Entanglement entropy of inhomogeneous XX spin chains with algebraic interactions

We introduce a family of inhomogeneous XX spin chains whose squared couplings are a polynomial of degree at most four in the site index. We show how to obtain an asymptotic approximation for the Rényi entanglement entropy of all such chains in a constant magnetic field at half filling by exploiting their connection with the conformal field theory of a massless Dirac fermion in a suitably curved static background. We study the above approximation for three particular chains in the family, two of them related to well-known quasi-exactly solvable quantum models on the line and the third one to classical Krawtchouk polynomials, finding an excellent agreement with the exact value obtained numerically when the Rényi parameter α is less than one. When α ≥ 1 we find parity oscillations, as expected from the homogeneous case, and show that they are very accurately reproduced by a modification of the Fagotti-Calabrese formula. We have also analyzed the asymptotic behavior of the Rényi entanglement entropy in the non-standard situation of arbitrary filling and/or inhomogeneous magnetic field. Our numerical results show that in this case a block of spins at each end of the chain becomes disentangled from the rest. Moreover, the asymptotic approximation for the case of half filling and constant magnetic field, when suitably rescaled to the region of non-vanishing entropy, provides a rough approximation to the entanglement entropy also in this general case.

Thermal Robustness of Entanglement in a Dissipative Two-Dimensional Spin System in an Inhomogeneous Magnetic Field

Recently new novel magnetic phases were shown to exist in the asymptotic steady states of spin systems coupled to dissipative environments at zero temperature. Tuning the different system parameters led to quantum phase transitions among those states. We study, here, a finite two-dimensional Heisenberg triangular spin lattice coupled to a dissipative Markovian Lindblad environment at finite temperature. We show how applying an inhomogeneous magnetic field to the system at different degrees of anisotropy may significantly affect the spin states, and the entanglement properties and distribution among the spins in the asymptotic steady state of the system. In particular, applying an inhomogeneous field with an inward (growing) gradient toward the central spin is found to considerably enhance the nearest neighbor entanglement and its robustness against the thermal dissipative decay effect in the completely anisotropic (Ising) system, whereas the beyond nearest neighbor ones vanish entirely. The spins of the system in this case reach different steady states depending on their positions in the lattice. However, the inhomogeneity of the field shows no effect on the entanglement in the completely isotropic (XXX) system, which vanishes asymptotically under any system configuration and the spins relax to a separable (disentangled) steady state with all the spins reaching a common spin state. Interestingly, applying the same field to a partially anisotropic (XYZ) system does not just enhance the nearest neighbor entanglements and their thermal robustness but all the long-range ones as well, while the spins relax asymptotically to very distinguished spin states, which is a sign of a critical behavior taking place at this combination of system anisotropy and field inhomogeneity.

Дифференциальный фон электрического сигнала, снимаемого с индукционной магнитной головки

Experimental dependences U(t) of the electric voltage taken from an induction magnetic head (MH) moving relative to a magnetic carrier (MH) are presented. The backgrounds of the edges of the MN, local defects of the MN, the background of the inhomogeneous magnetic field of the local source, the backgrounds of defects and structural inhomogeneities of the object, the etheric electromagnetic background, the background of the quality of the surface of the object and surface microscopic inhomogeneities of the material have been identified and investigated. The resonant backgrounds of self-excitation of the measuring system on the signals of the edges of the MN, defects of the MN, instrument and network pickups and interference, object defects, and etheric electromagnetic fields are revealed and investigated. Resonance peaks are the result of self-excitation of the measuring system, which includes the MG, and arise on the trailing edges of any signals of sufficient magnitude, the duration of the trailing edge of which is about a quarter of the period of natural oscillations of the measuring system. The amplitude and frequency spectra of the background signals of object defects, MI and noise and the analytical expressions describing them are determined. The results of the extraction of the useful signal from the complete signal recorded on the MN are shown. Investigations of the differential background of an electric signal allow, together with the previously developed methods of hysteresis interference, to control the properties of objects in an automatic mode with program control, which significantly increases the sensitivity and accuracy of control. To achieve this goal, it is recommended to set the parameters of the measurement system at the threshold of the onset of natural free oscillations in it.