Search Results (19)

In this paper, we investigate the stochastic Heisenberg ferromagnetic equation (SHFE) derived by a multiplicative Wiener process. We use a suitable transformation to change the SHF equation into another Heisenberg ferromagnetic equation with random variable coefficients (HFE-RVCs). We employ the mapping approach to obtain novel rational, trigonometric, elliptic and hyperbolic function solutions for HFE-RVCs. Following that, we can attain the solutions of the SHFE. For the first time in the Heisenberg ferromagnetic equation, we postulate that the solution to the wave equation is stochastic, whereas all previous investigations supposed that it was deterministic. Moreover, we give various visual representations to demonstrate the impact of the multiplicative Wiener process on the exact solutions to the stochastic Heisenberg ferromagnetic equation. Full article

We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of predictive state analysis of stochastic and complex systems theory but is intrinsically quantum. Predictive states of a subsystem are formed by equivalence classes of state vectors in the exterior Hilbert space that effectively predict the same future behavior of that subsystem for some time. As an illustrative example, we present calculations in the dynamics of an isotropic Heisenberg model spin chain and show that, in comparison to the entanglement entropy, the predictive complexity better signifies dynamically important events, such as magnon collisions. It can also serve as a local order parameter that can distinguish long and short range entanglement. Full article

The impact of Stratonovich integrals on the solutions of the Heisenberg ferromagnetic spin chain equation using the unified solver approach is examined in this study. In particular, using arbitrary parameters, the traveling wave arrangements of rational, trigonometric, and hyperbolic functions are developed. The detailed arrangements are exceptionally critical for clarifying diverse complex wonders in plasma material science, optical fiber, quantum mechanics, super liquids and so on. Here, the Itô stochastic calculus and the Stratonovich stochastic calculus are considered. To describe the dynamic behaviour of random solutions, some graphical representations for these solutions are described with appropriate parameters. Full article

This paper outlines a study into the exact solutions of the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation that is used to illustrate the ferromagnetic materials of magnetic ordering by applying two recent techniques, namely, the Sardar-subequation method and extended rational sine–cosine and sinh–cosh methods. Abundant exact solutions such as the bright soliton, dark soliton, combined bright–dark soliton, singular soliton and other periodic wave solutions expressed by the generalized trigonometric, generalized hyperbolic, trigonometric and hyperbolic functions are obtained. The numerical results are illustrated in the form of 3D plots, 2D contours and 2D curves by choosing proper parametric values to interpret the physical behavior of the model. The obtained results in this work are expected to provide a rich platform for constructing the soliton solutions of PDEs in physics. Full article

Two novel 1D heterobimetallic compounds {[Mn^III(SB²⁺)M^III(CN)₆]·4H₂O}_n (SB²⁺ = N,N′-ethylenebis(5-trimethylammoniomethylsalicylideneiminate) based on orbitally degenerate cyanidometallates [Os^III(CN)₆]³⁻ (1) and [Ru^III(CN)₆]³⁻ (2) and Mn^III Schiff base complex were synthesized and characterized structurally and magnetically. Their crystal structures consist of electrically neutral, well-isolated chains composed of alternating [M^III(CN)₆]³⁻ anions and square planar [Mn^III(SB²⁺)]³⁺ cations bridged by cyanide groups. These -ion magnetic anisotropy of Mn^III centers. These results indicate that the presence of compounds exhibit single-chain magnet (SCM) behavior with the energy barriers of Δτ₁/k_B = 73 K, Δτ₂/k_B = 41.5 K (1) and Δτ₁/k_B = 51 K, Δτ₂ = 27 K (2). Blocking temperatures of T_B = 2.8, 2.1 K and magnetic hysteresis with coercive fields (at 1.8 K) of 8000, 1600 Oe were found for 1 and 2, respectively. Theoretical analysis of the magnetic data reveals that their single-chain magnet behavior is a product of a complicated interplay of extremely anisotropic triaxial exchange interactions in M^III(4d/5d)–CN–Mn^III fragments: −J_xS_M^xS_Mn^x−J_yS_M^yS_Mn^y−J_zS_M^zS_Mn^z, with opposite sign of exchange parameters J_x = −22, J_y = +28, J_z = −26 cm⁻¹ and J_x = −18, J_y = +20, J_z = −18 cm⁻¹ in 1 and 2, respectively) and single orbitally degenerate [Os^III(CN)₆]³⁻ and [Ru^III(CN)₆]³⁻ spin units with unquenched orbital angular momentum in the chain compounds 1 and 2 leads to a peculiar regime of slow magnetic relaxation, which is beyond the scope of the conventional Glaubers’s 1D Ising model and anisotropic Heisenberg model. Full article

