Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userEntanglement properties of the time periodic Kitaev Chain
61
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The entanglement properties of the time periodic Kitaev chain with nearest neighbor and next nearest neighbor hopping, is studied. The cases of the exact eigenstate of the time periodic Hamiltonian, referred to as the Floquet ground state (FGS), as well as a physical state obtained from time-evolving an initial state unitarily under the influence of the time periodic drive are explored. Topological phases are characterized by different numbers of Majorana zero ($mathbb{Z}_0$) and $pi$ ($mathbb{Z}_{pi}$) modes, where the zero modes are present even in the absence of the drive, while the $pi$ modes arise due to resonant driving. The entanglement spectrum (ES) of the FGS as well as the physical state show topological Majorana modes whose number is different from that of the quasi-energy spectrum. The number of Majorana edge modes in the ES of the FGS vary in time from $|mathbb{Z}_0-mathbb{Z}_{pi}|$ to $mathbb{Z}_0+mathbb{Z}_{pi}$ within one drive cycle, with the maximal $mathbb{Z}_0+mathbb{Z}_{pi}$ modes appearing at a special time-reversal symmetric point of the cycle. For the physical state on the other hand, only the modes inherited from the initial wavefunction, namely the $mathbb{Z}_0$ modes, appear in the ES. The $mathbb{Z}_{pi}$ modes are absent in the physical state as they merge with the bulk excitations that are simultaneously created due to resonant driving. The topological properties of the Majorana zero and $pi$ modes in the ES are also explained by mapping the parent wavefunction to a Bloch sphere.
rate research
Read More
We gauge the fermion parity symmetry of the Kitaev chain. While the bulk of the model becomes an Ising chain of gauge-invariant spins in a tilted field, near the boundaries the global fermion parity symmetry survives gauging, leading to local gauge-invariant Majorana operators. In the absence of vortices, the Higgs phase exhibits fermionic symmetry-protected topological (SPT) order distinct from the Kitaev chain. Moreover, the deconfined phase can be stable even in the presence of vortices. We also undertake a comprehensive study of a gently gauged model which interpolates between the ordinary and gauged Kitaev chains. This showcases rich quantum criticality and illuminates the topological nature of the Higgs phase. Even in the absence of superconducting terms, gauging leads to an SPT phase which is intrinsically gapless due to an emergent anomaly.
Floquet Majorana edge modes capture the topological features of periodically driven superconductors. We present a Kitaev chain with multiple time periodic driving and demonstrate how the avoidance of bands crossing is altered, which gives rise to new regions supporting Majorana edge modes. A one dimensional generalized method was proposed to predict Majorana edge modes via the Zak phase of the Floquet bands. We also study the time independent effective Hamiltonian at high frequency limit and introduce diverse index to characterize topological phases with different relative phase between the multiple driving. Our work enriches the physics of driven system and paves the way for locating Majorana edge modes in larger parameter space.
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.
Thermal entanglement, magnetic and quadrupole moments properties of the mixed spin-1/2 and spin-1 Ising-Heisenberg model on a diamond chain are considered. Magnetization and quadrupole moment plateaus are observed for the antiferromagnetic couplings. Thermal negativity as a measure of quantum entanglement of the mixed spin system is calculated. Different behavior for the negativity is obtained for the various values of Heisenberg dipolar and quadrupole couplings. The intermediate plateau of the negativity has been observed at absence of the single-ion anisotropy and quadrupole interaction term. When dipolar and quadrupole couplings are equal there is a similar behavior of negativity and quadrupole moment.
A minimal Kitaev-Gamma model has been recently investigated to understand various Kitaev systems. In the one-dimensional Kitaev-Gamma chain, an emergent SU(2)$_1$ phase and a rank-1 spin ordered phase with $O_hrightarrow D_4$ symmetry breaking were identified using non-Abelian bosonization and numerical techniques. However, puzzles near the antiferromagnetic Kitaev region with finite Gamma interaction remained unresolved. Here we focus on this parameter region and find that there are two new phases, namely, a rank-1 ordered phase with an $O_hrightarrow D_3$ symmetry breaking, and a peculiar Kitaev phase. Remarkably, the $O_hrightarrow D_3$ symmetry breaking corresponds to the classical magnetic order, but appears in a region very close to the antiferromagnetic Kitaev point where the quantum fluctuations are presumably very strong. In addition, a two-step symmetry breaking $O_hrightarrow D_{3d}rightarrow D_3$ is numerically observed as the length scale is increased: At short and intermediate length scales, the system behaves as having a rank-2 spin nematic order with $O_hrightarrow D_{3d}$ symmetry breaking; and at long distances, time reversal symmetry is further broken leading to the $O_hrightarrow D_3$ symmetry breaking. Finally, there is no numerical signature of spin orderings nor Luttinger liquid behaviors in the Kitaev phase whose nature is worth further studies.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
