arXiv subjects

M. A. Yurishchev

Publications and source records attributed to M. A. Yurishchev.

16 recordsLinked to original sources

arXiv2013

Quantum discord for two-qubit CS states: Analytical solution

We found an universal local unitary (orthogonal) transformation which transforms any centrosymmetric (CS) density matrix ρ_{CS} into the X density matrix ρ_X: H\otimes Hρ_{CS}H\otimes H=ρ_X, where H is the Hadamard transformation. Because quantum discord is invariant under the local unitary transformations, this remarkable property allows to get the discord of general two-qubit CS states in the analytical form using the corresponding well-known formulas for the X states. Examples of systems with CS density matrices provided from the recent literature, including XXZ spin model with the Dzyaloshinsky-Moriya interaction, a gas of spin-carrying particles in closed nanopore, and a family of pseudopure states.

quant-ph↗

arXiv2013

Quantum discord in spin systems with dipole-dipole interaction

The behavior of total purely quantum correlation (discord) in dimers consisting of dipolar-coupled spins 1/2 is studied. We found that the discord Q=0 at the absolute zero temperature. With increasing the temperature $T$, at first the quantum correlations in the system increase, smoothly reach the maximum, and then turn again into zero according to the asymptotic law $T^{-2}$. It is also shown that in absence of external magnetic field $B$, the classical correlation $C$ at $T\to0$ is, vice versa, maximal. Our calculations predict that in crystalline gypsum ${\rm CaSO_4\cdot2H_2O}$ the value of natural (B=0) quantum discord between nuclear spins of hydrogen atoms is maximal at the temperature of 0.644 $μ$K, and for 1,2-dichloroethane ${\rm H_2ClC-CH_2Cl}$ the discord achieves the largest value at $T=0.517 μ$K. In both cases, the discord equals $Q\approx0.083$ bit/dimer what is 8.3% of its upper limit in two-qubit systems. We estimate also that for gypsum at room temperature $Q\sim10^{-18}$ bit/dimer, and for 1,2-dichloroethane at T=90 K the discord is $Q\sim10^{-17}$ bit per a dimer.

quant-ph↗

arXiv2012

Quantum correlations in a system of nuclear s=1/2 spins in a strong magnetic field

Entanglement and quantum discord for a pair of nuclear spins $s=1/2$ in a nanopore filled with a gas of spin-carrying molecules (atoms) are studied. The correlation functions describing dynamics of dipolar coupled spins in a nanopore are found. The dependence of spin-pair entanglement on the temperature and the number of spins is obtained from the reduced density matrix, which is centrosymmetric (CS). An analytic expression for the concurrence is obtained for an arbitrary CS density matrix. It is shown that the quantum discord as a measure of quantum correlations attains a significant value at low temperatures. It is shown also that the discord in the considered model has "flickering" character and disappears periodically in the course of the time evolution of the system. The geometric discord is studied for arbitrary $4\times 4$ CS density matrices.

quant-ph↗

arXiv2010

Entanglement Entropy Fluctuations in Quantum Ising Chains

The Ising chains in a transverse magnetic field of constant strength (h=1) and with the spin interaction value λare considered. In the case of infinitely long chain, exact analytical expressions are found for the second central moment (dispersion) of the entropy operator S^\hat=-lnρwith reduced density matrix ρwhich corresponds to a semi-infinite part of the model in the ground state. It is shown that in the vicinity of a critical point λ_c=1, the entanglement entropy fluctuation ΔS (square root of dispersion) diverges as \Delts S\sim[ln(1/|1-λ|)]^{1/2}. Taking into account the known behavior of the entanglement entropy S, this leads to that the value of relative entanglement fluctuation δS=(ΔS)/S vanishes at the critical point, i.e. in fact a state with nonfluctuating entanglement is realized.

quant-ph↗

arXiv2009

Fluctuations of Quantum Entanglement

It is emphasized that quantum entanglement determined in terms of the von Neumann entropy operator is a stochastic quantity and, therefore, can fluctuate. The rms fluctuations of the entanglement entropy of two-qubit systems in both pure and mixed states have been obtained. It has been found that entanglement fluctuations in the maximally entangled states are absent. Regions where the entanglement fluctuations are larger than the entanglement itself (strong fluctuation regions) have been revealed. It has been found that the magnitude of the relative entanglement fluctuations is divergent at the points of the transition of systems from an entangled state to a separable state. It has been shown that entanglement fluctuations vanish in the separable states.

