Even-odd effects in the $J_1-J_2$ SU($N$) Heisenberg spin chain

Abstract

The zero-temperature phase diagram of the $J_1-J_2$ SU($N$) antiferromagnetic Heisenberg spin chain is investigated by means of complementary field theory and numerical approaches for general $N$. A fully gapped SU($N$) valence bond solid made of $N$ sites is formed above a critical value of $J_2/J_1$ for all $N$. We find that the extension of this $N$-merized phase for larger values of $J_2$ strongly depends on the parity of $N$. For even $N$, the phase smoothly interpolates to the large $J_2$ regime where the model can be viewed as a zigzag SU($N$) two-leg spin ladder. The phase exhibits both a $N$-merized ground state and incommensurate spin-spin correlations. In stark contrast to the even case, we show that the $N$-merized phase with odd $N$ only has a finite extent with no incommensuration. A gapless phase in the SU($N$)${}_1$ universality class is stabilized for larger $J_2$ that stems from the existence of a massless renormalization group flow from SU($N$)${}_2$ to SU($N$)${}_1$ conformal field theories when $N$ is odd.

arXiv commentFinal version

References in corpus (68)

• Quantum Spin Liquids
• Entanglement entropy and conformal field theory
• Bosonization and Strongly Correlated Systems
• The ITensor Software Library for Tensor Network Calculations
• Dimerization and Incommensurate Spiral Spin Correlations in the Zigzag Spin Chain: Analogies to the Kondo Lattice
• A one-dimensional liquid of fermions with tunable spin
• Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism
• Theory of finite-entanglement scaling at one-dimensional quantum critical points
• An SU(N) Mott insulator of an atomic Fermi gas realized by large-spin Pomeranchuk cooling
• Numerical Evidence for Multiplicative Logarithmic Corrections from Marginal Operators
• Incommensurate spin correlations in Heisenberg spin-1/2 zig-zag ladders
• Spin-orbital quantum liquid on the honeycomb lattice
• Direct probing of the Mott crossover in the SU($N$) Fermi-Hubbard model
• Hidden symmetry and quantum phases in spin-3/2 cold atomic systems
• 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
• Criticality in self-dual sine-Gordon models
• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Anomaly and global inconsistency matching: $\theta$-angles, $SU(3)/U(1{)}^2$ nonlinear sigma model, $SU(3)$ chains and its generalizations
• Thermodynamics of the one-dimensional SU(4) symmetric spin-orbital model
• Valence bond solids for SU(n) spin chains: exact models, spinon confinement, and the Haldane gap
• Antiferromagnetic spin correlation of SU($\mathcal{N}$) Fermi gas in an optical super-lattice
• Metal-insulator transition in the one-dimensional SU(N) Hubbard model
• Observation of antiferromagnetic correlations in an ultracold SU($N$) Hubbard model
• Topological liquids and valence cluster states in two-dimensional SU(N) magnets
• Strongly reduced gap in the zigzag spin chain with a ferromagnetic interchain coupling
• Non-Abelian bosonization of the frustrated antiferromagnetic spin-1/2 chain
• Expectation values of local fields for a two-parameter family of integrable models and related perturbed conformal field theories
• SU(N) magnetism in chains of ultracold alkaline-earth-metal atoms: Mott transitions and quantum correlations
• One-dimensional sawtooth and zigzag lattices for ultracold atoms
• Generalization of the Haldane conjecture to SU(3) chains
• Symmetry-protected topological phases of alkaline-earth cold fermionic atoms in one dimension
• Exact results for SU(3) spin chains: trimer states, valence bond solids, and their parent Hamiltonians
• The SU(n)_1 WZW Models: Spinon Decomposition and Yangian Structure
• A scaling hypothesis for matrix product states
• Z_3 symmetry-protected topological phases in the SU(3) AKLT model
• Chiral spin liquids in triangular lattice SU(N) fermionic Mott insulators with artificial gauge fields
• Entropy dependence of correlations in one-dimensional SU(N) antiferromagnets
• Spinon confinement and the Haldane gap in SU(n) spin chains
• Haldane limits via Lagrangian embeddings
• 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
• Confinement in the q-state Potts field theory
• Abelian SU$(N{)}_1$ Chiral Spin Liquids on the Square Lattice
• DMRG simulations of SU(N) Heisenberg chains using standard Young tableaux: fundamental representation and comparison with finite-size Bethe ansatz
• Spontaneous trimerization in a bilinear-biquadratic S=1 zig-zag chain
• Chiral Haldane phases of SU(N) quantum spin chains in the adjoint representation
• Sigma Models on Flags
• Exact diagonalization of Heisenberg $SU(N)$ chains in the fully symmetric and antisymmetric representations
• Unified Phase Diagram of Antiferromagnetic SU(N) Spin Ladders
• Massless renormalization group flow in SU(N)${}_k$ perturbed conformal field theory
• Generalization of the Haldane conjecture to SU($n$) chains
• Variational Monte-Carlo investigation of SU($N$) Heisenberg chains
• Flag manifold sigma models: spin chains and integrable theories
• Topological chiral spin liquids and competing states in triangular lattice SU($N$) Mott insulators
• DMRG Simulation of the SU(3) AFM Heisenberg Model
• $\mathrm{SU}(4)$-Symmetric Quantum Spin-Orbital Liquids on Various Lattices
• Unveiling a critical stripy state in the triangular-lattice SU(4) spin-orbital model
• Coloron excitations of the SU(3) Haldane--Shastry model
• Symmetry-protected topological phases in two-leg SU(N) spin ladder with unequal spins
• Two-leg SU(2n) spin ladder: A low-energy effective field theory approach
• Mass generation by fractional instantons in SU($n$) chains
• 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
• Exact models for trimerization and tetramerization in spin chains
• Symmetry protected topological phases in two-orbital SU(4) fermionic atoms
• Logarithmic corrections to finite size spectrum of SU(N) symmetric quantum chains
• The Haldane gap in the SU(3) [3 0 0] Heisenberg chain

Cited by in corpus (4)

• Many-body Physics of Ultracold Alkaline-Earth atoms with SU($N$)-symmetric interactions
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Lieb-Schultz-Mattis constraints for the insulating phases of the one-dimensional SU($N$) Kondo lattice model
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders