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Universal Signatures of Quantum Critical Points from Finite-Size Torus Spectra: A Window into the Operator Content of Higher-Dimensional Conformal Field Theories

机译:有限尺寸环面谱的量子临界点的通用签名:进入高维共形场理论算子内容的窗口

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摘要

The low-energy spectra of many body systems on a torus, of finite size L, are well understood in magnetically ordered and gapped topological phases. However, the spectra at quantum critical points separating such phases are largely unexplored for (2 + 1)D systems. Using a combination of analytical and numerical techniques, we accurately calculate and analyze the low-energy torus spectrum at an Ising critical point which provides a universal fingerprint of the underlying quantum field theory, with the energy levels given by universal numbers times 1/L. We highlight the implications of a neighboring topological phase on the spectrum by studying the Ising* transition (i.e. the transition between a Z(2) topological phase and a trivial paramagnet), in the example of the toric code in a longitudinal field, and advocate a phenomenological picture that provides qualitative insight into the operator content of the critical field theory.
机译:在磁有序和有间隙的拓扑阶段中,人们充分了解了环形尺寸有限的环上许多人体系统的低能谱。但是,对于(2 +1)D系统,在分离此类相的量子临界点处的光谱尚未得到充分探索。使用分析和数值技术的组合,我们可以精确地计算和分析在Ising临界点的低能环形光谱,该临界点提供了基础量子场论的通用指纹,并且能级由通用数乘以1 / L给出。通过研究纵向场中的复曲面代码,我们通过研究Ising *跃迁(即Z(2)拓扑相与平凡顺磁体之间的跃迁)来突出显示相邻拓扑相对频谱的影响,并提倡现象学的图片,可以对临界场理论的算子内容进行定性分析。

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  • 来源
    《Physical review letters》 |2016年第21期|210401.1-210401.6|共6页
  • 作者单位

    Univ Innsbruck, Inst Theoret Phys, A-6020 Innsbruck, Austria;

    Harvard Univ, Dept Phys, Cambridge, MA 02138 USA;

    Univ Innsbruck, Inst Theoret Phys, A-6020 Innsbruck, Austria;

    Harvard Univ, Dept Phys, Cambridge, MA 02138 USA|Perimeter Inst Theoret Phys, Waterloo, ON N2L 2Y5, Canada;

    Univ Innsbruck, Inst Theoret Phys, A-6020 Innsbruck, Austria;

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