Quantization of geometric phase with integer and fractional topological characterization in a quantum Ising chain with long-range interaction

Critical scaling of a two-orbital topological model with extended neighboring couplings

Extended-range models are the interesting systems, which has been widely used to understand the non-local properties of the fermions at quantum scale. We aim to study the interplay between criticality and extended range couplings under various symmetry constraints. Here, we consider a two orbital Bernevig-Hughes-Zhang model in one dimension with longer (finite neighbor) and long-range (infinite neighbor) couplings. We study the behavior of model using scaling laws and universality class for models with Hermitian, parity-time ([Formula: see text]) symmetric and broken time-reversal symmetries. We observe the interesting results on multi-criticalities, where the universality class of critical exponent is different than the normal criticalities. Also, the results can be generalized by considering the interplay between criticalities and different symmetry classes of Hamiltonian. Also, with the introduction of extended-range of coupling, there occurs different criticalities, and we provide the analogy to characterize their universality classes. We also show the violation of Lorentz invariance at multi-criticalities and evaluation of short-range limit in long-range models as the highlights of this work.

Mixed state behavior of Hermitian and non-Hermitian topological models with extended couplings

Geometric phase is an important tool to define the topology of the Hermitian and non-Hermitian systems. Besides, the range of coupling plays an important role in realizing higher topological indices and transition among them. With a motivation to understand the geometric phases for mixed states, we discuss finite temperature analysis of Hermitian and non-Hermitian topological models with extended range of couplings. To understand the geometric phases for the mixed states, we use Uhlmann phase and discuss the merit-limitation with respect extended range couplings. We extend the finite temperature analysis to non-Hermitian models and define topological invariant for different ranges of coupling. We include the non-Hermitian skin effect, and provide the derivation of topological invariant in the generalized Brillouin zone and their mixed state behavior also. We also adopt mixed geometric phases through interferometric approach, and discuss the geometric phases of extended-range (Hermitian and non-Hermitian) models at finite temperature.

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.

Multi-critical topological transition at quantum criticality

The investigation and characterization of topological quantum phase transition between gapless phases is one of the recent interest of research in topological states of matter. We consider transverse field Ising model with three spin interaction in one dimension and observe a topological transition between gapless phases on one of the critical lines of this model. We study the distinct nature of these gapless phases and show that they belong to different universality classes. The topological invariant number (winding number) characterize different topological phases for the different regime of parameter space. We observe the evidence of two multi-critical points, one is topologically trivial and the other one is topologically active. Topological quantum phase transition between the gapless phases on the critical line occurs through the non-trivial multi-critical point in the Lifshitz universality class. We calculate and analyze the behavior of Wannier state correlation function close to the multi-critical point and confirm the topological transition between gapless phases. We show the breakdown of Lorentz invariance at this multi-critical point through the energy dispersion analysis. We also show that the scaling theories and curvature function renormalization group can also be effectively used to understand the topological quantum phase transitions between gapless phases. The model Hamiltonian which we study is more applicable for the system with gapless excitations, where the conventional concept of topological quantum phase transition fails.