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Magnetic and topological properties along with quantum correlations in terms of several entanglement measures have been investigated for an antiferromagnetic spin-1/2 XY model in the presence of transverse magnetic field and XZX$-$YZY type of three-spin interactions. Symmetries of the spin Hamiltonian have been identified. Under the Jordan-Wigner transformation, the spin Hamiltonian converted into spinless superconducting model with nearest neighbor hopping and Cooper pairing terms in addition to next nearest neighbor Cooper pairing potential. Long range antiferromagnetic order has been studied in terms of staggered spin-spin correlation functions, while the topological orders have been characterized by winding numbers. Magnetic and topological phase diagrams have been prepared. Faithful coexistence of magnetic and topological superconducting phases is found in the entire parameter regime. Boundaries of various quantum phases have been marked and positions of bicritical points have been identified., Comment: 9 pages, 7 captioned figures

In this study, a spin-1/2 extended anisotropic XY chain has been introduced in which both time reversal and SU(2) symmetries are broken but $Z_2$ symmetry is preserved. Magnetic and topological phase diagrams in the parameter space have been drawn in the presence of transverse magnetic field. Entanglement measures like mutual information and quantum discord are also evaluated and it indicates that these transitions are second order in nature. Quantum phase transition is noted at zero magnetic field, as well as magnetic long range order is found to withstand magnetic field of any strength. Exact analytic results for spin-spin correlation functions have been obtained in terms of Jordan Wigner fermionization. Existence of long range magnetic order has been investigated numerically by finding correlation functions as well as the Binder cumulant in the ground state. Dispersion relation, ground state energy, and energy gap are obtained analytically. In order to find the topologically nontrivial phase, sign of Pfaffian invariant and value of winding number have been evaluated. Both magnetic and topological phases are robust against the magnetic field and found to move coercively in the parameter space with the variation of its strength. Long range orders along two orthogonal directions and two different topological phases are found and their one-to-one correspondence has been found. Finally casting the spinless fermions onto Majorana fermions, properties of zero energy edge states are studied. Three different kinds of Majorana pairings are noted. In the trivial phase, next-nearest-neighbor Majorana pairing is found, whereas two different types of nearest-neighbor Majorana pairings are identified in the topological superconducting phase., Comment: 18 pages, 15 captioned figures

Existence of nontrivial topological phases in a tight binding Haldane-like model on the depleted Lieb lattice is reported. This two-band model is formulated by considering the nearest-neighbor, next-nearest-neighbor and next-next-nearest-neighbor hopping terms along with complex phase which breaks the time reversal symmetry of this semi-metallic system. Topological feature of this model is studied along with the presence of sublattice symmetry breaking staggered onsite energy. Combined effect of these two broken symmetries is found crucial for an additional transition between nontrivial and trivial phases. System exhibits two types of phase transitions, say, between two nontrivial phases and nontrivial to trivial phases. Nonzero Chern numbers, existence of Hall plateau and symmetry protected edge states confirm the presence of the nontrivial phases. This two-band system hosts four different types of phases where two are topological. Additionally topological properties of stacked bilayer of the depleted Lieb lattices is also studied with similar Haldane-like Hamiltonian. This four-band system is found to host Chern insulating phases, with higher values of Chern numbers supported by in-gap edge states., Comment: 10 pages, 8 figures

Simple route of engineering topological phases for any desired value of winding and Chern numbers is found in the Su-Schrieffer-Heeger (SSH) model by adding a further neighbor hopping term of varying distances. It is known that the standard SSH model yields a single topological phase with winding number, $\nu=1$. In this study it is shown that how one can generate topological phases with any values of winding numbers, for examples, $\nu=\pm 1,\pm 2,\pm 3,\cdots,$ in the presence of a single further neighbor term which preserves inversion, particle-hole and chiral symmetries. Quench dynamics of the topological and trivial phases are studied in the presence of a specific nonlinear term. Another version of SSH model with additional modulating nearest neighbor and next-nearest-neighbor hopping parameters was introduced before which exhibit a single topological phase characterized by Chern number, $\mathcal C=\pm 1$. Standard form of inversion, particle-hole and chiral symmetries are broken in this model. Here this model has been studied in the presence of several types of parametrization among which, for a special case the system is found to yield a series of phases with Chern numbers, $\mathcal C=\pm 1,\pm 2,\pm 3,\cdots.$ In another parametrization, multiple crossings within the edge states energy lines are found in both trivial and topological phases. Topological phase diagrams are drawn for every case. Emergence of spurious topological phases is also reported., Comment: 21 pages, 35 figures

