Wed·Sep 15, 2021Wednesday·September 15, 2021

1. 01*

   Bootstrapping More QM Systems

   David Berenstein🇺🇸 · George Hulsey🇺🇸

   We test the bootstrap approach for determining the spectrum of one dimensional Hamiltonians. In this paper we focus on problems that have a two parameter search space in the bootstrap approach: the double well and a periodic potential associated to the Mathieu equation. For the double well, we compare the energies with contributions from perturbative and non-perturbative results, finding good agreement. For the periodic potentials, we notice that the bootstrap approach gives the band structure of the periodic potential, but it has trouble finding the quasi-momentum of the system. To make further progress on the dispersion relation of the bands, new techniques are needed.

   ↳ hep-thhep-latquant-phJ.Phys.A(2022)·52 citations
2. 02*

   Part I: Staggered index and 3D winding number of Kramers-degenerate bands

   Alexander C. Tyner🇺🇸 · Pallab Goswami🇺🇸

   For three-dimensional (3D) crystalline insulators, preserving space-inversion ($\mathcal{P}$) and time-reversal ($\mathcal{T}$) symmetries, the third homotopy class of two-fold, Kramers-degenerate bands is described by a 3D winding number $n_{3,j}\in \mathbb{Z}$, where $j$ is the band index. It governs space group symmetry-protected, instanton or tunneling configurations of $SU(2)$ Berry connection, and the quantization of magneto-electric coefficient ${\theta }_j=n_{3,j}\pi$. We show that $|n_{3,j}|$ for realistic, \emph{ab initio} band structures can be identified from a staggered symmetry-indicator ${\kappa }_{AF,j}\in \mathbb{Z}$ and the gauge-invariant spectrum of $SU(2)$ Wilson loops. The procedure is elucidated for $4$-band and $8$-band tight-binding models and \emph{ab initio} band structure of Bi, which is a ${\mathbb{Z}}_2$-trivial, higher-order, topological crystalline insulator. When the tunneling is protected by $C_{nh}$ and $D_{nh}$ point groups, the proposed method can also identify the signed winding number $n_{3,j}$. Our analysis distinguishes between magneto-electrically trivial ($\theta =0$) and non-trivial ($\theta =2s\pi$, with $s\ne 0$) topological crystalline insulators. In Part II, we demonstrate $\mathbb{Z}$-classification of $\theta$ by computing induced electric charge (Witten effect) on magnetic Dirac monopoles.

   ↳ cond-mat.mtrl-scicond-mat.mes-hallcond-mat.str-elhep-lat+14 citations

* Reconstructed cohort: no mailing for this day survives in the archive. Papers are grouped by their submission times and arXiv's announcement cut-off, assuming announcement without delay; positions follow identifier order. Validated at ~91% exact-day agreement against the archived era.