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Geometric properties of loop condensed phases on the square lattice

机译：方格上环状凝聚相的几何性质

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摘要

Loop condensed phases are scale-invariant quantum liquid phases of matter. These phases include topologically ordered liquid phases such as the toric code as well as critical liquids such as the Rokhsar-Kivelson point of the quantum dimer model on the square lattice. To investigate the extent to which nonlocal geometric observables capture a signature of the nonlocal quantum order present in these phases, we compute geometric properties of such loop condensed states using directed loop Monte Carlo calculations. In particular, we investigate the loop condensed nature of ground state of the square lattice quantum dimer model at the Rokhsar-Kivelson point and compare with other loop condensed states on the square lattice, including those of the toric code and fully packed loop model. The common features of such liquids are a scale invariant distribution of loops and a fractal dimensionality of spanning loops. We find that the fractal dimension of the loop condensate of the square lattice quantum dimer model at the Rokhsar-Kivelson point is 3/2, which provides quantitative confirmation of the effective height model that is commonly used to describe this critical dimer liquid.
机译：环状凝聚相是物质的尺度不变量子液相。这些相包括拓扑排序的液相（例如复曲面代码）以及临界液体（例如，方形晶格上的量子二聚体模型的Rokhsar-Kivelson点）。为了研究非局部几何可观物捕获这些相中存在的非局部量子级数的特征的程度，我们使用定向环蒙特卡洛计算来计算此类环的凝聚态的几何性质。特别是，我们研究了Rokhsar-Kivelson点处的方格量子二聚体模型基态的环路凝聚性质，并与方格上的其他环路凝聚态进行了比较，包括复曲面编码和完全填充环路模型的那些。这种液体的共同特征是环的尺度不变分布和跨度环的分形维数。我们发现，在Rokhsar-Kivelson点处，方形晶格量子二聚体模型的回路冷凝物的分形维数为3/2，这为有效高度模型的定量确认提供了有效的高度模型，该模型通常用于描述这种临界二聚体液体。

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  • 来源
    《Physical review》 |2013年第15期|155150.1-155150.6|共6页
  • 作者

    C. M. Herdman; K. B. Whaley;

  • 作者单位

    Berkeley Center for Quantum Information and Computation, University of California, Berkeley, California 94720, USA,Department of Physics, University of California, Berkeley, California 94720, USA,Department of Chemistry, University of California, Berkeley, California 94720, USA,Department of Physics, University of Vermont, Burlington, Vermont 05405, USA;

    Berkeley Center for Quantum Information and Computation, University of California, Berkeley, California 94720, USA,Department of Chemistry, University of California, Berkeley, California 94720, USA;

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  • 正文语种 eng
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  • 关键词

    quantum statistical mechanics; lattice theory and statistics; numerical simulation studies;

    机译：量子统计力学;格理论和统计学;数值模拟研究;

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