quant-ph↗

arXiv2009

Quantum Entanglement in Nitrosyl Iron Complexes

Recent magnetic susceptibility measurements for polycrystalline samples of binuclear nitrosyl iron complexes [Fe_2(C_3H_3N_2S)_2(NO)_4] (I) and [Fe_2(SC_3H_5N_2)_2(NO)_4] (II), suggest that quantum-mechanical entanglement of the spin degrees of freedom exists in these compounds. Entanglement E exists below the temperature T_E that we have estimated for complexes I and II to be 80-90 and 110-120 K, respectively. Using an expression of entanglement in terms of magnetic susceptibility for a Heisenberg dimer, we find the temperature dependence of the entanglement for complex II. Having arisen at the temperature T_E, the entanglement increases monotonically with decreasing temperature and reaches 90-95% in this complex at T=25 K, when the subordinate effects are still small.

quant-ph↗

arXiv2006

Magnetic susceptibility of quasi-one-dimensional Ising superantiferromagnets FeTAC and MCl_2*2NC_5H_5 (M=Co, Fe): Approximations with L x oo and L x L x oo chain clusters

The temperature dependence of the zero-field susceptibilities of 2D and 3D Ising lattices with anisotropic coupling is analyzed. Infinite 2D and 3D lattices are approximated, respectively, by ensembles of independent L x oo and L x L x oo chain clusters that are infinitely long in the strong-coupling (J) direction. This approach is used as a basis for a quantitative description of available experimental data on the magnetic susceptibilities of the 2D anisotropic Ising magnet [(CH_3)_3NH]FeCl_3*2H_2O (FeTAC) and the quasi-one-dimensional 3D magnets CoCl_2*2NC_5H_5 and FeCl_2*2NC_5H_5 in the entire experimental temperature range. A method is proposed for determining the relative interchain coupling strength J'/J from the maximum susceptibility value, which improves the accuracy of estimates for J'/J by more than an order of magnetude.

cond-mat.mtrl-sci↗

arXiv2004

Universality in the partially anisotropic three-dimensional Ising lattice

Using transfer-matrix extended phenomenological renormalization-group methods the critical properties of spin-1/2 Ising model on a simple-cubic lattice with partly anisotropic coupling strengths ${\vec J}=(J',J',J)$ are studied. Universality of both fundamental critical exponents $y_t$ and $y_h$ is confirmed. It is shown that the critical finite-size scaling amplitude ratios $U=A_{χ^{(4)}}A_κ/A_χ^2$, $Y_1=A_{κ^{''}}/A_χ$, and $Y_2=A_{κ^{(4)}}/A_{χ^{(4)}}$ are independent of the lattice anisotropy parameter $Δ=J'/J$. By this for the last above invariant of the three-dimensional Ising universality class we give the first quantitative estimate: $Y_2\simeq2.013$ (shape $L\times L\times\infty$, periodic boundary conditions in both transverse directions).

cond-mat.stat-mech↗

arXiv2003

Anisotropic simple-cubic Ising lattice: extended phenomenological renormalization-group treatment

Using transfer-matrix extended phenomenological renormalization-group methods [M.A.Yurishchev, Nucl. Phys. B (Proc. Suppl.) 83-84, 727 (2000); hep-lat/9908019; J. Exp. Theor. Phys. 91, 332 (2000); cond-mat/0108002] the improved estimates for the critical temperature of spin-1/2 Ising model on a simple-cubic lattice with partly anisotropic coupling strengths ${\vec J}=(J',J',J)$ are obtained. Universality of both fundamental critical exponents $y_t$ and $y_h$ is confirmed. We show also that the critical finite-size scaling amplitude ratios $A_{χ^{(4)}}A_κ/A_χ^2$, $A_{κ^{''}}/A_χ$, and $A_{κ^{(4)}}/A_{χ^{(4)}}$ are independent of the lattice anisotropy parameter $Δ=J'/J$.

