Efficient density matrix renormalization group algorithm to study Y junctions with integer and half-integer spin

An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y junctions, systems with three arms of n sites that meet at a central site. The accuracy is comparable to DMRG of chains. As in chains, new sites are always bonded to the most recently added sites and the superblock Hamiltonian contains only new or once renormalized operators. Junctions of up to N = 3n + 1 approximate to 500 sites are studied with antiferromagnetic (AF) Heisenberg exchange J between nearest-neighbor spins S or electron transfer t between nearest neighbors in half-filled Hubbard models. Exchange or electron transfer is exclusively between sites in two sublattices with N-A not equal N-B. The ground state (GS) and spin densities rho(r) = < S-r(z)> at site r are quite different for junctions with S = 1/2, 1, 3/2, and 2. The GS has finite total spin S-G = 2S(S) for even (odd) N and for M-G = S-G in the S-G spin manifold, rho(r) > 0(< 0) at sites of the larger (smaller) sublattice. S = 1/2 junctions have delocalized states and decreasing spin densities with increasing N. S = 1 junctions have four localized S-z = 1/2 states at the end of each arm and centered on the junction, consistent with localized states in S = 1 chains with finite Haldane gap. The GS of S = 3/2 or 2 junctions of up to 500 spins is a spin density wave with increased amplitude at the ends of arms or near the junction. Quantum fluctuations completely suppress AF order in S = 1/2 or 1 junctions, as well as in half-filled Hubbard junctions, but reduce rather than suppress AF order in S = 3/2 or 2 junctions.

I. Nuclear spin-internal-rotation-coupling. II. Fluorine spin-rotation interaction and magnetic shielding in fluorobenzene

Part I.

The interaction of a nuclear magnetic moment situated on an internal top with the magnetic fields produced by the internal as well as overall molecular rotation has been derived following the method of Van Vleck for the spin-rotation interaction in rigid molecules. It is shown that the Hamiltonian for this problem may be written

H_SR = Ῑ · M · Ĵ + Ῑ · M” · Ĵ”

Where the first term is the ordinary spin-rotation interaction and the second term arises from the spin-internal-rotation coupling.

The F¹⁹ nuclear spin-lattice relaxation time (T₁) of benzotrifluoride and several chemically substituted benzotrifluorides, have been measured both neat and in solution, at room temperature by pulsed nuclear magnetic resonance. From these experimental results it is concluded that in benzotrifluoride the internal rotation is crucial to the spin relaxation of the fluorines and that the dominant relaxation mechanism is the fluctuating spin-internal-rotation interaction.

Part II.

The radiofrequency spectrum corresponding to the reorientation of the F¹⁹ nuclear moment in flurobenzene has been studied by the molecular beam magnetic resonance method. A molecular beam apparatus with an electron bombardment detector was used in the experiments. The F¹⁹ resonance is a composite spectrum with contributions from many rotational states and is not resolved. A detailed analysis of the resonance line shape and width by the method of moments led to the following diagonal components of the fluorine spin-rotational tensor in the principal inertial axis system of the molecule:

F/Caa = -1.0 ± 0.5 kHz

F/Cbb = -2.7 ± 0.2 kHz

F/Ccc = -1.9 ± 0.1 kHz

From these interaction constants, the paramagnetic contribution to the F¹⁹ nuclear shielding in C₆H₅F was determined to be -284 ± ppm. It was further concluded that the F¹⁹ nucleus in this molecule is more shielded when the applied magnetic field is directed along the C-F bond axis. The anisotropy of the magnetic shielding tensor, σ_” - σ_⊥, is +160 ± 30 ppm.

Influência da reorientação de spin nas propriedades termomagnéticas dos compostos da série Ho1-yGdyAl2

Neste trabalho foram estudadas as propriedades estruturais e termomagnéticas dos pseudobinários Ho1-yGdyAl2, através de abordagens experimentais e teóricas. A parte experimental envolveu a preparação de cinco amostras, com as concentrações y = 0, 0,25, 0,5, 0,75 e 1, assim como medidas de magnetização, calor especifico e da variação adiabática da temperatura. Na parte teórica usamos um hamiltoniano modelo que leva em consideração a interação dos íons com o campo magnético aplicado, com o campo elétrico cristalino e a troca entre os íons magnéticos. A entropia da rede foi considerada na aproximação de Debye e a entropia eletrônica na aproximação do gás de elétrons livres. A influência das reorientações de spin, espontâneas e induzidas pelo campo magnético, na magnetização e no calor especifico foram investigadas sistematicamente tanto a partir de dados experimentais quanto teoricamente. Também obtemos resultados teóricos para a variação de entropia e variação adiabática da temperatura alterando a intensidade ou a direção do campo magnético.