The global pandemic due to the outbreak of COVID-19 ravages the whole world for more than two years in which all the countries are suffering a lot since December 2019. In order to control this ongoing waves of epidemiological infections, attempts have been made to understand the dynamics of this pandemic in deterministic approach with the help of several mathematical models. In this article characteristics of a multi-wave SIR model have been studied which successfully explains the features of this pandemic waves in India. Stability of this model has been studied by identifying the equilibrium points as well as by finding the eigen values of the corresponding Jacobian matrices. Complex eigen values are found which ultimately give rise to the oscillatory solutions for the three categories of populations, say, susceptible, infected and removed. In this model, a finite probability of the recovered people for becoming susceptible again is introduced which eventually lead to the oscillatory solution in other words. The set of differential equations has been solved numerically in order to obtain the variation for numbers of susceptible, infected and removed people with time. In this phenomenological study, finally an additional modification is made in order to explain the aperiodic oscillation which is found necessary to capture the feature of epidemiological waves particularly in India., Comment: Five pages, two-column, six figures

Magnetic field induced multiple non-Dirac nodal-lines are found to emerge in the triplet dispersion bands of a frustrated spin-1/2 antiferromagnetic model on the CaVO lattice. Plaquette and bond operator formalisms have been employed to obtain the triplet plaquette and bond excitations for two different parameter regimes in the presence of nearest and next-nearest-neighbor Heisenberg interactions based on the plaquette-resonating-valence-bond and dimerized ground states, respectively. In the absence of magnetic field a pair of six-fold degenerate nodal-loops with distinct topological feature is noted in the plaquette excitations. They are found to split into three pairs of two-fold degenerate nodal-loops in the presence of magnetic field. In the other parameter regime, system hosts two-fold degenerate multiple nodal-lines with a variety of shapes in the triplon dispersion bands in the presence of magnetic field. Ground state energy and spin gap have been determined additionally for the two regimes. Those nodal-lines are expected to be detectable in neutron scattering experiment on the frustrated antiferromagnet, CaV$_4$O$_9$., Comment: 15 pages, 17 figures

A number of topological phases are found to emerge in the ferromagnetic Kitaev-Heisenberg model on CaVO lattice in the presence of Dzyaloshinskii-Moriya interaction. Heisenberg and Kitaev terms have been considered on nearest and next-nearest neighbor bonds in a variety of ways. Both isotropic and anisotropic couplings are taken into account. Topological phases are characterized by Chern numbers for the distinct magnon bands as well as the number of modes for topologically protected gapless magnon edge states. Band structure, dispersion relation along the high-symmetric points of first Brillouin zone, density of states and thermal Hall conductance have been evaluated for every phase. An extensive Phase diagram has been constructed. Topological phase transition in the parameter space is also studied., Comment: 12 pages, 13 figures

In this work, topological properties of a ferromagnetic Heisenberg model on a breathing kagome lattice are investigated extensively in the presence of Dzyaloshinskii-Moriya interaction. While the kagome ferromagnet hosts only a single first order topological phase, the breathing kagome system exhibits multiple first and second order topological phases along with their coexistence. Magnon dispersion relation is obtained by using linear spin wave theory. Flat band and Dirac cones are obtained in the absence of Dzyaloshinskii-Moriya interaction. A topological phase diagram is presented where several first and second order phases as well as their overlap are identified. Values of thermal Hall conductivity for all the first order phases are obtained. Distinct first order phases are characterized by different sets of Chern numbers in association with the necessary chiral edge states in accordance to the first order bulk-boundary-correspondence rule. Second order phase is characterized by polarization along with the emergence of corner states. Violation of the second order bulk-corner-correspondence rule has been noted in some regions., Comment: 9 pages, 8 figures