cond-mat.stat-mech↗

arXiv2002

Critical temperature of a fully anisotropic three-dimensional Ising model

The critical temperature of a three-dimensional Ising model on a simple cubic lattice with different coupling strengths along all three spatial directions is calculated via the transfer matrix method and a finite size scaling for L x L oo clusters (L=2 and 3). The results obtained are compared with available calculations. An exact analytical solution is found for the 2 x 2 oo Ising chain with fully anisotropic interactions (arbitrary J_x, J_y and J_z).

cond-mat.stat-mech↗

arXiv2001

Double Potts chain and exact results for some two-dimensional models

A closed-form exact analytical solution for the q-state Potts model on a ladder 2 x oo with arbitrary two-, three-, and four-site interactions in a unit cell is presented. Using the obtained solution it is shown that the finite-size internal energy equation yields an accurate value of the critical temperature for the triangular Potts lattice with three-site interactions in alternate triangular faces. It is argued that the above equation is exact at least for self-dual models on isotropic lattices.

cond-mat.stat-mech↗

arXiv2001

Self-Duality and Statistical Systems without Internal Energy Scaling Terms at Criticality

It is argued that self-duality of one system leads to the zero finite-size scaling amplitude of the critical internal energy for all system belonging to the same universality class. For such models, we may expect that condition of equality (up to correction-to-scaling terms) of the internal energies for systems with different sizes will yield more accurate estimates for the critical temperature than the scaling equation for the inverse correlation lengths which is used in the standard phenomenological renormalization-group approach. Analytical and numerical evidences confirming the above conjecture are given for examples of two-dimensional next-nearest-neighbour and spin-1 Ising lattices.

hep-lat↗

arXiv2001

Improved Phenomenological Renormalization Schemes

An analysis is made of various methods of phenomenological renormalization based on finite-size scaling equations for inverse correlation lengths, the singular part of the free energy density, and their derivatives. The analysis is made using two-dimensional Ising and Potts lattices and the three-dimensional Ising model. Variants of equations for the phenomenological renormalization group are obtained which ensure more rapid convergence than the conventionally used Nightingale phenomenological renormalization scheme. An estimate is obtained for the critical finite-size scaling amplitude of the internal energy in the three-dimensional Ising model. It is shown that the two-dimensional Ising and Potts models contain no finite-size corrections to the internal energy so that the positions of the critical points for these models can be determined exactly from solutions for strips of finite width. It is also found that for the two-dimensional Ising model the scaling finite-size equation for the derivative of the inverse correlation length with respect to temperature gives the exact value of the thermal critical exponent.

cond-mat.stat-mech↗

arXiv1999

Improved Transfer-Matrix Schemes of Phenomenological Renormalization

Different phenomenological RG transformations based on scaling relations for the derivatives of the inverse correlation length and singular part of the free-energy density are considered. These transformations are tested on the 2D square Ising and Potts models as well as on the 3D simple-cubic Ising model. Variants of RG equations yielding more accurate results than Nightingale's RG scheme are obtained. In the 2D case the finite-size equations which give the {\it exact} values of the critical point or the critical exponent are found.

hep-lat↗

arXiv1995

Critical Finite-Size-Scaling Amplitudes of a Fully Anisotropic Three-Dimensional Ising Model

A fully anisotropic simple-cubic Ising lattice in the geometry of periodic cylinders $n\times n\times\infty$ is investigated by the transfer-matrix finite-size scaling method. In addition to the previously obtained critical amplitudes of the inverse correlation lengths and singular part of the free energy [M. A. Yurishchev, Phys. Rev. B 50, 13 533 (1994)], the amplitudes of the usual (``linear'') and nonlinear susceptibilities and the amplitude of the second derivative of the spin-spin inverse correlation length with respect to the external field are calculated. The behavior of critical amplitude combinations (which, in accordance with the Privman-Fisher equations, do not contain in their composition the nonuniversal metric coefficients and geometry prefactor) are studied as a function of the interaction anisotropy parameters.

cond-mat↗

arXiv1994

Hyperuniversality of Fully Anisotropic Three-Dimensional Ising Model

For the fully anisotropic simple-cubic Ising lattice, the critical finite-size scaling amplitudes of both the spin-spin and energy-energy inverse correlation lengths and the singular part of the reduced free-energy density are calculated by the transfer-matrix method and a finite-size scaling for cyclic L x L x oo clusters with L=3 and 4. Analysis of the data obtained shows that the ratios and the directional geometric means of above amplitudes are universal.

cond-mat↗