Haldane conjectures the fundamental difference in the energy spectrum of the Heisenberg antiferromagnetic (HAF) of the spin S chain is that the half-integer and the integer S chain have gapless and gapped energy spectrums, respectively. The ground state (gs) of the HAF spin-1/2 and spin-1 chains have a quasi-long-range and short-range correlation, respectively. We study the effect of the exchange interaction between an HAF spin-1/2 and an HAF spin-1 chain forming a normal ladder system and its gs properties. The inter-chain exchange interaction $J_{\perp }$ can be either ferromagnetic (FM) or antiferromagnetic (AFM). Using the density matrix renormalization group method, we show that in the weak AFM/FM coupling limit of $J_{\perp }$, the system behaves like two decoupled chains. However, in the large AFM $J_{\perp }$ limit, the whole system can be visualized as weakly coupled spin-1/2 and spin-1 pairs which behave like an effective spin-1/2 HAF chain. In the large FM $J_{\perp }$ limit, coupled spin-1/2 and spin-1 pairs can form pseudo spin-3/2 and the whole system behaves like an effective spin-3/2 HAF chain. We also derive the effective model Hamiltonian in both strong FM and AFM rung exchange coupling limits. Full article

Quantum process tomography is a fundamental and critical benchmarking and certification tool that is capable of fully characterizing an unknown quantum process. Standard quantum process tomography suffers from an exponentially scaling number of measurements and complicated data post-processing due to the curse of dimensionality. On the other hand, non-unitary operators are more realistic cases. In this work, we put forward a variational quantum process tomography method based on the supervised quantum machine learning framework. It approximates the unknown non-unitary quantum process utilizing a relatively shallow depth parametric quantum circuit and fewer input states. Numerically, we verified our method by reconstructing the non-unitary quantum mappings up to eight qubits in two cases: the weighted sum of the randomly generated quantum circuits and the imaginary time evolution of the Heisenberg XXZ spin chain Hamiltonian. Results show that those quantum processes could be reconstructed with high fidelities (>99%) and shallow depth parametric quantum circuits ($d\le 8$), while the number of input states required is at least two orders of magnitude less than the demands of the standard quantum process tomography. Our work shows the potential of the variational quantum process tomography method in characterizing non-unitary operators. Full article

Investigating the favorable configurations for non-classical correlations preservation has remained a hotly debated topic for the last decade. In this regard, we present a two-qubit Heisenberg spin chain system exposed to a time-dependent external magnetic field. The impact of various crucial parameters, such as initial strength and angular frequency of the external magnetic field along with the state’s purity and anisotropy of the spin-spin on the dynamical behavior of quantum correlations are considered. We utilize local quantum uncertainty (LQU) and quantum interferometric power (QIP) to investigate the dynamics of quantum correlations. We show that under the critical angular frequency of the external magnetic field and the spin-spin anisotropy, quantum correlations in the system can be successfully preserved. LQU and QIP suffer a drop as the interaction between the system and field is initiated, however, are quickly regained by the system. This tendency is confirmed by computing a measure of non-classical correlations according to the Clauser–Horne–Shimony–Holt inequality. Notably, the initial and final preserved levels of quantum correlations are only varied when variation is caused in the state’s purity. Full article

