Symmetry-protected topological phases in two-leg SU(N) spin ladder with unequal spins

Abstract

Chiral Haldane phases are examples of one-dimensional topological states of matter which are protected by projective SU($N$) group (or its subgroup ${\mathbb{Z}}_N\times {\mathbb{Z}}_N$) with $N>2$. The unique feature of these symmetry protected topological (SPT) phases is that they are accompanied by inversion-symmetry breaking and the emergence of different left and right edge states which transform, for instance, respectively in the fundamental ($\mathbf{N}$) and anti-fundamental ($\overline{\mathbf{N}}$) representations of SU($N$). We show, by means of complementary analytical and numerical approaches, that these chiral SPT phases as well as the non-chiral ones are realized as the ground states of a generalized two-leg SU($N$) spin ladder in which the spins in the first chain transform in $\mathbf{N}$ and the second in $\overline{\mathbf{N}}$. In particular, we map out the phase diagram for $N=3$ and $4$ to show that {\em all} the possible symmetry-protected topological phases with projective SU($N$)-symmetry appear in this simple ladder model.

arXiv comment21 pages

References in corpus (61)

• The density-matrix renormalization group in the age of matrix product states
• Surprises on the Way from 1D to 2D Quantum Magnets: the Novel Ladder Materials
• Entanglement spectrum of a topological phase in one dimension
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Bosonization and Strongly Correlated Systems
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Topological phases of fermions in one dimension
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Classifying quantum phases using Matrix Product States and PEPS
• Dimerization and Incommensurate Spiral Spin Correlations in the Zigzag Spin Chain: Analogies to the Kondo Lattice
• Antiferromagnetic spin ladders: crossover between spin S = 1/2 and S = 1 chains
• Detection of Symmetry Protected Topological Phases in 1D
• Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain
• Incommensurate spin correlations in Heisenberg spin-1/2 zig-zag ladders
• One-dimensional spin-liquid without magnon excitations
• Equivalence of the antiferromagnetic Heisenberg ladder to a single $S=1$ chain
• Confinement of fractional quantum number particles in a condensed matter system
• Dimerized phase and transitions in a spatially anisotropic square lattice antiferromagnet
• Phases of one-dimensional SU(N) cold atomic Fermi gases --from molecular Luttinger liquids to topological phases
• An extended massless phase and the Haldane phase in a spin-1 isotropic antiferromagnetic chain
• Phase Transitions Between Topologically Distinct Gapped Phases in Isotropic Spin Ladders
• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Metal-insulator transition in the one-dimensional SU(N) Hubbard model
• Topological liquids and valence cluster states in two-dimensional SU(N) magnets
• Non-Abelian bosonization of the frustrated antiferromagnetic spin-1/2 chain
• Phase Diagram of a Spin Ladder with Cyclic Four Spin Exchange
• SU(N) magnetism in chains of ultracold alkaline-earth-metal atoms: Mott transitions and quantum correlations
• On topological phases of spin chains
• Rigorous results on a first-order phase transition in antiferromagnetic spin-1/2 coupled chains
• The fate of spinons in spontaneously dimerised spin-1/2 ladders
• The hidden symmetry-breaking picture of symmetry-protected topological order
• Symmetry-protected topological phases of alkaline-earth cold fermionic atoms in one dimension
• Topological Order, Dimerization, and Spinon Deconfinement in Frustrated Spin Ladders
• Z_3 symmetry-protected topological phases in the SU(3) AKLT model
• DMRG studies of critical SU(N) spin chains
• Spontaneous plaquette formation in the SU(4) Spin-Orbital ladder
• Magnetization and dimerization profiles of the cut two-leg spin ladder and spin-1 chain
• From symmetry-protected topological order to Landau order
• Entanglement in an SU(n) Valence-Bond-Solid State
• Phase diagram of the frustrated spin ladder
• Non-Abelian SU(N-1)-singlet fractional quantum Hall states from coupled wires
• Phase diagrams of one-dimensional half-filled two-orbital SU(N) cold fermions systems
• Phase Diagram of the Heisenberg Spin Ladder with Ring Exchange
• DMRG simulations of SU(N) Heisenberg chains using standard Young tableaux: fundamental representation and comparison with finite-size Bethe ansatz
• Scalar chiral ground states of spin ladders with four-spin exchanges
• Chiral Haldane phases of SU(N) quantum spin chains in the adjoint representation
• A discriminating string order parameter for topological phases of gapped SU(N) spin chains
• Unified Phase Diagram of Antiferromagnetic SU(N) Spin Ladders
• Competing Orders and Hidden Duality Symmetries in Two-leg Spin Ladder Systems
• Phases of the generalized two-leg spin ladder: A view from the SU(4) symmetry
• DMRG investigation of constrained models: from quantum dimer and quantum loop ladders to hard-boson and Fibonacci anyon chains
• Novel families of $\mathrm{SU}(N)$ AKLT states with arbitrary self-conjugate edge states
• Spontaneous Parity Violation in a Quantum Spin Chain
• Quantum Entanglement and Topological Order in Hole-Doped Valence Bond Solid States
• Two-leg SU(2n) spin ladder: A low-energy effective field theory approach
• Topological qubits from valence bond solids
• Spinon excitation spectra of the $J_1$-$J_2$ chain from analytical calculations in the dimer basis and exact diagonalization
• "Haldane" phases with ultracold fermionic atoms in double-well optical lattices
• Symmetry protected topological phases in two-orbital SU(4) fermionic atoms
• Symmetry-protected topological order in SU(N) Heisenberg magnets --quantum entanglement and non-local order parameters

Cited by in corpus (11)

• Boundary deconfined quantum criticality at transitions between symmetry-protected topological chains
• Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes
• Symmetry-protected topological phases in the SU(N) Heisenberg spin chain: a Majorana-fermion approach
• The Haldane gap in the SU(3) [3 0 0] Heisenberg chain
• Even-odd effects in the $J_1-J_2$ SU($N$) Heisenberg spin chain
• Lieb-Schultz-Mattis constraints for the insulating phases of the one-dimensional SU($N$) Kondo lattice model
• Nonabelian ferromagnets with three-body interactions
• Non-Landau quantum phase transition in modulated SU(N) Heisenberg spin chains
• 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
• Adjoint ferromagnets