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In lattice models with quadratic finite-range Hermitian Hamiltonians, the inherently non-Hermitian transfer matrix (TM) governs the band dispersion. The van Hove singularities (VHSs) are special points in the band dispersion where the density of states (DOS) diverge. Considering a lattice chain with hopping of a finite range $n$, we find a direct fundamental connection between VHSs and exceptional points (EPs) of TM, both of arbitrary order. In particular, we show that VHSs are EPs of TM of the same order, thereby connecting two different types of critical points usually studied in widely different branches of physics. Consequently, several properties of band dispersion and VHSs can be analyzed in terms of spectral properties of TM. We further provide a general prescription to generate any order EP of the TM and therefore corresponding VHS. For a given range of hopping $n$, our analysis provides restrictions on allowed orders of EPs of TM. Finally, we exemplify all our results for the case $n=3$.

Recently, it has been shown that, in one dimensional fermionic systems, close to band edges, the zero temperature conductance scales as $1/N^2$, where $N$ is the system length. This universal subdiffusive scaling of conductance at band edges has been tied to an exceptional point (EP) of the transfer matrix of the system that occur at every band edge. Further, in presence of bulk dephasing probes, this EP has been shown to lead to a counterintuitive superballistic scaling of conductance, where the conductance increases with $N$ over a finite but large regime of system lengths. In this work, we explore how these behaviors are affected by the order of the transfer matrix EP at the band edge. We consider a one-dimensional fermionic lattice chain with a finite range of hopping. Depending on the range of hopping and the hopping parameters, this system can feature band edges which correspond to arbitrarily higher order EPs of the associated transfer matrix. Using this system we establish in generality that, in absence of bulk dephasing, surprisingly, the universal $1/N^2$ scaling of conductance is completely unaffected by the order of the EP. This is despite the fact that existence of transfer matrix EP is crucial for such behavior. In presence of bulk dephasing, however, the phase coherence length, the extent of the superballisitic scaling regime and the exponent of superballistic scaling, all encode the order of the transfer matrix EP.

We consider an analytically tractable model that exhibits the main features of the Page curve characterizing the evolution of entanglement entropy during evaporation of a black hole. Our model is a gas of non-interacting fermions on a lattice that is released from a box into the vacuum. More precisely, our Hamiltonian is a tight-binding model with a defect at the junction between the filled box and the vacuum. In addition to the entanglement entropy we consider several other observables, such as the spatial density profile and current, and show that the semiclassical approach of generalized hydrodynamics provides a remarkably accurate description of the quantum dynamics including that of the entanglement entropy at all times. Our hydrodynamic results agree closely with those obtained via exact microscopic numerics. We find that the growth of entanglement is linear and universal, i.e, independent of the details of the defect. The decay shows $1/t$ scaling for conformal defect while for non-conformal defects, it is slower. Our study shows the power of the semiclassical approach and could be relevant for discussions on the resolution of the black hole information paradox.

We investigate the emergence and corresponding nature of exceptional points located on exceptional hyper-surfaces of non-hermitian transfer matrices for finite-range one-dimensional lattice models. We unravel the non-trivial role of these exceptional points in determining the system size scaling of electrical conductance in non-equilibrium steady state. We observe that the band edges of the system always correspond to the transfer matrix exceptional points. Interestingly, albeit the lower band edge always occurs at wave-vector $k=0$, the upper band edge may or may not correspond to $k=\pi$. Nonetheless, in all the cases, the system exhibits universal subdiffusive transport for conductance at every band edge with scaling $N^{-b}$ with scaling exponent $b= 2$. However, for cases when the upper band edge is not located at $k=\pi$, the conductance features interesting oscillations with overall $N^{-2}$ scaling. Our work further reveals that this setup is uniquely suited to systematically generate higher order transfer matrix exceptional points at upper band edge when one considers finite range hoppings beyond nearest neighbour. Additional exceptional points other than those at band edges are shown to occur, although interestingly, these do not give rise to anomalous transport.

