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Register a new userCritical phase boundaries of static and periodically kicked long-range Kitaev chain
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We study the static and dynamical properties of a long-range Kitaev chain, i.e., a $p$-wave superconducting chain in which the superconducting pairing decays algebraically as $1/l^{alpha}$, where $l$ is the distance between the two sites and $alpha$ is a positive constant. Considering very large system sizes, we show that when $alpha >1$, the system is topologically equivalent to the short-range Kitaev chain with massless Majorana modes at the ends of the system; on the contrary, for $alpha <1$, there exist symmetry protected massive Dirac end modes. We further study the dynamical phase boundary of the model when periodic $delta$-function kicks are applied to the chemical potential; we specially focus on the case $alpha >1$ and analyze the corresponding Floquet quasienergies. Interestingly, we find that new topologically protected massless end modes are generated at the quasienergy $pi/T$ (where $T$ is the time period of driving) in addition to the end modes at zero energies which exist in the static case. By varying the frequency of kicking, we can produce topological phase transitions between different dynamical phases. Finally, we propose some bulk topological invariants which correctly predict the number of massless end modes at quasienergies equal to 0 and $pi/T$ for a periodically kicked system with $alpha > 1$.
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We describe a method to probe the quantum phase transition between the short-range topological phase and the long-range topological phase in the superconducting Kitaev chain with long-range pairing, both exhibiting subgap modes localized at the edges. The method relies on the effects of the finite mass of the subgap edge modes in the long-range regime (which survives in the thermodynamic limit) on the single-particle scattering coefficients through the chain connected to two normal leads. Specifically, we show that, when the leads are biased at a voltage V with respect to the superconducting chain, the Fano factor is either zero (in the short-range correlated phase) or 2e (in the long-range correlated phase). As a result, we find that the Fano factor works as a directly measurable quantity to probe the quantum phase transition between the two phases. In addition, we note a remarkable critical fractionalization effect in the Fano factor, which is exactly equal to e along the quantum critical line. Finally, we note that a dual implementation of our proposed device makes it suitable as a generator of large-distance entangled two-particle states.
Anti-site disorder is one of the most important issues that arises in synthesis of double perovskite for spintronic applications. Although it is known that anti-site disorder leads to a proliferation of structural defects, known as the anti-phase boundaries that separate ordered anti-phase domains in the sample, little is known about the magnetic correlation across these anti-phase boundaries on a microscopic level. Motivated by this, we report resonant elastic X-ray scattering study of room temperature magnetic and structural correlation in a thin-film sample of Sr$_2$CrReO$_6$, which has one of the highest $mathrm{T_C}$ among double perovskites. Structurally, we discovered existence of anti-phase nanodomains of $sim$15~nm in the sample. Magnetically, the ordered moments are shown to lie perpendicular to the $c$ direction. Most remarkably, we found that the magnetic correlation length far exceeds the size of individual anti-phase nanodomains. Our results therefore provide conclusive proof for existence of robust magnetic correlation across the anti-phase boundaries in Sr$_2$CrReO$_6$.
Periodically driven quantum many-body systems support anomalous topological phases of matter, which cannot be realized by static systems. In many cases, these anomalous phases can be many-body localized, which implies that they are stable and do not heat up as a result of the driving. What types of anomalous topological phenomena can be stabilized in driven systems, and in particular, can an anomalous phase exhibiting non-Abelian anyons be stabilized? We address this question using an exactly solvable, stroboscopically driven 2D Kitaev spin model, in which anisotropic exchange couplings are boosted at consecutive time intervals. The model shows a rich phase diagram which contains anomalous topological phases. We characterize these phases using weak and strong scattering-matrix invariants defined for the fermionic degrees of freedom. Of particular importance is an anomalous phase whose zero flux sector exhibits fermionic bands with zero Chern numbers, while a vortex binds a pair of Majorana modes, which as we show support non-Abelian braiding statistics. We further show that upon adding disorder, the zero flux sector of the model becomes localized. However, the model does not remain localized for a finite density of vortices. Hybridization of Majorana modes bound to vortices form vortex bands, which delocalize by either forming Chern bands or a thermal metal phase. We conclude that while the model cannot be many-body localized, it may still exhibit long thermalization times, owing to the necessity to create a finite density of vortices for delocalization to occur.
With optimal control theory, we compute the maximum possible quantum Fisher information about the interaction parameter for a Kitaev chain with tunable long-range interactions in the many-particle Hilbert space. We consider a wide class of decay laws for the long-range interaction and develop rigorous asymptotic analysis for the scaling of the quantum Fisher information with respect to the number of lattice sites. In quantum metrology nonlinear many-body interactions can enhance the precision of quantum parameter estimation to surpass the Heisenberg scaling, which is quadratic in the number of lattice sites. Here for the estimation of the long-range interaction strength, we observe the Heisenberg to super-Heisenberg transition in such a $linear$ model, related to the slow decaying long-range correlations in the model. Finally, we show that quantum control is able to improve the prefactor rather than the scaling exponent of the quantum Fisher information. This is in contrast with the case where quantum control has been shown to improve the scaling of quantum Fisher information with the probe time. Our results clarify the role of quantum controls and long-range interactions in many-body quantum metrology.
We study the Floquet phase diagram of two-dimensional Dirac materials such as graphene and the one-dimensional (1D) spin-1/2 $XY$ model in a transverse field in the presence of periodic time-varying terms in their Hamiltonians in the low drive frequency ($omega$) regime where standard $1/omega$ perturbative expansions fail. For graphene, such periodic time dependent terms are generated via the application of external radiation of amplitude $A_0$ and time period $T = 2pi/omega$, while for the 1D $XY$ model, they result from a two-rate drive protocol with time-dependent magnetic field and nearest-neighbor couplings between the spins. Using the adiabatic-impulse method, we provide several semi-analytic criteria for the occurrence of changes in the topology of the phase bands of such systems. For irradiated graphene, we point out the role of the symmetries of $H(t)$ and $U$ behind such topology changes. Our analysis reveals that at low frequencies, phase band topology changes may also happen at $t= T/3, 2T/3$ (apart from $t=T$). We chart out the phase diagrams at $t=T/3, 2T/3,, {rm and }, T$ as a function of $A_0$ and $T$ using exact numerics, and compare them with the prediction of the adiabatic-impulse method. We show that several characteristics of these phase diagrams can be analytically understood from results obtained using the adiabatic-impulse method and point out the crucial contribution of the high-symmetry points in the graphene Brillouin zone to these diagrams. Finally we study the 1D $XY$ model with a two-rate driving protocol using the adiabatic-impulse method and exact numerics revealing a phase band crossing at $t=T/2$ and $k=pi/2$. We also study the anomalous end modes generated by such a drive. We suggest experiments to test our theory.
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