Interaction effects on persistent current of ballistic cylindrical nanostructures

We investigate clean cylindrical nanostructures with an applied longitudinal static magnetic field. The ground state of these systems becomes degenerate for particular values of the field due to Aharonov-Bohm effect. The Coulomb interaction introduces couplings between the electronic configurations. Consequently, depending on particular selection rules, the ground state may become, in the interacting case, a many body state at the degeneracy points: a gap is then opened. To study this problem, we propose a variational multireference wave function which goes beyond the Hartree-Fock approximation. Using this ansatz, in addition to the replacements of some crossings by avoided crossings, two other important effects of the electron-electron interaction are pointed out: (i) the long-range part of the Coulomb potential tends to shift the position in magnetic field of the crossing or avoided crossing points and, (ii) at the points of degeneracy or near degeneracy, the interaction can drive the system from a singlet to a triplet state inducing new real crossing points in the ground state energy curve as function of the field. In any case, the crossing points that are due to either orbital or spin effects, should manifest themselves in various experiments as sudden changes in the response of the system (magnetoconductance, magnetopolarisability, ...) when the magnetic field is tuned.     

Quantum Phase Transition and Thermal Entanglement in the Isotropic XXX Model

We investigate the quantum phase transition (QPT) and the pairwise thermal entanglement in the three-qubit Heisenberg XXX chain with Dzyaloshinskii--Moriya (DM) interaction under a magnetic field. The ground states of the system exist crossing points, which shows that the system exhibits a QPT. At a given temperature, the entanglement undergoes two sudden changes (platform-like behavior) as the DM interaction or external magnetic field increases. This special property can be used as the entanglement switch, which is also influenced by the temperature. We can modulate the DM interaction or external magnetic field to control the entanglement switch.     

Effect of Dzyaloshinskii−Moriya interactions on Kagome anti-ferromagnetic clusters

The low energy and low temperature behavior of a few finite size Kagome clusters, including mixed spin systems of S=1/2 and S=1, with the nearest neighbor Heisenberg antiferromagnetic model is studied under the influence of out-of-plane Dzyaloshinskii?Moriya interactions (DMI) within the exact diagonalization formalism. The ground state of all the finite size systems is found to be present in the lowest spin sector with a finite gap to the lowest magnetic excitation irrespective of the strength of out-of-plane DMI. The energy level structures within the non-magnetic ground state and the lowest magnetic state have been studied for all the systems as a function of DMI. The characteristic signature of such low-lying non-magnetic excitations is reflected in the low temperature behavior of the specific heat. It is also found that the ground state chiral structure (characterized by the vector chiral order of the system) in the xy-plane shows sharp changes as a function of out-of-plane DMI at level crossing or avoided crossing regions. The in-plane spin ordering for each system is also studied with the estimation of static structure factor as a response to the varying strength of DMI.     

A Realization of Yangian and Its Applications to the Bi-spin System in an External Magnetic Field

Yangian Y(sl(2)) is realized in the bi-spin system coupled with a time-dependent external magnetic field. It is shown that Y(sl(2)) generators can describe the transitions between the "spin triplet" and the "spin singlet" that evolve with time. Furthermore, new transition operators between the states with Berry phase factor and those between the states of nuclear magnetic resonance are presented.     

Quantum Teleportation via Completely Anisotropic Heisenberg Chain in Inhomogeneous Magnetic Field

The quantum teleportation with the entangled thermal state is investigated based on the completely anisotropic Heisenberg chain in the presence of the externally inhomogeneous magnetic field. The effects of the anisotropy and magnetic field for the quantum fidelity are studied in detail. The zero temperature limit and the features of the nonzero temperature for this nonclassical fidelity are obt8ained. We find that the quantum teleportation demands more stringent conditions than the thermal entanglement of the resource by investigating the threshold temperature of the thermal concurrence and the critical temperature of the maximal teleportation fidelity. The useful quantum teleportation should avoid the point of the phase transition of the system and the anisotropy of the chain and the external magnetic field can control the applicability of the resource in the quantum teleportation.     

Application of Y（sl（2）） Algebra for Entanglement of Two-Qubit System

We construct the transition operators in terms of the generators of the general Yangian and the reduced Yangian. By acting these operators on a two-qubit pure state, we find that the entanglement degrees of the states are all decreased from the certain values to zero for the reduced Yangian algebra, which makes the state disentangled. This result sheds new light on the physical meaning of Y （sl（2） ） in quantum information.     

