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Chiral spin liquids on the kagome lattice

机译：kagome晶格上的手性自旋液体

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摘要

We study the nearest-neighbor XX Z Heisenberg quantum antiferromagnet on the kagome lattice. Here we consider the effects of several perturbations: (a) a chirality term, (b) a Dzyaloshinski-Moriya term, and (c) a ring-exchange type term on the bowties of the kagome lattice, and inquire if they can support chiral spin liquids as ground states. The method used to study these Hamiltonians is a flux attachment transformation that maps the spins on the lattice to fermions coupled to a Chern-Simons gauge field on the kagome lattice. This transformation requires us to consistently define a Chern-Simons term on the kagome lattice. We find that the chirality term leads to a chiral spin liquid even in the absence of an uniform magnetic field, with an effective spin Hall conductance of σ_(xy)~s = 1/2 in the regime of XY anisotropy. The Dzyaloshinski-Moriya term also leads a similar chiral spin liquid but only when this term is not too strong. An external magnetic field also has the possibility of giving rise to additional plateaus which also behave like chiral spin liquids in the XY regime. Finally, we consider the effects of a ring-exchange term and find that, provided its coupling constant is large enough, it may trigger a phase transition into a chiral spin liquid by the spontaneous breaking of time-reversal invariance.
机译：我们研究了kagome晶格上最近的XX Z Heisenberg量子反铁磁体。在这里，我们考虑几种扰动的影响：（a）手性项，（b）Dzyaloshinski-Moriya项，（c）kagome晶格上的蝴蝶结上的环交换类型项，并询问它们是否可以支持手性旋转液体作为基态。研究这些哈密顿量的方法是一种通量附着变换，该变换将晶格上的自旋映射到与kagome晶格上的Chern-Simons规范场耦合的费米子。这种转换要求我们在kagome晶格上一致地定义一个Chern-Simons术语。我们发现，即使在没有均匀磁场的情况下，手性项仍会导致手性自旋液体，在XY各向异性的情况下，有效自旋霍尔电导为σ_（xy）〜s = 1/2。 Dzyaloshinski-Moriya术语也可导致类似的手性纺丝液，但前提是该术语不太强。外部磁场还可能引起额外的平稳期，这些平稳期的行为也类似于XY态的手性自旋液体。最后，我们考虑了环交换项的影响，并发现，只要其耦合常数足够大，它就可以通过自发打破时间反转不变性而引发向手性自旋液体的相变。

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  • 来源
    《Physical review》 |2015年第9期|094433.1-094433.17|共17页
  • 作者

    Krishna Kumar; Kai Sun; Eduardo Fradkin;

  • 作者单位

    Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois, 61801-3080, USA;

    Department of Physics, Randall Laboratory, University of Michigan, Ann Arbor, Michigan 48109, USA;

    Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois, 61801-3080, USA,Kavli Institute for Theoretical Physics, University of California Santa Barbara, Santa Barbara, California 93106-4030, USA,Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellon Ⅰ, 1428 Buenos Aires, Argentina;

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