We study the transport properties of Dirac electrons across a two-dimensional normal metal-barrier-normal metal (NBN) interfaces in monolayer borophane. We analyse the transmission probability with variation of the width of the barrier region, the incidence energy and transverse momentum. We demonstrate that a gap exists in the transmission probability spectrum and the position, width of transmission gap can be tuned by the barrier strength and transverse momentum respectively. We point out the variation of the ballistic tunneling conductance as a function of the width of the barrier region and incident energy. We find that the oscillatory or decaying nature of the conductance with variation in barrier width depends upon the number of propagating and evanescent modes which are controlled by the incident energy and barrier strength. We show that the conductance as a function of incident energy drops to a minimum value when the incident energy becomes identical to the barrier height and identify that this effect is caused by the presence of evanescent modes inside the barrier. Based on these findings we propose a perfectly tunable wavevector filter for Borophane. We expect our findings posses useful applications in borophane based nano-electronic devices., Comment: Ten pages, double column, Eleven figures

Emergence of multiple topological phases with a series of Chern numbers, $\pm 1$, $\mp 1$, $\pm 2$, $\mp 2$, $\pm 3$ and $\mp 4$, are observed in a ferromagnetic Kitaev-Heisenberg-spin-anisotropic model on honeycomb lattice with further neighbor interactions in the presence of an external magnetic field. Magnon Chern insulating dispersions of this two-band model are studied by using linear spin-wave theory formulated on the exact ferromagnetic ground state. Magnon edge states are obtained for the respective topological phases along with density of states. A topological phase diagram of this model is presented. Behavior of thermal Hall conductivity for those phases is studied. Sharp jumps of thermal hall conductivity is noted near the vicinity of phase transition points. Topological phases of the Kitaev spin-liquid compounds, $\alpha$-RuCl$_3$, X$_2$IrO$_3$, X = (Na, Li) and CrY$_3$, Y = (Cl, Br, I) are characterized based on this theoretical findings., Comment: 7 pages, 9 figures

Antikink dispersion of the asymmetric $J_1$-$J_2$ sawtooth spin-1/2 anisotropic Heisenberg antiferromagnetic chain has been derived. Value of spin-gap is obtained by estimating the minimum of dispersion relation variationally. The exact doubly-degenerate ground state energy has been derived at the symmetric point, $J_1=J_2$, for the whole anisotropic regime. Analytic form of dispersion relations of three different antikink states is obtained and their validity in the parameter space is discussed. The value of spin-gap, specific heat and susceptibility are estimated numerically by diagonalizing the Hamiltonian for chains of finite length. The inherent frustration of this antiferromagnetic model leads to the appearance of additional peak at low-temperatures in the specific heat., Comment: Single column, 19 pages, 6 figures

In this study, a tight-binding model on square octagon lattice with nearest-neighbour and next-nearest-neighbour hoppings is considered. The system is topologically trivial although it exhibits quadratic band-touching points in its band-structure. It is shown that the system drives towards topologically non-trivial phases as soon as it is exposed to monochromatic circularly polarized light. Multiple topological phases are found to emerge with the variation of amplitude of light. An effective time-independent Hamiltonian of the system is obtained following the Floquet-Bloch formulation. Quasi-energy band-structures along with definite values of Chern numbers for respective bands are obtained. Characterization of topological phases are made in terms of band structure and Chern numbers. In addition, Hall conductance and topologically protected chiral edge states are obtained to explain the topological properties. Density of states is obtained in every case. The system undergoes a series of topological phase transitions among various topological phases upon variations of both amplitude of light and hopping strengths. It exhibits Chern insulating and Chern semimetallic phases depending on the values of lattice filling., Comment: 9 pages, 6 figures

