Two-dimensional lattice with an imaginary magnetic field
- URL: http://arxiv.org/abs/2307.14635v2
- Date: Fri, 9 Feb 2024 00:01:01 GMT
- Title: Two-dimensional lattice with an imaginary magnetic field
- Authors: Tomoki Ozawa and Tomoya Hayata
- Abstract summary: We introduce a two-dimensional non-Hermitian lattice model with an imaginary magnetic field.
We show that the energy spectrum does not converge as lattice size is made larger, which comes from the intrinsic nonperiodicity of the model.
We also find an analog of the Aharonov-Bohm effect; the net change of the norm of the wave function upon adiabatically forming a closed path is determined by the imaginary magnetic flux enclosed by the path.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We introduce a two-dimensional non-Hermitian lattice model with an imaginary
magnetic field and elucidate various unique features which are absent in
Hermitian lattice models with real magnetic fields. To describe the imaginary
magnetic field, we consider both the Landau gauge and the symmetric gauge,
which are related by a generalized gauge transformation, changing not only the
phase but also the amplitude of the wave function. We discuss the complex
energy spectrum and the non-Hermitian Aharonov-Bohm effect as examples of
properties which are due to the imaginary magnetic field independent of the
generalized gauge transformation. We show that the energy spectrum does not
converge as the lattice size is made larger, which comes from the intrinsic
nonperiodicity of the model. However, we have found that the energy spectrum
does converge if one fixes the length of one side and makes the other side
longer; this asymptotic behavior can be understood in the framework of the
non-Bloch band theory. We also find an analog of the Aharonov-Bohm effect; the
net change of the norm of the wave function upon adiabatically forming a closed
path is determined by the imaginary magnetic flux enclosed by the path, which
provides an experimentally observable feature of the imaginary magnetic field.
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