For a four-stroke asymmetrically driven quantum Otto engine with working medium modeled by a single qubit, we study the bounds on non-equilibrium fluctuations of work and heat. We find strict relations between the fluctuations of work and individual heat for hot and cold reservoirs in arbitrary operational regimes. Focusing on the engine regime, we show that the ratio of non-equilibrium fluctuations of output work to input heat from the hot reservoir is both upper and lower bounded. As a consequence, we establish hierarchical relation between the relative fluctuations of work and heat for both cold and hot reservoirs and further make a connection with the thermodynamic uncertainty relations. We discuss the fate of these bounds also in the refrigerator regime. The reported bounds, for such asymmetrically driven engines, emerge once both the time-forward and the corresponding reversed cycles of the engine are considered on an equal footing. We also extend our study and report bounds for a parametrically driven harmonic oscillator Otto engine., Comment: 14 pages, 6 figures

We find that, in the presence of weak incoherent effects from surrounding environments, the zero temperature conductance of nearest neighbour tight-binding chains exhibits a counter-intuitive power-law growth with system length at band-edges, indicating superballistic scaling. This fascinating environment assisted superballistic scaling of conductance occurs over a finite but extended regime of system lengths. This scaling regime can be systematically expanded by decreasing the coupling to the surrounding environments. There is no corresponding analog of this behavior for isolated systems. This superballistic scaling stems from an intricate interplay of incoherent effects from surrounding environments and exceptional points of the system's transfer matrix that occur at every band-edge.

We discover a deep connection between parity-time (PT) symmetric optical systems and quantum transport in one-dimensional fermionic chains in a two-terminal open system setting. The spectrum of one dimensional tight-binding chain with periodic on-site potential can be obtained by casting the problem in terms of $2 \times 2$ transfer matrices. We find that these non-Hermitian matrices have a symmetry exactly analogous to the PT-symmetry of balanced-gain-loss optical systems, and hence show analogous transitions across exceptional points. We show that the exceptional points of the transfer matrix of a unit cell correspond to the band edges of the spectrum. When connected to two zero temperature baths at two ends, this consequently leads to subdiffusive scaling of conductance with system size, with an exponent $2$, if the chemical potential of the baths are equal to the band edges. We further demonstrate the existence of a dissipative quantum phase transition as the chemical potential is tuned across any band edge. Remarkably, this feature is analogous to transition across a mobility edge in quasiperiodic systems. This behavior is universal, irrespective of the details of the periodic potential and the number of bands of the underlying lattice. It, however, has no analog in absence of the baths.

Quasi-periodic lattice systems offer diverse transport properties. In this work, we investigate the environment induced effects on transport properties for quasi-periodic systems, namely the one-dimensional Aubry-Andr\'e-Harper (AAH) lattice chain and its generalized version (GAAH) by considering the B\"uttiker probe approach. We first consider voltage probe situation and study the electrical conductance properties in the linear response regime. At zero temperature, we observe enhancement in conductance at all the no-transport regimes, located both inside and outside of the band of the original system, for small probe coupling strength $\gamma$ with a power-law scaling $\gamma^4$. Whereas, for large probe coupling strengths, the conductance at all Fermi energies is the same and decays as a power-law with scaling $1/\gamma^4$. This particular scaling survives even in the finite-temperature limit. Interestingly, this scaling result is different from the one recently predicted following the local Lindblad master equation approach. The transport eventually becomes diffusive for all energy ranges and in all regimes of the original model for a sufficiently strong coupling with the probes. We further extend our study and consider voltage-temperature probes to analyze the thermoelectric performance of the chain in terms of the figure of merit. We also demonstrate the validity of two recently obtained bounds on thermoelectric efficiency that are tighter than the seminal Carnot bound and express the same in terms of the Onsager's transport coefficients.

We show that a one-dimensional ordered fermionic lattice system with power-law-decaying hopping, when connected to two baths at its two ends with different chemical potentials at zero temperature, features two phases showing sub-diffusive scaling of conductance with system size. These phases have no analogues in the isolated system (i.e, in absence of the baths) where the transport is perfectly ballistic. In the open system scenario, interestingly, there occurs two chemical-potential-driven sub-diffusive to ballistic phase transitions at zero temperature. We discuss how these phase transitions, to our knowledge, are different from all the known non-equilibrium quantum phase transitions. We provide a clear understanding of the microscopic origin of these phases and argue that the sub-diffusive phases are robust against the presence of arbitrary number-conserving many-body interactions in the system. These phases showing sub-diffusive scaling of conductance with system size in a two-terminal set-up are therefore universal properties of all ordered one-dimensional number-conserving fermionic systems with power-law-decaying hopping at zero temperature.