The $T=0$ excitation spectra of the antiferromagnetic ($J>0$) anisotropic Heisenberg chain of spins 1/2 are studied using the Bethe Ansatz equations for $\Delta =cos(\pi /n)$, $n=3,4$ and 5. The number of unknown functions is $n-1$ for $\Delta =cos(\pi /n)$ and can be solved numerically for a finite external field. The low-energy excitations form a Luttinger liquid parametrized by a conformal field theory with conformal charge of $c=1$. For higher energy excitations, the spectral functions display deviations from the Luttinger behavior arising from the curvature in the dispersion. Adding a corrective term of the form of a mobile impurity coupled to the Luttinger liquid modes corrects this difference. The “impurity” is an irrelevant operator, which if treated non-perturbatively, yields the threshold singularities in the one-spinwave particle and hole Green’s function correctly. Full article

We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signaling function of quantum order–disorder transitions. We discuss the possibility for such transitions to characterize interesting physical phenomena, as quantum phase transitions, or abrupt variations in correlation distributions. We apply our measure on two exactly solvable Hamiltonian models: the $1D$-Quantum Ising Model (in the single-particle reduced state), and on Heisenberg XXZ spin-$1/2$ chain (in the two-particle reduced state). We analyze its behavior across quantum phase transitions for finite system sizes, as well as in the thermodynamic limit by using Bethe Ansatz technique. Full article

The stochastic fractional (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation (SFHFSCE), which is driven in the Stratonovich sense by a multiplicative Wiener process, is considered here. The analytical solutions of the SFHFSCE are attained by utilizing the Jacobi elliptic function method. Various kinds of analytical fractional stochastic solutions, for instance, the elliptic functions, are obtained. Physicists can utilize these solutions to understand a variety of important physical phenomena because magnetic solitons have been categorized as one of the interesting groups of non-linear excitations representing spin dynamics in semi-classical continuum Heisenberg systems. To study the impact of the Wiener process on these solutions, the 3D and 2D surfaces of some achieved exact fractional stochastic solutions are plotted. Full article

We determined the spin exchanges between the Cu²⁺ ions in the kagomé layers of volborthite, Cu₃V₂O₇(OH)₂·2H₂O, by performing the energy-mapping analysis based on DFT+U calculations, to find that the kagomé layers of Cu²⁺ ions are hardly spin-frustrated, and the magnetic properties of volborthite below ~75 K should be described by very weakly interacting antiferromagnetic uniform chains made up of effective S = 1/2 pseudospin units. This conclusion was verified by synthesizing single crystals of not only Cu₃V₂O₇(OH)₂·2H₂O but also its deuterated analogue Cu₃V₂O₇(OD)₂·2D₂O and then by investigating their magnetic susceptibilities and specific heats. Each kagomé layer consists of intertwined two-leg spin ladders with rungs of linear spin trimers. With the latter acting as S = 1/2 pseudospin units, each two-leg spin ladder behaves as a chain of S = 1/2 pseudospins. Adjacent two-leg spin ladders in each kagomé layer interact very weakly, so it is required that all nearest-neighbor spin exchange paths of every two-leg spin ladder remain antiferromagnetically coupled in all spin ladder arrangements of a kagomé layer. This constraint imposes three sets of entropy spectra with which each kagomé layer can exchange energy with the surrounding on lowering the temperature below ~1.5 K and on raising the external magnetic field B. We discovered that the specific heat anomalies of volborthite observed below ~1.5 K at B = 0 are suppressed by raising the magnetic field B to ~4.2 T, that a new specific heat anomaly occurs when B is increased above ~5.5 T, and that the imposed three sets of entropy spectra are responsible for the field-dependence of the specific heat anomalies. Full article

