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Boson topological insulators: A window into highly entangled quantum phases

机译：玻色子拓扑绝缘体：进入高度纠缠的量子相的窗口

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摘要

We study several aspects of the realization of global symmetries in highly entangled phases of quantum matter. Examples include gapped topological ordered phases, gapless quantum spin liquids, and non-Fermi liquid phases. An insightful window into such phases is provided by recent developments in the theory of short-ranged entangled symmetry protected topological (SPT) phases. First, they generate useful no-go constraints on how global symmetry may be implemented in a highly entangled phase. Possible symmetry implementation in gapped topological phases and some proposed gapless spin/Bose liquids are examined in this light. We show that some previously proposed spin liquid states for 2D quantum magnets do not in fact have consistent symmetry implementation unless they occur as the surface of a 3D SPT phase. A second SPT-based insight into highly entangled states is the development of a view point of such states as SPT phases of one of the emergent excitations. We describe this in the specific context of time-reversal symmetric 3D U( 1) quantum spin liquids with an emergent photon. Different such spin liquids are shown to be equivalent to different SPT insulating phases of the emergent monopole excitation of such phases. The highly entangled states also in turn enrich our understanding of SPT phases. We use the insights obtained from our results to provide an explicit construction of bosonic SPT phases in 3D in a system of coupled layers. This includes construction of a time-reversal symmetric SPT state that is not currently part of the cohomology classification of such states.
机译：我们研究了量子物质高度纠缠相中整体对称性实现的几个方面。示例包括带隙拓扑有序相，无间隙量子自旋液相和非费米液相。短程纠缠对称受保护拓扑（SPT）相理论的最新进展为此类相提供了有见地的窗口。首先，它们对如何在高度纠缠的阶段实现全局对称性产生有用的禁忌约束。在这种情况下，研究了在空位拓扑阶段可能实现的对称性以及一些提议的无间隙自旋/玻色液体。我们表明，某些先前提出的用于2D量子磁体的自旋液体状态实际上并不具有一致的对称性实现，除非它们出现在3D SPT相的表面上。对高度纠缠态的第二种基于SPT的见解是对诸如激发激发之一的SPT相位之类的状态的观点的发展。我们在时间反向对称3D U（1）量子自旋液体与新兴光子的特定上下文中描述此。示出了不同的这样的自旋液体等效于这样的相的出现的单极激发的不同的SPT绝缘相。高度纠缠的状态反过来又丰富了我们对SPT阶段的理解。我们使用从结果中获得的见解，在耦合层系统中提供3D的Bosonic SPT相的显式构造。这包括构造时间反转对称SPT状态，该状态当前不属于此类状态的同调分类。

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  • 来源
    《Physical review》 |2013年第23期|235122.1-235122.16|共16页
  • 作者

    Chong Wang; T. Senthil;

  • 作者单位

    Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA;

    Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA;

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  • 原文格式 PDF
  • 正文语种 eng
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  • 关键词

    strongly correlated electron systems; heavy fermions;

    机译：强相关电子系统;重费米子;

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