Quantum metric of non-Hermitian Su-Schrieffer-Heeger systems

Abstract

Topological insulators have been studied intensively over the last decades. Earlier research focused on Hermitian Hamiltonians, but recently, peculiar and interesting properties were found by introducing non-Hermiticity. In this work, we apply a quantum geometric approach to various Hermitian and non-Hermitian versions of the Su-Schrieffer-Heeger (SSH) model. We find that this method allows one to correctly identify different topological phases and topological phase transitions for all SSH models, but only when using the metric tensor containing both left and right eigenvectors. Whereas the quantum geometry of Hermitian systems is Riemannian, introducing non-Hermiticity leads to pseudo-Riemannian and complex geometries, thus significantly generalizing from the quantum geometries studied thus far. One remarkable example of this is the mathematical agreement between topological phase transition curves and lightlike paths in general relativity, suggesting a possibility of simulating space-times in non-Hermitian systems. We find that the metric in non-Hermitian phases degenerates in such a way that it effectively reduces the dimensionality of the quantum geometry by one. This implies that within linear response theory, one can perturb the system by a particular change of parameters while maintaining a zero excitation rate.

v2 has added a change in the acknowledgment; v3 has added minimal changes and a few new references. Remarkably, the additional "i" in Eq. (25) has been removed; v4 is the published version on Physical Review Research

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• Programmable non-Hermitian photonic quantum walks via dichroic metasurfaces
• Non-Hermitian topological superconductivity with symmetry-enriched spectral and eigenstate features
• Direct measurement of the quantum geometric tensor in pseudo-Hermitian systems
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• Quantum geometric tensors from sub-bundle geometry
• Non-Hermitian wave-packet dynamics and its realization within a non-Hermitian chiral cavity
• Quantum geometric tensor in systems with fractional band dispersion
• Fidelity and quantum geometry approach to Dirac exceptional points in diamond nitrogen-vacancy centers
• Emergence of Imaginary Time Crystals in the non-Hermitian Su-Schrieffer-Heeger model
• Scaling of Quantum Geometry Near the Non-Hermitian Topological Phase Transitions