Equivalence and superposition of real and imaginary quasiperiodicities
- URL: http://arxiv.org/abs/2111.01567v1
- Date: Tue, 2 Nov 2021 12:45:54 GMT
- Title: Equivalence and superposition of real and imaginary quasiperiodicities
- Authors: Xiaoming Cai and Shaojian Jiang
- Abstract summary: We take non-Hermitian Aubry-Andr'e-Harper models and quasiperiodic Kitaev chains as examples to demonstrate the equivalence and superposition of real and imaginary quasiperiodic potentials.
We prove this equivalence by analytically computing Lyapunov exponents for systems with purely real and purely imaginary QPs.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We take non-Hermitian Aubry-Andr\'{e}-Harper models and quasiperiodic Kitaev
chains as examples to demonstrate the equivalence and superposition of real and
imaginary quasiperiodic potentials (QPs) on inducing localization of
single-particle states. We prove this equivalence by analytically computing
Lyapunov exponents (or inverse of localization lengths) for systems with purely
real and purely imaginary QPs. Moreover, when superposed and with the same
frequency, real and imaginary QPs are coherent on inducing the localization,
under a way which is determined by the relative phase between them. The
localization induced by a coherent superposition can be simulated by the
Hermitian model with an effective strength of QP, implying that models are in
the same universality class. When their frequencies are different and
relatively incommensurate, they are incoherent and their superposition leads to
less correlation effects. Numerical results show that the localization happens
earlier and there is an intermediate mixed phase lacking of mobility edge.
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