Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Emerging (2+1)D electrodynamics and topological instanton in pseudo-Hermitian two-level systems

Kuangyin Deng, Ran Cheng

Abstract

We reveal a hidden electrodynamical structure emerging from a general $2\times2$ pseudo-Hermitian system that exhibits real spectra. Even when the Hamiltonian does not explicitly depend on time, the Berry curvature can be mapped onto a $2+1$ dimensional electromagnetic field arising from an artificial spacetime instanton, in sharp contrast to the Hermitian systems where the Berry curvature is equivalent to the static magnetic field of a magnetic monopole in three spatial dimensions. The instanton appearing as a spacetime singularity carries a topological charge that quantizes the jump of magnetic flux of the Berry curvature at the time origin. Our findings are demonstrated in a simple example related to antiferromagnetic magnons.

Emerging (2+1)D electrodynamics and topological instanton in pseudo-Hermitian two-level systems

Abstract

We reveal a hidden electrodynamical structure emerging from a general pseudo-Hermitian system that exhibits real spectra. Even when the Hamiltonian does not explicitly depend on time, the Berry curvature can be mapped onto a dimensional electromagnetic field arising from an artificial spacetime instanton, in sharp contrast to the Hermitian systems where the Berry curvature is equivalent to the static magnetic field of a magnetic monopole in three spatial dimensions. The instanton appearing as a spacetime singularity carries a topological charge that quantizes the jump of magnetic flux of the Berry curvature at the time origin. Our findings are demonstrated in a simple example related to antiferromagnetic magnons.
Paper Structure (3 sections, 55 equations, 1 figure)

This paper contains 3 sections, 55 equations, 1 figure.

Table of Contents

  1. Berry phase is real for a general PH Hamiltonian with real spectra
  2. Flux of the Dual Field $\tilde{\bm{F}}$ involving $\Phi_{\rm cone}$ and $\Phi_{\rm lid}$
  3. Example System: Antiferromagnetic Magnons

Figures (1)

  • Figure 1: (a) Vector plot of the emerging gauge fields $(B,E_x,E_y)$ with its norm scaled logarithmically, on three parallel cutting planes within the light cone. The instanton ($Q=1$ for $\varepsilon_-$) is indicated by a red dot. (b) Gauss' surface enclosing the instanton, with the dual field vector $\tilde{\bm{F}}$ plotted on two cutting planes for positive and negative $t$.