DTADH and quantum critical phenomena caused by anisotropy and external magnetic field for spin-1/2 Heisenberg diamond chains

Using the transfer matrix renormalization group (TMRG) method, we study the connection between the first derivative of the thermal average of driving-term Hamiltonian (DTADH) and the trace of quantum critical behaviors at finite temperatures. Connecting with the exact diagonalization method, we give the phase diagrams and analyze the properties of each phase for both the ferromagnetic and anti-ferromagnetic frustrated J(3) anisotropy diamond chain models. The finite-temperature scaling behaviors near the critical regions are also investigated. Further, we show the critical behaviors driven by external magnetic field, analyze the formation of the 1/3 magnetic plateau and the influence of different interactions on those critical points for both the ferrimagnetic and anti-ferromagnetic distorted diamond chains.

Spin-Hall effect in the generalized honeycomb lattice with Rashba spin-orbit interaction

We study the spin-Hall effect in a generalized honeycomb lattice, which is described by a tight-binding Hamiltonian including the Rashba spin-orbit coupling and inversion-symmetry breaking terms brought about by a uniaxial pressure. The calculated spin-Hall conductance displays a series of exact or approximate plateaus for isotropic or anisotropic hopping integral parameters, respectively. We show that these plateaus are a consequence of the various Fermi-surface topologies when tuning epsilon(F). For the isotropic case, a consistent two-band analysis, as well as a Berry-phase interpretation. are also given. (C) 2009 Elsevier B.V. All rights reserved.

Symmetry and optical transition rule for low-dimensional semiconductor system with spin-orbit interaction and magnetic field

Starting from effective mass Hamiltonian, we systematically investigate the symmetry of low-dimensional structures with spin-orbit interaction and transverse magnetic field. The position-dependent potentials are assumed to be space symmetric, which is ever-present in theory and experiment research. By group theory, we analyze degeneracy in different cases. Spin-orbit interaction makes the transition between Zeeman sub-levels possible, which is originally forbidden within dipole approximation. However, a transition rule given in this paper for the first time shows that the transition between some levels is forbidden for space symmetric potentials. (C) 2009 Elsevier Ltd. All rights reserved.

Spin-polarized tunneling through a diluted magnetic semiconductor quantum dot

Spin-polarized tunneling through a diluted magnetic semiconductor quantum dot embedded in a tunneling barrier is investigated using the Bardeen transfer Hamiltonian. The tunneling current oscillates with an increasing magnetic field for a fixed bias. Many peaks are observed with an increasing external bias under a fixed magnetic field. Spin polarization of the tunneling current is tuned by changing the external bias under a weak magnetic field.

Spin states and persistent currents in mesoscopic rings: Spin-orbit interactions

We investigate theoretically electron spin states in one-dimensional and two-dimensional (2D) hard-wall mesoscopic rings in the presence of both the Rashba spin-orbit interaction (RSOI) and the Dresselhaus spin-orbit interaction (DSOI) in a perpendicular magnetic field. The Hamiltonian of the RSOI alone is mathematically equivalent to that of the DSOI alone using an SU(2) spin rotation transformation. Our theoretical results show that the interplay between the RSOI and DSOI results in an effective periodic potential, which consequently leads to gaps in the energy spectrum. This periodic potential also weakens and smoothens the oscillations of the persistent charge current and spin current and results in the localization of electrons. For a 2D ring with a finite width, higher radial modes destroy the periodic oscillations of persistent currents.

CALCULATION OF SPIN-REORIENTATION TEMPERATURE IN ND2FE14B

The spin-reorientation phenomenon in Nd2Fe14B has been investigated using an angular dependent free energy approach. A magnetic Hamiltonian which includes the crystal electric field term and the exchange term has been established using realistic band structure results. The temperature dependence of the molecular field is accounted for by introducing the Brillouin function and the magnetic Hamiltonian is diagonalized within the ground state multiplet of the Nd ion. The eigenstates are then used to form the partition function for the free energy. At each temperature, the direction of the molecular field is obtained by searching for the minimum in the angular parameter space of the free energy. Our calculations show that for Nd2Fe14B, the net magnetic anisotropy direction is canted away from the c axis at a temperature close to the experimentally reported spin-reorientation temperature of 150 K. The temperature dependence of the magnetic structure is found to be very sensitive to the size of the second order crystal field parameter B20.

