Valence bond solids for SU(n) spin chains: exact models, spinon confinement, and the Haldane gap

Abstract

To begin with, we introduce several exact models for SU(3) spin chains: (1) a translationally invariant parent Hamiltonian involving four-site interactions for the trimer chain, with a three-fold degenerate ground state. We provide numerical evidence that the elementary excitations of this model transform under representation 3bar of SU(3) if the original spins of the model transform under rep. 3. (2) a family of parent Hamiltonians for valence bond solids of SU(3) chains with spin reps. 6, 10, and 8 on each lattice site. We argue that of these three models, only the latter two exhibit spinon confinement and hence a Haldane gap in the excitation spectrum. We generalize some of our models to SU(n). Finally, we use the emerging rules for the construction of VBS states to argue that models of antiferromagnetic chains of SU(n) spins in general possess a Haldane gap if the spins transform under a representation corresponding to a Young tableau consisting of a number of boxes λwhich is divisible by n. If λand n have no common divisor, the spin chain will support deconfined spinons and not exhibit a Haldane gap. If λand n have a common divisor different from n, it will depend on the specifics of the model including the range of the interaction.

26 pages two-column style, 15 figures, revtex4; references added

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Cited by in corpus (87)

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• Exact Excited States of Non-Integrable Models
• Bipartite Fluctuations as a Probe of Many-Body Entanglement
• Phases of one-dimensional SU(N) cold atomic Fermi gases --from molecular Luttinger liquids to topological phases
• Anomaly and global inconsistency matching: $\theta$-angles, $SU(3)/U(1{)}^2$ nonlinear sigma model, $SU(3)$ chains and its generalizations
• Spin squeezing inequalities for arbitrary spin
• Class of exactly solvable SO(n) symmetric spin chains with matrix product ground states
• Molecular superfluid phase in systems of one-dimensional multicomponent fermionic cold atoms
• SU(N) magnetism in chains of ultracold alkaline-earth-metal atoms: Mott transitions and quantum correlations
• 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
• Simplex solid states of SU(N) quantum antiferromagnets
• Anomaly matching and symmetry-protected critical phases in $SU(N)$ spin systems in 1+1 dimensions
• Z_3 symmetry-protected topological phases in the SU(3) AKLT model
• DMRG studies of critical SU(N) spin chains
• Constant-depth preparation of matrix product states with adaptive quantum circuits
• Spinon confinement and the Haldane gap in SU(n) spin chains
• Entanglement in an SU(n) Valence-Bond-Solid State
• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• Valence bond solid states with symplectic symmetry
• Existence of a Spectral Gap in the Affleck-Kennedy-Lieb-Tasaki Model on the Hexagonal Lattice
• Topologically distinct classes of valence bond solid states with their parent Hamiltonians
• DMRG simulations of SU(N) Heisenberg chains using standard Young tableaux: fundamental representation and comparison with finite-size Bethe ansatz
• Qudit quantum computation on matrix product states with global symmetry
• Competing quantum paramagnetic ground states of the Heisenberg antiferromagnet on the star lattice
• Supersymmetric Valence Bond Solid States
• 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
• Exact diagonalization of Heisenberg $SU(N)$ chains in the fully symmetric and antisymmetric representations
• The matrix product representations for all valence bond states
• Skeleton of Matrix-Product-State-Solvable Models Connecting Topological Phases of Matter
• Entanglement and corner Hamiltonian spectra of integrable open spin chains
• Entanglement entropy in quantum spin chains with broken reflection symmetry
• Generalization of the Haldane conjecture to SU($n$) chains
• Flag manifold sigma models: spin chains and integrable theories
• Fermion sign bounds theory in quantum Monte Carlo simulation
• Entanglement in Valence-Bond-Solid States
• Kitaev honeycomb tensor networks: exact unitary circuits and applications
• Spinon confinement and deconfinement in spin-1 chains
• Tetramerization in a SU(4)-Heisenberg model on the honeycomb lattice
• Mapping of Parent Hamiltonians: from Abelian and non-Abelian Quantum Hall States to Exact Models of Critical Spin Chains
• Entanglement and SU(n) symmetry in one-dimensional valence bond solid states
• Novel families of $\mathrm{SU}(N)$ AKLT states with arbitrary self-conjugate edge states
• Entanglement in valence-bond-solid states on symmetric graphs
• Baryon squishing in synthetic dimensions by effective $SU(M)$ gauge fields
• Spontaneous Parity Violation in a Quantum Spin Chain
• Exact diagonalization of $\mathrm{SU}(N)$ Heisenberg and AKLT chains using the full $\mathrm{SU}(N)$ symmetry
• Quasi-exact quantum computation
• Phase diagram of the SO(n) bilinear-biquadratic chain from many-body entanglement
• Haldane Gap of the Three-Box Symmetric $\mathrm{SU}(3)$ Chain
• Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes
• Spontaneous trimerization in two-dimensional Antiferromagnets
• Spin 3/2 dimer model
• Topological qubits from valence bond solids
• Hidden Bethe states in a partially integrable model
• Hidden Order and Dynamics in Supersymmetric Valence Bond Solid States -- Super-Matrix Product State Formalism
• Exact ground states for coupled spin trimers
• The matrix product representation for the q-VBS state of one-dimensional higher integer spin model
• SU(3) quantum critical model emerging from a spin-1 topological phase
• Proposal of a spin-one chain model with competing dimer and trimer interactions
• Exact models for trimerization and tetramerization in spin chains
• Entanglement spectra of q-deformed higher spin VBS states
• SU(3) Quantum Spin Ladders as a Regularization of the CP(2) Model at Non-Zero Density: From Classical to Quantum Simulation
• Self-conjugate representation SU(3) chains
• Possible SU(3) Chiral Spin Liquid on the Kagome Lattice
• Symmetry breaking in low-dimensional SU(N) antiferromagnets
• Symmetry-protected topological phases in the SU(N) Heisenberg spin chain: a Majorana-fermion approach
• Symmetry protected topological phases in two-orbital SU(4) fermionic atoms
• Exact renormalization in quantum spin chains
• Non-Abelian Statistics in one dimension: topological momentum spacings and SU(2) level $k$ fusion rules
• Two-orbital physics of high spin fermionic alkaline earth atoms confined in a one-dimensional chain
• Ordering of Energy Levels for Extended SU(N) Hubbard Chain
• Spin-spin correlation functions of the q-VBS state of an integer spin model
• Even-odd effects in the $J_1-J_2$ SU($N$) Heisenberg spin chain
• Quantum phases of collective SU(3) spin systems with bipartite symmetry
• Lowest-energy states in parity-transformation eigenspaces of SO(N) spin chain
• Colored Spin Systems, BKP Evolution and finite N_c effects
• Phase transition of an SU(3) symmetric spin-1 chain
• Momentum classification of SU($n$) spin chains using extended Young Tableaux
• Superradiance, charge density waves and lattice gauge theory in a generalized Rabi-Hubbard chain
• 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
• Critical phenomena around the SU(3) symmetric tri-critical point of a spin-1 chain
• Edge states and universality class of the critical two-box symmetric SU(3) chain
• A brief note on the G${}_2$ Affleck-Kennedy-Lieb-Tasaki chain
• Bosonic realization of SU(3) chiral Haldane phases