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Gauge-fixed Wannier wave functions for fractional topological insulators

机译：分数拓扑绝缘子的量规固定的Wannier波函数

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摘要

We propose an improved scheme to construct many-body trial wave functions for fractional Chern insulators (FCI), using one-dimensional localized Wannier basis. The procedure borrows from the original scheme on a continuum cylinder, but is adapted to finite-size lattice systems with periodic boundaries. It fixes several issues of the continuum description that made the overlap with the exact ground states insignificant. The constructed lattice states are translationally invariant, and have the correct degeneracy as well as the correct relative and total momenta. Our prescription preserves the (possible) inversion symmetry of the lattice model, and is isotropic in the limit of flat Berry curvature. By relaxing the maximally localized hybrid Wannier orbital prescription, we can form an orthonormal basis of states which, upon gauge fixing, can be used in lieu of the Landau orbitals. We find that the exact ground states of several known FCI models at v = 1/3 filling are well captured by the lattice states constructed from the Laughlin wave function. The overlap is higher than 0.99 in some models when the Hilbert space dimension is as large as 3 x 104 in each total momentum sector.
机译：我们提出了一种改进的方案，使用一维局部Wannier基础构造分数Chern绝缘子（FCI）的多体试验波函数。该程序借鉴了连续圆柱体上的原始方案，但适用于具有周期性边界的有限尺寸晶格系统。它修复了连续描述中的几个问题，这些问题使得与确切的基态的重叠变得无关紧要。构造的晶格状态是平移不变的，并具有正确的简并性以及正确的相对和总动量。我们的处方保留了晶格模型的（可能）反演对称性，并且在平坦的Berry曲率极限内具有各向同性。通过放宽最大局部化的混合Wannier轨道处方，我们可以形成状态的正交基础，通过轨距固定，可以代替Landau轨道。我们发现，由Laughlin波函数构造的晶格状态可以很好地捕获v = 1/3填充时几个已知FCI模型的精确基态。在某些模型中，当每个总动量扇区中的希尔伯特空间维数最大为3 x 104时，重叠率将高于0.99。

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  • 来源
    《Physical review》 |2012年第8期|085129.1-085129.31|共31页
  • 作者

    Yang-Le Wu; N. Regnault; B. Andrei Bernevig;

  • 作者单位

    Department of Physics, Princeton University, Princeton, New Jersey 08544, USA;

    Department of Physics, Princeton University, Princeton, New Jersey 08544, USA,Laboratoire Pierre Aigrain, ENS and CNRS, 24 rue Lhomond, 75005 Paris, France;

    Department of Physics, Princeton University, Princeton, New Jersey 08544, USA;

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  • 关键词

    quantum hall effects; lattice fermion models (hubbard model; etc.);

    机译：量子霍尔效应格子费米子模型（哈伯德模型;等）;

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