Can the symmetrical Dewar pyridine be observed experimentally? A theoretical study

ABSTRACT

In this work we study the possibility of the photochemical formation of the symmetrical Dewar pyridine (1-azabicyclo-[2,2,0]-hexa-2,5-diene), by applying the complete active space self-consistent field method and the multiconfigurational second-order perturbation theory to explore the corresponding ground and excited state potential energy surfaces. According to our theoretical calculations there are three possible paths that can be followed, one is a biphotonic process which involves irradiating pyridine in its ground state with a 358?nm laser guiding the system to an intersystem crossing S₁/T₁/S₀ of triple character whereby deactivation to the ground state, S₀, Dewar minimum occurs, the second one, which is a ground state thermal reaction involves the use of a far-Infra-Red laser where planar pyridine is vibrationally excited to a very high vibrational level whose energy is comparable to that of the ground state transition structure, S₀(TS), connecting the symmetrical S₀ Dewar pyridine and the ground state of planar pyridine. The third process is also a biphotonic one involving excitation of planar pyridine with an energy which is in the limits of its ionisation potential. In this case there is a theoretically accessible S₁/S₀ Conical Intersection which leads directly to the ground state of the symmetrical Dewar pyridine.     

Hofstadter spectrum in electric and magnetic fields

The problem of Bloch electrons in two dimensions subjected to magnetic and intense electric fields is investigated. Magnetic translations, electric evolution, and energy translation operators are used to specify the solutions of the Schrödinger equation. For rational values of the magnetic flux quanta per unit cell and commensurate orientations of the electric field relative to the original lattice, an extended superlattice can be defined and a complete set of mutually commuting space-time symmetry operators is obtained. Dynamics of the system is governed by a finite difference equation that exactly includes the effects of: an arbitrary periodic potential, an electric field orientated in a commensurable direction of the lattice, and coupling between Landau levels. A weak periodic potential broadens each Landau level in a series of minibands, separated by the corresponding minigaps. The addition of the electric field induces a series of avoided and exact crossing of the quasienergies, for sufficiently strong electric field the spectrum evolves into equally spaced discreet levels, in this “magnetic Stark ladder” the energy separation is an integer multiple of hE/aB, with a the lattice parameter.     

Field-induced transitions and spatial chaos in the classical XY spin chain

We study the lowest-lying excitation of a classical ferromagnetic XY spin chain, in the presence of a symmetry breaking magnetic field. Extremizing the energy of this system leads to a two-dimensional nonlinear map, whose allowed phase space shrinks with increasing field in a nontrivial manner. The orbits of the map represent the set of extremum energy spin configurations. For each field, we compute the energy of the members of this set and find the lowest energy among them, excluding the obvious ground state configuration with all spins parallel along the field direction. This state turns out to be the unstable fixed point of the map. We show that up to a certain (primary) critical field, a separatrixlike 2pi soliton configuration is the lowest-energy excitation, with an energy very close to the ground state energy. For any field beyond this critical field, the soliton disappears and lowest excitation is a librational configuration corresponding to the outermost orbit in the phase plot at that field. Further, its energy is found to be much higher than the ground state energy, leading to a sharp jump in the difference in energy between the former and the latter at this field. With further increase in the field, sharp jumps in the excitation energy arise at certain secondary critical fields as well. We show that these appear when the corresponding spin configurations become commensurate. This complex behavior of the energy is interpreted and its effect on the magnetization and static susceptibility of the system is also studied.     

Energy landscape of 3D spin Hamiltonians with topological order

We explore the feasibility of a quantum self-correcting memory based on 3D spin Hamiltonians with topological quantum order in which thermal diffusion of topological defects is suppressed by macroscopic energy barriers. To this end we characterize the energy landscape of stabilizer code Hamiltonians with local bounded-strength interactions which have a topologically ordered ground state but do not have stringlike logical operators. We prove that any sequence of local errors mapping a ground state of such a Hamiltonian to an orthogonal ground state must cross an energy barrier growing at least as a logarithm of the lattice size. Our bound on the energy barrier is tight up to a constant factor for one particular 3D spin Hamiltonian.     