Spontaneous spin polarization and electron localization in constrained geometries: The Wigner transition in nanowires

The Wigner transition in a jellium model of cylindrical nanowires has been investigated by density-functional computations using the local spin-density approximation. A wide range of background densities rho(b) has been explored from the nearly ideal metallic regime (r(s)=[3/4 pi rho(b)](1/3)=1) to the high correlation limit (r(s)=100). Computations have been performed using an unconstrained plane wave expansion for the Kohn-Sham orbitals and a large simulation cell with up to 480 electrons. The electron and spin distributions retain the cylindrical symmetry of the Hamiltonian at high density, while electron localization and spin polarization arise nearly simultaneously in low-density wires (r(s)similar to 30). At sufficiently low density (r(s)>= 40), the ground-state electron distribution is the superposition of well defined and nearly disjoint droplets, whose charge and spin densities integrate almost exactly to one electron and 1/2 mu(B), respectively. Droplets are arranged on radial shells and define a distorted lattice whose structure is intermediate between bcc and fcc. Dislocations and grain boundaries are apparent in the droplets' configuration found by our simulations. Our computations aim at modeling the behavior of experimental low-carried density systems made of lightly doped semiconductor nanostructures or conducting polymers.

Hamiltonian Tomography in an Access-Limited Setting without State Initialization

We propose a scheme for the determination of the coupling parameters in a chain of interacting spins. This requires only time-resolved measurements over a single particle, simple data postprocessing and no state initialization or prior knowledge of the state of the chain. The protocol fits well into the context of quantum-dynamics characterization and is efficient even when the spin chain is affected by general dissipative and dephasing channels. We illustrate the performance of the scheme by analyzing explicit examples and discuss possible extensions.

From perfect to fractal transmission in spin chains

Perfect state transfer is possible in modulated spin chains [Phys. Rev. Lett. 92, 187902 (2004)], imperfections, however, are likely to corrupt the state transfer. We study the robustness of this quantum communication protocol in the presence of disorder both in the exchange couplings between the spins and in the local magnetic field. The degradation of the fidelity can be suitably expressed, as a function of the level of imperfection and the length of the chain, in a scaling form. In addition the time signal of fidelity becomes fractal. We further characterize the state transfer by analyzing the spectral properties of the Hamiltonian of the spin chain.

Quantum cloning in spin networks

We introduce an approach to quantum cloning based on spin networks and we demonstrate that phase covariant cloning can be realized using no external control but only with a proper design of the Hamiltonian of the system. In the 1-->2 cloning we find that the XY model saturates the value for the fidelity of the optimal cloner and gives values comparable to it in the general N-->M case. We finally discuss the effect of external noise. Our protocol is much more robust to decoherence than a conventional procedure based on quantum gates.

Global quantum correlations in finite-size spin chains

We perform an extensive study of the properties of global quantum correlations in finite-size one-dimensional quantum spin models at finite temperature. By adopting a recently proposed measure for global quantum correlations (Rulli and Sarandy 2011 Phys. Rev. A 84 042109), called global discord, we show that critical points can be neatly detected even for many-body systems that are not in their ground state. We consider the transverse Ising model, the cluster-Ising model where three-body couplings compete with an Ising-like interaction, and the nearest-neighbor XX Hamiltonian in transverse magnetic field. These models embody our canonical examples showing the sensitivity of global quantum discord close to criticality. For the Ising model, we find a universal scaling of global discord with the critical exponents pertaining to the Ising universality class.

Dynamics of the entanglement spectrum in spin chains

We study the dynamics of the entanglement spectrum, that is the time evolution of the eigenvalues of the reduced density matrices after a bipartition of a one-dimensional spin chain. Starting from the ground state of an initial Hamiltonian, the state of the system is evolved in time with a new Hamiltonian. We consider both instantaneous and quasi adiabatic quenches of the system Hamiltonian across a quantum phase transition. We analyse the Ising model that can be exactly solved and the XXZ for which we employ the time-dependent density matrix renormalisation group algorithm. Our results show once more a connection between the Schmidt gap, i.e. the difference of the two largest eigenvalues of the reduced density matrix and order parameters, in this case the spontaneous magnetisation.