Fractional Topological States in Quantum Spin Chains with Periodical Modulation

Abstract

We report the findings of fractional topological states in one-dimensional periodically modulated quantum spin chains with up to third neighbor interactions. By exact numerical studies, we demonstrate the existence of topologically nontrivial degenerate ground states at some specific magnetizations, which can be characterized by the nonzero-integer total Chern numbers of the degenerate ground states and the emergence of nontrivial edge states under open boundary conditions. We find that the low-energy excitations obey bosonic $\nu =1/2$ fractional statistics for the spin-$1/2$ system and $\nu =1$ non-Abelian statistics for the spin-$1$ system, respectively. The discovered fractional quantum states provide another route to the theoretical exploration of fractional quantum states in correlated spin systems.

5 pages, 4 figures

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Cited by in corpus (8)

• Fractional charge pumping of interacting bosons in one-dimensional superlattice
• Topological Gaps in Quasi-Periodic Spin Chains: A Numerical and K-Theoretic Analysis
• Topological Mott Insulator with Bosonic Edge Modes in 1D Fermionic Superlattices
• Bulk-edge Correspondence in the Adiabatic Heuristic Principle
• Topological end states in a one-dimensional spatially modulated interaction spinless fermion model
• Fractional transconductance via non-adiabatic topological Cooper pair pumping
• Enhanced superconductivity and various edge modes in modulated $t$-$J$ chains
• Mapping Chern numbers in quasi-periodic interacting spin chains