We develop a theoretical scheme to perform a read-out of the properties of a quasi-periodic system by coupling it to one or two qubits. We show that the decoherence dynamics of a single qubit coupled via a pure dephasing type term to a 1D quasi-periodic system with a potential given by the Andr\'e-Aubry-Harper (AAH) model and its generalized versions (GAAH model) is sensitive to the nature of the single particle eigenstates (SPEs). More specifically, we can use the non-markovianity of the qubit dynamics as quantified by the backflow of information to clearly distinguish the localized, delocalized, and mixed regimes with a mobility edge of the AAH and GAAH model and evidence the transition between them. By attaching two qubits at distinct sites of the system, we demonstrate that the transport property of the quasi-periodic system is encoded in the scaling of the threshold time to develop correlations between the qubits with the distance between the qubits. This scaling can also be used to distinguish and infer different regimes of transport such as ballistic, diffusive and no transport engendered by SPEs that are delocalized, critical and localized respectively. When there is a mobility edge allowing the coexistence of different kinds of SPEs in the spectrum, such as the coexistence of localized and delocalized states in the GAAH models, we find that the transport behaviour and the scaling of the threshold time with qubit separation is governed by the fastest spreading states.

Localization in one-dimensional disordered or quasiperiodic non-interacting systems in presence of power-law hopping is very different from localization in short-ranged systems. Power-law hopping leads to algebraic localization as opposed to exponential localization in short-ranged systems. Exponential localization is synonymous with insulating behavior in the thermodynamic limit. Here we show that the same is not true for algebraic localization. We show, on general grounds, that depending on the strength of the algebraic decay, the algebraically localized states can be actually either conducting or insulating in thermodynamic limit. We exemplify this statement with explicit calculations on the Aubry-Andr\'e-Harper model in presence of power-law hopping, with the power-law exponent $\alpha>1$, so that the thermodynamic limit is well-defined. We find a phase of this system where there is a mobility edge separating completely delocalized and algebraically localized states, with the algebraically localized states showing signatures of super-diffusive transport. Thus, in this phase, the mobility edge separates two kinds of conducting states, ballistic and super-diffusive. We trace the occurrence of this behavior to near-resonance conditions of the on-site energies that occur due to the quasi-periodic nature of the potential.

We reveal interesting universal transport behavior of ordered one-dimensional fermionic systems with power-law hopping. We restrict ourselves to the case where the power-law decay exponent $\alpha>1$, so that the thermodynamic limit is well-defined. We explore the quantum phase-diagram of the non-interacting model in terms of the zero temperature Drude weight, which can be analytically calculated. Most interestingly, we reveal that for $1<\alpha<2$, there is a phase where the zero temperature Drude weight diverges as filling fraction goes to zero. Thus, in this regime, counter intuitively, reducing number of particles increases transport and is maximum for a sub-extensive number of particles. Being a statement about zero-filling, this transport behavior is immune to adding number conserving interaction terms. We have explicitly checked this using two different interacting systems. We propose that measurement of persistent current due to a flux through a mesoscopic ring with power-law hopping will give an experimental signature of this phase. In persistent current, the signature of this phase survives up to a finite temperature for a finite system. At higher temperatures, a crossover is seen. The maximum persistent current shows a power-law decay at high temperatures. This is in contrast with short ranged systems, where the persistent current decays exponentially with temperature.

We report transport properties and particle current rectification operation in a double-stranded tight-binding ladder network within non-equilibrium Green's function (NEGF) formalism that can easily be generalized in multi-stranded systems. First, we explore the rectification operation considering the model of an artificial double-stranded DNA (dsDNA) molecular system with Fibonacci type substitutional sequence. Substitutional sequences form quasi-periodic potentials. This analysis may shed new light in designing efficient nanoscale rectifier. It can also be directly implemented to different biomolecular systems like nucleic acids and most proteins as they follow quasi-periodic orders. Motivated with this fact, we consider different configurations depending on the choices of on-site energies and/or inter or intra strand nearest-neighbor hopping integrals in the form of Aubry-Andr\'{e}-Harper (AAH) model (that also obeys quasi-periodic order), and in all the cases we find almost $100\%$ current rectification even at very low bias region. Along with this, we observe that the phase (positive or negative) of rectification can suitably be engineered by tuning the Fermi energy and AAH phase. The effects of electron-electron (e-e) interaction and temperature are also studied, which show that a reasonably large rectification can be observed even for moderate temperature range and e-e interaction strength., Comment: 14 pages, 20 figures [Accepted for publication in Journal of Physics D: Applied Physics]