两体相互作用费米系统在自旋轨道耦合和塞曼场中的基态转变

在超冷费米系统中实现人造规范势的突破,吸引了许多新问题的研究,展现了许多新奇的物理现象.本文研究了在环阱中,具有自旋轨道耦合和塞曼作用的两体相互作用费米模型.通过平面波展开的方法,解析求解了两体费米系统的本征能态.系统的总动量为守恒量,可以在不同总动量空间中研究能谱.研究发现:随着塞曼相互作用增大,在不同总动量空间,两体费米系统的本征能量均逐渐降低,系统基态从总动量为零空间转变到有限值空间.从吸引到排斥相互作用,无塞曼相互作用时,基态总动量始终为零,有塞曼相互作用时,基态总动量从零转变为有限值.通过单粒子和基态动量分布研究,本文直观地揭示了由塞曼能级劈裂引起的基态转变.     

Induced Jahn-Teller transition in DyPO4 caused by a change in ground state upon level crossing

The transition caused by a change in the ground state of a rare-earth ion upon level crossing, an analogue of the induced Jahn-Teller transition in rare-earth compounds, is observed. It is shown that a jumpwise change in the Jahn-Teller interactions of α and γ symmetries, caused by a change in the corresponding quadrupole moments in DyPO₄ upon level crossing, diminishes the critical field by ～20 kOe and leads to a sharper change in magnetization M and differential magnetic susceptibility dM/dH near the crossover point.     

Trace Distance and Level Crossing in Spin-Bosen Model with Added Classical Driving Fields

By making use of the trace distance as a measure we investigate the influence of classical driving fields on a open quantum system when the system and its environment are initially in a correlated state. It is shown that the amount of trace distance is sensitive to the classical driving fields which implies that the information flowing between open system and its environment can be controlled by the classical driving fields. Furthermore, we also explore the dependence of the trace distance on the initial parameters when the total system is considered in the thermal equilibrium state. We find that the trace distance on the coupling strength can be used to demonstrate the level crossing of the ground state of the system. In particular, the classical driving fields have significant effect on the level crossing of the ground state.     

Finite Size XXZ Spin Chain with Anisotropy Parameter Δ= \frac{1} {2}

We find an analytic solution of the Bethe–Ansatz equations (BAE) for the special case of a finite XXZ spin chain with free boundary conditions and with a complex surface field which provides for U_q(sl(2)) symmetry of the Hamiltonian. More precisely, we find one nontrivial solution, corresponding to the ground state of the system with anisotropy parameter Δ= $\frac{1}{2}$ corresponding to q³=?1. With a view to establishing an exact representation of the ground state of the finite size XXZ spin chain in terms of elementary functions, we concentrate on the crossing parameter η dependence around η=π/3 for which there is a known solution. The approach taken involves the use of a physical solution Q of Baxter's T-Q equation, corresponding to the ground state, as well as a non-physical solution P of the same equation. The calculation of P and then of the ground state derivative is covered. Possible applications of this derivative to the theory of percolation have yet to be investigated. As far as the finite XXZ spin chain with periodic boundary conditions is concerned, we find a similar solution for an assymetric case which corresponds to the 6-vertex model with a special magnetic field. For this case we find the analytic value of the “magnetic moment” of the system in the corresponding state.     

Generation of entanglement in finite spin systems via adiabatic quantum computation

For a finite XY chain and a finite two-dimensional Ising lattice, it is shown that the paramagnetic ground state is adiabatically transformed to the Greenberger-Horne-Zeilinger state in the ferromagnetic phase by changing slowly the external magnetic field. It is found that the fidelity between the Greenberger-Horne-Zeilinger state and an adiabatically evolved state depends on the interpolation schemes as well as the energy gap between the ground and exited states. A possibility whether quantum phase transitions can be simulated on adiabatic quantum computation is discussed.     

Ground state fidelity from tensor network representations

For any D-dimensional quantum lattice system, the fidelity between two ground state many-body wave functions is mapped onto the partition function of a D-dimensional classical statistical vertex lattice model with the same lattice geometry. The fidelity per lattice site, analogous to the free energy per site, is well defined in the thermodynamic limit and can be used to characterize the phase diagram of the model. We explain how to compute the fidelity per site in the context of tensor network algorithms, and demonstrate the approach by analyzing the two-dimensional quantum Ising model with transverse and parallel magnetic fields.     

