scholarly journals Entanglement entropy of inhomogeneous XX spin chains with algebraic interactions

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Federico Finkel ◽  
Artemio González-López
Keyword(s):  
Magnetic Field ◽  
Constant Magnetic Field ◽  
Asymptotic Approximation ◽  
Entanglement Entropy ◽  
Inhomogeneous Magnetic Field ◽  
Spin Chains ◽  
Dirac Fermion ◽  
Krawtchouk Polynomials ◽  
Rough Approximation ◽  
Half Filling

Abstract 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.

scholarly journals Path integral for confined Dirac fermions in a constant magnetic field

2015 ◽  
Vol 30 (27) ◽  
pp. 1550174 ◽  
Author(s):  
Abdeldjalil Merdaci ◽  
Ahmed Jellal ◽  
Lyazid Chetouani
Keyword(s):  
Magnetic Field ◽  
Path Integral ◽  
Constant Magnetic Field ◽  
Laguerre Polynomials ◽  
Nonrelativistic Limit ◽  
Dirac Fermion ◽  
Physical Parameters ◽  
Dirac Fermions ◽  
Quantum Numbers ◽  
The Green Function

In this paper, we consider Dirac fermion confined in harmonic potential and submitted to a constant magnetic field. The corresponding solutions of the energy spectrum are obtained by using the path integral techniques. For this, we begin by establishing a symmetric global projection, which provides a symmetric form for the Green function. Based on this, we show that it is possible to end up with the propagator of the harmonic oscillator for one charged particle. After some transformations, we derive the normalized wave functions and the eigenvalues in terms of different physical parameters and quantum numbers. By interchanging quantum numbers, we show that our solutions have interesting properties. The density of current and the nonrelativistic limit are analyzed where different conclusions are obtained. Finally, the completeness of the Dirac oscillator eigenfunctions is proved by using the standard properties of the generalized Laguerre polynomials.

Monte Carlo calculation of the energy parameters and spatial distribution of the cathodic arc ions while passing through the macro-particles filters

2018 ◽  
Vol 1 (1) ◽  
pp. 30-34 ◽  
Author(s):  
Alexey Chernogor ◽  
Igor Blinkov ◽  
Alexey Volkhonskiy
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Monte Carlo ◽  
Monte Carlo Calculation ◽  
Inhomogeneous Magnetic Field ◽  
Flow Energy ◽  
Wide Range ◽  
Field Concentrator ◽  
Cathodic Arc ◽  
The Magnetic Field

The flow, energy distribution and concentrations profiles of Ti ions in cathodic arc are studied by test particle Monte Carlo simulations with considering the mass transfer through the macro-particles filters with inhomogeneous magnetic field. The loss of ions due to their deposition on filter walls was calculated as a function of electric current and number of turns in the coil. The magnetic field concentrator that arises in the bending region of the filters leads to increase the loss of the ions component of cathodic arc. The ions loss up to 80 % of their energy resulted by the paired elastic collisions which correspond to the experimental results. The ion fluxes arriving at the surface of the substrates during planetary rotating of them opposite the evaporators mounted to each other at an angle of 120° characterized by the wide range of mutual overlapping.

A CMT Device for Electric Energy Meter Detection

2020 ◽  
Vol 13 ◽  
Author(s):  
Zhi Zeng ◽  
Yongfu Zhou
Keyword(s):  
Magnetic Field ◽  
Constant Magnetic Field ◽  
Electromagnetic Interference ◽  
Production Efficiency ◽  
Electric Energy ◽  
Labor Cost ◽  
Automatic Testing ◽  
National Standard ◽  
Measurement Instruments ◽  
Detection Technology

Background: Detection technology is a product development technique that serves as a basis for quality assurance. As electric energy meters (EEMs) are measurement instruments whose use is mandatory in several nations, their accuracy, which directly depends on their reliability and proper functioning, is paramount. In this study, to eliminate electromagnetic interference, a device is developed for testing a set of EEMs under a constant magnetic field interference. The detection device can simultaneously test 6 electric meters; moreover, in the future, it will be able to measure the influence of magnetic field strength on the measurement accuracy of EEMs, thereby improving the production efficiency of electric meter manufacturers. Methods: In this study, we first design a 3D model of the detection device for a single meter component; then, we establish a network, which includes a control system, and perform the planning of the path of a block that generates a constant magnetic field. Finally, we control the three-axis motion and rotation of the block using a PLC to implement detection for the five sides of the EEM. Results & Discussion: The proposed device can accurately determine whether an EEM can adequately function, within the error range prescribed by a national standard, under electromagnetic interference; this can enable reliable, automatic testing and fault detection for EEMs. Experiments show that our device can decrease the labor cost for EEM manufacturers.

scholarly journals Ground state and stability of the fractional plateau phase in metallic Shastry–Sutherland system TmB4

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Matúš Orendáč ◽  
Slavomír Gabáni ◽  
Pavol Farkašovský ◽  
Emil Gažo ◽  
Jozef Kačmarčík ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Phase Diagram ◽  
Ground State ◽  
Constant Magnetic Field ◽  
Paramagnetic Phase ◽  
The Other ◽  
Zero Field ◽  
Plateau Phase ◽  
Low Field ◽  
Zero Field Cooling

AbstractWe present a study of the ground state and stability of the fractional plateau phase (FPP) with M/Msat = 1/8 in the metallic Shastry–Sutherland system TmB4. Magnetization (M) measurements show that the FPP states are thermodynamically stable when the sample is cooled in constant magnetic field from the paramagnetic phase to the ordered one at 2 K. On the other hand, after zero-field cooling and subsequent magnetization these states appear to be of dynamic origin. In this case the FPP states are closely associated with the half plateau phase (HPP, M/Msat = ½), mediate the HPP to the low-field antiferromagnetic (AF) phase and depend on the thermodynamic history. Thus, in the same place of the phase diagram both, the stable and the metastable (dynamic) fractional plateau (FP) states, can be observed, depending on the way they are reached. In case of metastable FP states thermodynamic paths are identified that lead to very flat fractional plateaus in the FPP. Moreover, with a further decrease of magnetic field also the low-field AF phase becomes influenced and exhibits a plateau of the order of 1/1000 Msat.

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