We report the appearance of nontrivial topological phases in a tight-binding model on the stuffed honeycomb lattice. The model contains nearest neighbor and next nearest neighbor hopping terms coupled with an additional phase depending on the direction of hopping. Chern insulating and semi-metallic phases emerge with the change of hopping parameters. Nonzero Chern numbers characterizing the bands and the existence of topologically protected edge states in the gap between the relevant bands confirm the presence of those phases. We show that adding an extra basis to Haldane's honeycomb model can lead to an additional topological phase characterized by Chern number $\pm2$. Transition between different topological phases driven by the hopping parameters has been illustrated in the topological phase diagram of the system. Zero temperature Hall conductivity along with density of states is evaluated. Topological properties of another tight-binding model on the stuffed square lattice are also reported in this article., Comment: 8 pages, 6 figures

A number of topological nodes including Dirac, quadratic and triple band touching points as well as a pair of degenerate Dirac line nodes are found to emerge in the triplet plaquette excitations of the frustrated spin-1/2 $J_1$-$J_2$ antiferromagnetic Heisenberg honeycomb model when the ground state of the system lies in a spin-disordered plaquette-valence-bond-solid phase. A six-spin plaquette operator theory of this honeycomb model has been developed for this purpose by using the eigenstates of an isolated Heisenberg hexagonal plaquette. Spin-1/2 operators are thus expressed in the Fock space spanned by the plaquette operators those are obtained in terms of exact analytic form of eigenstates for a single frustrated Heisenberg hexagon. Ultimately, an effective interacting boson model of this system is obtained on the basis of low energy singlets and triplets plaquette operators by employing a mean-field approximation. The values of ground state energy and spin gap of this system have been estimated and the validity of this formalism has been tested upon comparison with the known results. Emergence of topological point and line nodes on the basis of spin-disordered ground state noted in this investigation is very rare on any frustrated system as well as the presence of triplet flat band. Evolution of those topological nodes is studied throughout the full frustrated regime. Finally, emergence of topological phases has been reported upon adding a time-reversal-symmetry breaking term to the Hamiltonian. Coexistence of spin gap with either topological nodes or phases turns this honeycomb model an interesting one., Comment: 21 pages, 17 figures

Tight-binding Hamiltonian on the prismatic pentagonal lattice is exactly solved to obtain the analytic expressions of dispersion relations and eigenvectors. This lattice is made of prismatic pentagon which is different from Cairo pentagon. Six different dispersion relations and total density of states are obtained. Dispersion relations are symmetric about the zero energy at a particular point in the parameter space. Although a large gap is found for the Cairo pentagonal lattice, no gap as well as no Dirac cone is found to appear in the tight-binding band structure for this prismatic pentagonal lattice. Instead, a pair of van Hove singularities has been identified at two different energy values in the band structure., Comment: 11 pages, single column, 3 figures. arXiv admin note: substantial text overlap with arXiv:1611.06029

Thermally stable quantum states with multipartite entanglements led by frustration are found in the antiferromagnetic spin-1/2 Heisenberg hexagon. The model has been solved exactly to obtain all analytic expressions of eigenvalues and eigenfunctions. Detection and characterizations for various types of entanglements have been carried out in terms of concurrence and entanglement witnesses based on several thermodynamic observables. Variations of entanglement properties with respect to temperature and frustration are discussed. Even though the frustration opposes the bipartite entanglement, it favors the multipartite entanglement. Entangled states exhibit robustness against the thermal effects in the presence of frustration and they are found to survive at any temperature., Comment: 25 pages, double space, single column, 5 figures

Multiple gaps in the tight-binding band of a pentagonal lattice are found. Unlike the Cairo pentagonal lattice this lattice is made of irregular pentagons with arms of different lengths. The tight-binding Hamiltonian is exactly solved to obtain analytic expressions of dispersion relations and eigenvectors. Four different band-gaps are identified along with two distinct indirect band-gaps at the Harrison point. Multiple band-gaps in this model may give rise to exotic electronic properties., Comment: This paper has been withdrawn by the authors to rectify crucial errors in the derivations