Topological Phases in Half-Integer Higher Spin $J_1$-$J_2$ Heisenberg Chains

Abstract

We study the ground state properties of antiferromagnetic $J_1$-$J_2$ chains with half-integer spins ranging from $S=\frac{3}{2}$ to $S=\frac{11}{2}$ using the density-matrix renormalization group method. We map out the ground-state phase diagrams as a function of $\frac{J_2}{J_1}$ containing topological phases with alternating $\frac{2S-1}{2}$ and $\frac{2S+1}{2}$ valence bonds. We identify these topological phases and their boundaries by calculating the string order parameter, the dimer order parameter, and the spin gap for those high-$S$ systems in thermodynamic limit (finite size scaling). We find that these topological regions narrow down inversely with $S$ and converge to a single point at $\frac{J_2}{J_1}=\frac{1}{4}$ in the classical limit -- a critical threshold between commensurate and incommensurate orders. In addition, we extend the discussion of the Majumder-Ghosh state, previously noted only for $S=\frac{1}{2}$, and speculate its possible presence as a ground state in half-integer high spin systems over a substantial range of $\frac{J_2}{J_1}$ values.

6 pages, 4 figures, Supplementary Material

References in corpus (15)

• Topological Insulators
• Topological insulators and superconductors
• New directions in the pursuit of Majorana fermions in solid state systems
• Entanglement spectrum of a topological phase in one dimension
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Symmetry Protected Topological phases of Quantum Matter
• Ground State Phase Diagram of S=1 XXZ Chains with Uniaxial Single-Ion-Type Anisotropy
• Numerical Study of the $S=1$ Antiferrromagnetic Spin Chain with Bond Alternation
• Order Parameter to Characterize Valence-Bond-Solid States in Quantum Spin Chains
• Ground State Phase Diagrams of Frustrated Spin-S XXZ Chains: Chiral Ordered Phases
• Frustrated antiferromagnetic quantum spin chains for spin length S > 1
• Floating, critical and dimerized phases in a frustrated spin-3/2 chain
• From SU(2)${}_5$ to SU(2)${}_3$ Wess-Zumino-Witten transitions in a frustrated spin-5/2 chain
• Entanglement properties of the Haldane phases: A finite system-size approach
• Sequential quantum phase transitions in $J_1$-$J_2$ Heisenberg chains with integer spins ($S>1$): Quantized Berry phase and valence-bond solids

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