Some measurements have shown that the second-order exchange interaction is non-negligible in ferromagnetic compounds whose microscopic interactions are described by means of half-odd integer quantum spins. In these spin systems the ground state is either ferromagnetic or antiferromagnetic when the bilinear exchange interaction is dominant. Instead, in ferromagnetic systems characterized by bilinear and biquadratic exchange interactions of comparable magnitude, the energy minimum occurs when spins are in a canting ground-state. To this aim, a one-dimensional (1D) quantum spin chain and a two-dimensional (2D) lattice of quantum spins subjected to periodic boundary conditions are modeled via the generalized quantum Heisenberg Hamiltonian containing, in addition to the isotropic and short-range bilinear exchange interaction of the Heisenberg type, a second-order interaction, the isotropic and short-range biquadratic exchange interaction between nearest-neighbors quantum spins. For these 1D and 2D quantum systems a generalization of the Mermin–Wagner–Hohenberg theorem (also known as Mermin–Wagner–Berezinksii or Coleman theorem) is given. It is demonstrated, by means of quantum statistical arguments, based on Bogoliubov’s inequality, that, at any finite temperature, (1) there is absence of long-range order and that (2) the law governing the vanishing of the order parameter is the same as in the bilinear case for both 1D and 2D quantum ferromagnetic systems. The physical implications of the absence of a spontaneous spin symmetry breaking in 1D spin chains and 2D spin lattices modeled via a generalized quantum Heisenberg Hamiltonian are discussed. Full article

One-dimensional (1D) oxalate-bridged homometallic {[Mn(bpy)(C₂O₄)]·1.5H₂O}_n (1) (bpy = 2,2’-bipyridine) and heterodimetallic {[CrCu₃(bpy)₃(CH₃OH)(H₂O)(C₂O₄)₄][Cu(bpy)Cr(C₂O₄)₃]·CH₂Cl₂·CH₃OH·H₂O}_n (2) coordination polymers, as well as the three-dimensional (3D) heterotrimetallic {[CaCr₂Cu₂(phen)₄(C₂O₄)₆]·4CH₃CN·2H₂O}_n (3) (1,10-phenanthroline) network, have been synthesized by a building block approach using a layering technique, and characterized by single-crystal X-ray diffraction, infrared (IR) and impedance spectroscopies and magnetization measurements. During the crystallization process partial decomposition of the tris(oxalato)chromate(III) happened and 1D polymers 1 and 2 were formed. The antiferromagnetic interactions between the manganese(II) ions were mediated by oxalate ligands in the chain [Mn(bpy)(C₂O₄)]_n of 1, with intra-chain super-exchange interaction $J$ = (−3.134 ± 0.004) K; magnetic interaction between neighbouring chains is negligible making this system closer than other known Mn-chains to the ideal 1D Heisenberg antiferromagnet. Compound 2 comprises a 1D coordination anion [Cu(bpy)Cr(C₂O₄)₃]_nⁿ⁻ (Cr2–Cu4) with alternating [Cr(C₂O₄)₃]³⁻ and [Cu(bpy)]²⁺ units mutually bridged through the oxalate group. Another chain (Cr1–Cu3) is similar, but involves a homodinuclear unit [Cu(bpy)(H₂O)(µ-C₂O₄)Cu(bpy)(CH₃OH)]²⁺ (Cu1–Cu2) coordinated as a pendant group to a terminal oxalate oxygen. Magnetic measurements showed that the Cu1−Cu2 cationic unit is a strongly coupled antiferromagnetic dimer, independent from the other magnetic ions within ferromagnetic chains Cr1–Cu3 and Cr2–Cu4. A 3D polymer {[CaCr₂Cu₂(phen)₄(C₂O₄)₆]·4CH₃CN·2H₂O}_n (3) comprising three different metal centers (Ca²⁺, Cr³⁺ and Cu²⁺) oxalate-bridged, contains Ca²⁺ atoms as nodes connected with four Cr³⁺ atoms through oxalate ligands. The network thus formed can be reduced to an underlying graph of diamondoid (dia) or (6⁶) topology. Magnetization of 3 shows the ferromagnetic oxalate-bridged dimers [Cu^IICr^III], whose mutual interaction could possibly originate through the spin polarization of Ca²⁺ orbitals. Compounds 1 and 3 exhibit lower electrical conductivity at room temperature (RT) in comparison to compound 2. Full article

This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of $N=30$. Full article