Topological insulator and quantum memory

Measurements done on the quantum systems are too specific. Contrary to their classical counterparts, quantum measurements can be invasive and destroy the state of interest. Besides, quantumness limits the accuracy of measurements done on quantum systems. Uncertainty relations define the universal accuracy limit of the quantum measurements. Relatively recently, it was discovered that quantum correlations and quantum memory might reduce the uncertainty of quantum measurements. In the present work, we study two different types of measurements done on the topological system. Namely, we discuss measurements done on the spin operators and the canonical pair of operators: momentum and coordinate. We quantify the spin operator's measurements through the entropic measures of uncertainty and exploit the concept of quantum memory. While for the momentum and coordinate operators, we exploit the improved uncertainty relations. We discovered that quantum memory reduces the uncertainties of spin measurements. On the hand, we proved that the uncertainties in the measurements of the coordinate and momentum operators depend on the value of the momentum and are substantially enhanced at small distances between itinerant and localized electrons (the large momentum limit). We note that the topological nature of the system leads to the spin-momentum locking. The momentum of the electron depends on the spin and vice versa. Therefore, we suggest the indirect measurement scheme for the momentum and coordinate operators through the spin operator. Due to the factor of quantum memory, such indirect measurements in topological insulators have smaller uncertainties rather than direct measurements

Many-body localization phase in a spin-driven chiral multiferroic chain

Many-body localization (MBL) is an emergent phase in correlated quantum systems with promising applications, particularly in quantum information. Here, we unveil the existence and analyze this phase in a chiral multiferroic model system. Conventionally, MBL occurrence is traced via level statistics by implementing a standard finite-size scaling procedure. Here, we present an approach based on the full distribution of the ratio of adjacent energy spacings. We find a strong broadening of the histograms of counts of these level spacings directly at the transition point from MBL to the ergodic phase. The broadening signals reliably the transition point without relying on an averaging procedure. The fast convergence of the histograms even for relatively small systems allows monitoring the MBL dynamics with much less computational effort. Numerical results are presented for a chiral spin chain with a dynamical Dzyaloshinskii-Moriya interaction, an established model to describe the spin excitations in a single-phase spin-driven multiferroic system. The multiferroic MBL phase is uncovered and it is shown how to steer it via electric fields

From chaos to many-body localization: some introductory notes

Staring from the kicked rotator as a paradigm for a system exhibiting classical chaos, we discuss the role of quantum coherence resulting in dynamical localization in the kicked quantum rotator. In this context, the disorder-induced Anderson localization is also discussed. Localization in interacting, quantum many-body systems (many-body localization) may also occur in the absence of disorder, and a practical way to identify its occurrence is demonstrated for an interacting spin chain

Effect of Rashba Spin-Orbit Coupling on the Spin Polarization of Holes in Two-Dimensional GaMnAs Magnetic Semiconductors

We consider the effect of the Rashba spin-orbital coupling in two-dimensional GaAs semiconductor heavily doped with Mn, on the spin polarization of holes. Due to the strong internal spin-orbit interaction in GaAs, the spin of a hole is not a good quantum number but the hole in some energy state has a certain mean value of spin, which can be strongly affected by the Rashba spin-orbital interaction related to the substrate for 2D material

Effect of Rashba Spin-Orbit Coupling on the Spin Polarization of Holes in Two-Dimensional GaMnAs Magnetic Semiconductors

We consider the effect of the Rashba spin-orbital coupling in two-dimensional GaAs semiconductor heavily doped with Mn, on the spin polarization of holes. Due to the strong internal spin-orbit interaction in GaAs, the spin of a hole is not a good quantum number but the hole in some energy state has a certain mean value of spin, which can be strongly affected by the Rashba spin-orbital interaction related to the substrate for 2D material

Strain Designed Magnetic Properties of III-V Magnetic Semiconductors

We present the theoretical analysis of a possibility of the magnetic anisotropy control using various components of the strain tensor in III-V magnetic semiconductor. We used the Kane model of the valence bands for the numerical simulations of the influence of strain on the Mn doped GaAs valence band structure. Calculating numerically the energy structure of deformed GaMnAs magnetic semiconductor, we also found the total energy of electron system as a function of orientation of the average magnetization vector. Our calculations show how the direction of the magnetization easy axis can be effectively rotated by using different types of deformation

Galois Properties of the Eigenproblem of the Hexagonal Magnetic Heisenberg Ring

We analyse the number field-theoretic properties of solutions of the eigenproblem of the Heisenberg Hamiltonian for the magnetic hexagon with the single-node spin 1/2 and isotropic exchange interactions. It follows that eigenenergies and eigenstates are expressible within an extension of the prime field ℚ of rationals of degree $2^3$ and $2^4$, respectively. In quantum information setting, each real extension of rank 2 represents an arithmetic qubit. We demonstrate in detail some actions of the Galois group on the eigenproblem

Influence of Acoustic Phonons on the Magnetic Anisotropy in GaMnAs Magnetic Semiconductors

We present a theoretical description of the influence of incoherent acoustic phonons on the magnetic anisotropy of magnetic semiconductors. Our theory is based on the six-band Kane model of the electron energy spectrum describing the valence band with k· p Hamiltonian including the hole-phonon interaction term. We include the effect of incoherent phonons through the hole self-energy in the six-band model, and assume a strong laser-pulse-induced flux of non-equilibrium acoustic phonons. The results of numerical calculations of magnetic anisotropy performed for (GaMn)(AsP) magnetic alloy semiconductors demonstrate the essential role of incoherent phonons