Symmetry fractionalization: Symmetry-protected topological phases of the bond-alternating spin-$1/2$ Heisenberg chain

Abstract

We study different phases of the one-dimensional bond-alternating spin-$1/2$ Heisenberg model by using the symmetry fractionalization mechanism. We employ the infinite matrix-product state representation of the ground state (through the infinite-size density matrix renormalization group algorithm) to obtain inequivalent projective representations of the (unbroken) symmetry groups of the model, which are used to identify the different phases. We find that the model exhibits trivial as well as symmetry-protected topological phases. The symmetry-protected topological phases are Haldane phases on even/odd bonds, which are protected by the time-reversal (acting on the spin as $\sigma \to -\sigma$), parity (permutation of the chain about a specific bond), and dihedral ($\pi$-rotations about a pair of orthogonal axes) symmetries. Additionally, we investigate the phases of the most general two-body bond-alternating spin-$1/2$ model, which respects the time-reversal, parity, and dihedral symmetries, and obtain its corresponding twelve different types of the symmetry-protected topological phases.

9 pages, 5 figures

References in corpus (4)

• The density-matrix renormalization group in the age of matrix product states
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• The iTEBD algorithm beyond unitary evolution
• Symmetry breaking and criticality in tensor-product states

Cited by in corpus (6)

• Unveiling the phase diagram of a bond-alternating spin-$\frac{1}{2}$ $K$-$\Gamma$ chain
• Construction of topological quantum magnets from atomic spins on surfaces
• Optimization schemes for unitary tensor-network circuit
• Quantum phase transition as an interplay of Kitaev and Ising interactions
• Promising regimes for the observation of topological degeneracy in spin chains
• Frustrated mixed-spin ladders: Evidence for a bond order wave phase between rung-singlet and Haldane phases