Chern-Simons theory of the magnetization plateaus of the spin-1/2 quantum XXZ Heisenberg model on Kagome Lattice

Abstract

Frustrated spin systems on Kagome lattices have long been considered to be a promising candidate for realizing exotic spin liquid phases. Recently, there has been a lot of renewed interest in these systems with the discovery of materials such as Volborthite and Herbertsmithite that have Kagome like structures. In the presence of an external magnetic field, these frustrated systems can give rise to magnetization plateaus of which the plateau at $m=\frac{1}{3}$ is considered to be the most prominent. Here we study the problem of the antiferromagnetic spin-1/2 quantum XXZ Heisenberg model on a Kagome lattice by using a Jordan-Wigner transformation that maps the spins onto a problem of fermions coupled to a Chern-Simons gauge field. This mapping relies on being able to define a consistent Chern-Simons term on the lattice. Using a recently developed method to rigorously extend the Chern-Simons term to the frustrated Kagome lattice we can now formalize the Jordan-Wigner transformation on the Kagome lattice. We then discuss the possible phases that can arise at the mean-field level from this mapping and focus specifically on the case of $\frac{1}{3}$-filling ($m=\frac{1}{3}$ plateau) and analyze the effects of fluctuations in our theory. We show that in the regime of $XY$ anisotropy the ground state at the $1/3$ plateau is equivalent to a bosonic fractional quantum Hall Laughlin state with filling fraction $1/2$ and that at the $5/9$ plateau it is equivalent to the first bosonic Jain daughter state at filling fraction $2/3$.

21 pages, 4 figures (fig. 3 is new) and 35 references (ref. 28 and 35 are new). Improved presentation, new section on the Jordan-Wigner transformation (II E), old sections II and IV are merged into section III, expanded conclusions section

References in corpus (4)

• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Spin Liquid States on the Triangular and Kagome Lattices: A Projective Symmetry Group Analysis of Schwinger Boson States
• Projected wave function study of Z2 spin liquids on the kagome lattice for the spin-1/2 quantum Heisenberg antiferromagnet
• Quantum kagome antiferromagnet in a magnetic field: Low-lying non-magnetic excitations versus valence-bond crystal order

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• Lattice effects on Laughlin wave functions and parent Hamiltonians
• The spin-1/2 Kagome XXZ model in a field: competition between lattice nematic and solid orders
• Staircase of crystal phases of hard-core bosons on the Kagome lattice
• Coexistence of non-Abelian chiral spin liquid and magnetic order in a spin-1 antiferromagnet
• Anatomy of Z2 fluxes in anyon Fermi liquids and Bose condensates
• From Fractional Quantum Anomalous Hall Smectics to Polar Smectic Metals: Nontrivial Interplay Between Electronic Liquid Crystal Order and Topological Order in Correlated Topological Flat Bands
• Jordan-Wigner fermionization of quantum spin systems on arbitrary 2D lattices: A mutual Chern-Simons approach
• Jordan-Wigner composite-fermion liquids in 2D quantum spin-ice
• Microscopic theory of field-tuned topological transitions in the Kitaev honeycomb model