The spin momentum non-orthogonality in 3D topological insulators leads to modification of the spin texture and brings in an out-of-plane spin polarization component. Apart from spin texture, the anomalous thermoelectric properties of these materials are worth studying. In this paper, we have pointed out that the off resonant light used to irradiate the surface states, induces a gap, which becomes momentum dependent due to the presence of non-orthogonal terms in the Hamiltonian. Importantly, to maintain the off resonant condition of light, the momentum value should satisfy a bound. Furthermore, the momentum dependent gap causes a topological transition at higher value of momentum, which is important to analyse the unusual double peak structure of the Nernst and electrical conductivities., Comment: Accepted for publication in Journal of Applied Physics

We address an unexpectedly large rectification using a simple quantum wire with correlated site potentials. The external electric field, associated with voltage bias, leads to unequal charge currents for two different polarities of external bias and this effect is further enhanced by incorporating the asymmetry in wire-to-electrode coupling. Our calculations suggest that in some cases almost cent percent rectification is obtained for a wide bias window. This performance is valid against disorder configurations and thus we can expect an experimental verification of our theoretical analysis in near future., Comment: 4 pages, 7 figures (Accepted for Publication in Physica E: Low-Dimensional Systems and Nanostructures)

We investigate characteristic features of both non-interacting and interacting electrons in a M\"{o}bius strip, the simplest possible one-sided topological system, in presence of an Aharonov-Bohm flux $\phi$. Using Hartree-Fock mean field theory we determine energy eigenvalues for the interacting model, while for the non-interacting system an analytical prescription is given. The interplay between longitudinal and vertical motions of electrons along with on-site Hubbard interaction yield several anomalous features of persistent current associated with energy-flux characteristics. The variation of current with system size and its temperature dependences are also critically examined. Current is highly sensitive to both these two factors, and we find that for a particular system size it decreases exponentially with temperature. Our analysis can be helpful in investigating electronic transport through any non-trivial topological material., Comment: 9 pages, 14 figures (Accepted for Publication in Superlattices and Microstructures)

The interplay between Hubbard interaction, long-range hopping and disorder on persistent current in a mesoscopic one-dimensional conducting ring threaded by a magnetic flux $\phi$ is analyzed in detail. Two different methods, exact numerical diagonalization and Hartree-Fock mean field theory, are used to obtain numerical results from the many-body Hamiltonian. The current in a disordered ring gets enhanced as a result of electronic correlation and it becomes more significant when contributions from higher order hoppings, even if they are too small compared to nearest-neighbor hopping, are taken into account. Certainly this can be an interesting observation in the era of long-standing controversy between theoretical and experimental results of persistent current amplitudes. Along with these we also find half-flux quantum periodic current for some typical electron fillings and kink-like structures at different magnetic fluxes apart from $\phi=0$ and $\pm \phi_0/2$. The scaling behavior of current is also discussed for the sake of completeness of our present analysis., Comment: 13 pages, 25 figures (Accepted for Publication in Physica E: Low-Dimensional Systems and Nanostructures)

We calculate persistent current of one-dimensional rings of fermions neglecting the spin degrees of freedom considering only nearest-neighbor Coulomb interactions with different electron fillings in both ordered and disordered cases. We treat the interaction exactly and find eigenenergies by exact diagonalization of many-body Hamiltonian and compute persistent current by numerical derivative method. We also determine Drude weight to estimate the conducting nature of the system. From our numerical results, we obtain a metal-insulator transition in half-filled case with increasing correlation strength U but away from half-filling no such transition is observed even for large U., Comment: 5 pages, 9 figures (Accepted for Publication in: Physics Letters A)