Non-Hermitian generalizations of extended Su-Schrieffer-Heeger models

Anomalous Non-Hermitian Open-Boundary Spectrum

For a long time, it was presumed that continuum bands could be readily encompassed by open-boundary spectra, irrespective of the system's modest dimensions. However, our findings reveal a nuanced picture: under open-boundary conditions, the proliferation of complex eigenvalues progresses in a sluggish, oscillating manner as the system expands. Consequently, even in larger systems, the overlap between continuum bands and open-boundary eigenvalues becomes elusive, with the surprising twist that the count of these complex eigenvalues may actually diminish with increasing system size. This counterintuitive trend underscores that the pursuit of an ideal, infinite-sized system scenario does not necessarily align with enlarging the system size. Notably, despite the inherent non-Hermiticity of our system, the eigenstates distribute themselves in a manner reminiscent of Bloch waves. These discoveries hold potential significance for both theoretical explorations and experimental realizations of non-Hermitian systems.

Aperiodic dynamical quantum phase transition in multi-band Bloch Hamiltonian and its origin

We investigate the dynamical quantum phase transition (DQPT) in the multi-band Bloch Hamiltonian of the one-dimensional periodic Kitaev model, focusing on quenches from a Bloch band. By analyzing the dynamical free energy and Pancharatnam geometric phase (PGP), we show that the critical times of DQPTs deviate from periodic spacing due to the multi-band effect, contrasting with results from two-band models. We propose a geometric interpretation to explain this non-uniform spacing. Additionally, we clarify the conditions needed for DQPT occurrence in the multi-band Bloch Hamiltonian, highlighting that a DQPT only arises when the quench from the Bloch states collapses the band gap at the critical point. Moreover, we establish that the dynamical topological order parameter, defined by the winding number of the PGP, is not quantized but still exhibits discontinuous jumps at DQPT critical times due to periodic modulation. Additionally, we extend our analysis to mixed-state DQPT and find its absence at non-zero temperatures.

Observation of higher-order topological corner states in photonic two-dimensional trimer lattices

We demonstrate the first, to the best of our knowledge, experimental observation of higher-order topological corner states in the photonic two-dimensional (2D) trimer lattices. Using a femtosecond laser direct writing technology, we experimentally fabricate a series of 2D trimer lattices with different open boundary conditions and thereby observe two kinds of 0D topological corner states, i.e., topological corner states and topological defect corner states. Interestingly, these corner states and defect corner states can not only exist in the bandgap but also coexist with the bulk states and show obvious localization properties. This work provides fresh perspectives on higher-order topology in artificial microstructures.

Topological edge states in photonic decorated trimer lattices

In recent years, topological insulators have been extensively studied in one-dimensional periodic systems, such as Su-Schrieffer-Heeger and trimer lattices. The remarkable feature of these one-dimensional models is that they support topological edge states, which are protected by lattice symmetry. To further study the role of lattice symmetry in one-dimensional topological insulators, here we design a modified version of the conventional trimer lattices, i.e., decorated trimer lattices. Using the femtosecond laser writing technique, we experimentally establish a series of one-dimensional photonic decorated trimer lattices with and without inversion symmetry, thereby directly observing three kinds of topological edge state. Interestingly, we demonstrate that the additional vertical intracell coupling strength in our model can change the energy band spectrum, thereby generating unconventional topological edge states with a longer localization length in another boundary. This work offers novel insight into topological insulators in one-dimensional photonic lattices.

Topological quantum criticality in non-Hermitian extended Kitaev chain

An attempt is made to study the quantum criticality in non-Hermitian system with topological characterization. We use the zero mode solutions to characterize the topological phases and, criticality and also to construct the phase diagram. The Hermitian counterpart of the model Hamiltonian possess quite a few interesting features such as Majorana zero modes (MZMs) at criticality, unique topological phase transition on the critical line and hence these unique features are of an interest to study in the non-Hermitian case also. We observe a unique behavior of critical lines in presence of non-Hermiticity. We study the topological phase transitions in the non-Hermitian case using parametric curves which also reveal the gap closing point through exceptional points. We study bulk and edge properties of the system where at the edge, the stability dependence behavior of MZMs at criticality is studied and at the bulk we study the effect of non-Hermiticity on the topological phases by investigating the behavior of the critical lines. The study of non-Hermiticity on the critical lines revels the rate of receding of the topological phases with respect to the increase in the value of non-Hermiticity. This work gives a new perspective on topological quantum criticality in non-Hermitian quantum system.

Non-Hermitian topological phase transitions in superlattices and the optical Dirac equation

Optical superlattices with sublattice symmetry subjected to a synthetic imaginary gauge field undergo a topological phase transition in the Bloch energy spectrum, characterized by the change of a spectral winding number. For a narrow gap, the phase transition is of universal form and described by a non-Hermitian Dirac equation with Lorentz-symmetry violation. A simple photonic system displaying such a phase transition is discussed, which is based on light coupling in co-propagating gratings.

Quantum phase transition in a non-HermitianXYspin chain with global complex transverse field

In this work, we investigate the quantum phase transition in a non-HermitianXYspin chain. The phase diagram shows that the critical points of Ising phase transition expand into a critical transition zone after introducing a non-Hermitian effect. By analyzing the non-Hermitian gap and long-range correlation function, one can distinguish different phases by means of different gap features and decay properties of correlation function, a tricky problem in traditionalXYmodel. Furthermore, the results reveal the relationship among different regions of the phase diagram, non-Hermitian energy gap and long-range correlation function.