Magnetic field effect on the binding energy of a hydrogenic impurity in coaxial GaAs/ AlxGa1−xAs quantum well wires

We propose a coaxial cylindrical quantum well wire (QWW) system, in which two conducting cylindrical layers are separated by an insulating layer. The ground state binding energy of a hydrogenic impurity subjected to uniform magnetic field applied parallel to the wire axis is studied within a variational scheme as a function of the inner barrier thickness for two different impurity positions and various barrier potentials. The ground state energy and wave function in the presence of a magnetic field is directly calculated using the fourth-order Runge–Kutta method. It is found that the binding energy in critical barrier thickness shows a sharp increase or decrease depending on the impurity position and magnetic field strength. The main result is that a sharp variation in the binding energy, which may be important in device applications, depends strongly not only on the location of the impurity but also on the magnetic field and the geometry of the wire.     

Phase transition in antiferromagnets with anisotropic exchange interactions and uniaxial anisotropy

Abstract

Following the Bogoliubov variational principle, the equilibrium and stability equations of the free energy for the two sublattice antiferromagnetic system with inter- and intrasublattice exchange interactions and with an external magnetic field are investigated. For the Ising spin system with uniaxial anisotropy, the phase diagrams have been calculated for various values of anisotropy constant d and the ratio of intra- to intersublattice interaction constants γ. It is shown that first-order, as well as second-order transitions, occur for γ > 0, whereas only a second-order transition occurs for γ ≦ 0, irrespective of the sign of d. Furthermore, similar calculations are extended for the anisotropic Heisenberg spin system and quite interesting phase diagrams have been obtained. Next, the effects of the anisotropic exchange interactions on the magnetic ordered states and the magnetizations of the singlet ground state system of spin one and with a uniaxial anisotropy term are investigated in the vicinity of the level crossing field H ? D/gμ _B . A field-induced ordered state without the transverse component of magnetization is shown to appear in a certain range of magnetic field as the spin dimensionality decreases. It has also turned out that the phase transition between this ordered state and the canted antiferromagnetic state ordinarily found for the isotropic singlet ground state system is of first order. Lastly, the stable spin configurations at a temperature of absolute zero for a two-sublattice uniaxial antiferromagnet under an external magnetic field of arbitrary direction are studied. In particular, the effects of a single ionic anisotropy D-term and anisotropy in the exchange interactions on the magnetic phases are investigated. The antiferromagnetic state has turned out to appear only for the external magnetic field along the easy axis of sublattice magnetization, and makes a first-order phase transition to the canted-spin state or the ferromagnetic state. For other field directions, no antiferromagnetic state appears and only a second-order phase transition between the canted-spin and the ferromagnetic states occurs. The critical field as a function of external field direction has been calculated for several D-values.     

Quantum Teleportation via a Two-Qubit Ising Heisenberg Chain with an Arbitrary Magnetic Field

The quantum teleportation via a two-qubit Ising Heisenberg chain in the presence of an external magnetic field with an arbitrary direction are investigated. The effect of the orientation of an external magnetic field on the entanglement teleportation has been analyzed numerically. It is found that the teleported thermal concurrence and average fidelity can be maximized by rotating the magnetic field (with fixed magnitude) to an optimal direction. The ferromagnetic channel is not suitable to teleportation. A minimal entanglement of the thermal state is needed to realize the entanglement teleportation for antiferromagnetic channel. It is also found that the entanglement of the channel cannot completely reflect the teleported concurrence and average fidelity. There exist double-value phenomena between them.     

Entanglement and teleportation through thermal equilibrium state of spins in the XXZ model

We study the pairwise entanglement of a three-qubit spins in the XXZ model, and teleport an unknown state using the spin chain in the thermal equilibrium as a quantum channel. The effects of coupling strength, magnetic field, the anisotropy and temperature on the entanglement and fidelity are investigated. We find that the ferromagnetic spin chain is suitable for quantum teleportation, while the anti-ferromagnetic one is not. We give the maximal average fidelity, and the condition under which the maximal average fidelity is obtained. In addition, the relation between the entanglement and fidelity is studied, and we find that the considered entanglement cannot completely reflect the fidelity.