invariant from a given non-degenerate gapped ground state wave function. Discontinuous jumps in the discrete topological order that arise when varying physical couplings in the Hamiltonian may be used to detect quantum phase transitions between different topological phases.

15 pages, 4 figures

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Cited by in corpus (27)

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• On topological phases of spin chains
• Generalization of the Haldane conjecture to SU(3) chains
• Symmetry-protected topological phases of alkaline-earth cold fermionic atoms in one dimension
• Z_3 symmetry-protected topological phases in the SU(3) AKLT model
• From symmetry-protected topological order to Landau order
• DMRG simulations of SU(N) Heisenberg chains using standard Young tableaux: fundamental representation and comparison with finite-size Bethe ansatz
• Chiral Haldane phases of SU(N) quantum spin chains in the adjoint representation
• Symmetry-protected topological states for interacting fermions in alkaline-earth-like atoms
• Exact diagonalization of Heisenberg $SU(N)$ chains in the fully symmetric and antisymmetric representations
• Variational Monte-Carlo investigation of SU($N$) Heisenberg chains
• Generalization of the Haldane conjecture to SU($n$) chains
• Ising order parameter and topological phase transitions: Toric code in a uniform magnetic field
• Brane parity orders in the insulating state of Hubbard ladders
• Exact diagonalization of $\mathrm{SU}(N)$ Heisenberg and AKLT chains using the full $\mathrm{SU}(N)$ symmetry
• n-cluster models in a transverse magnetic field
• Symmetry-protected topological phases in two-leg SU(N) spin ladder with unequal spins
• Symmetry-protected topological phases and transition in a frustrated spin-$\frac{1}{2}$ XXZ chain
• SU(3) quantum critical model emerging from a spin-1 topological phase
• Symmetry protected topological phases in two-orbital SU(4) fermionic atoms
• Z_N Berry phase and symmetry protected topological phases of SU(N) antiferromagnetic Heisenberg chain
• Identifying quantum phases from injectivity of symmetric matrix product states
• Two-orbital physics of high spin fermionic alkaline earth atoms confined in a one-dimensional chain
• Measuring Non-local Brane Order with Error-corrected Parity Snapshots
• Exact quantization of topological order parameter in SU($N$) spin models, $N$-ality transformation and ingappabilities
• Density Matrix Renormalization Group simulations of the SU(N) Fermi-Hubbard chain implementing the full SU(N) symmetry via Semi-Standard Young Tableaux and Unitary Group Subduction Coefficients
• Bosonic realization of SU(3) chiral Haldane phases