Ultra‐Fast Control of Magnetic Relaxation in a Periodically Driven Hubbard Model

Motivated by cold atom and ultra‐fast pump‐probe experiments we study the melting of long‐range antiferromagnetic order of a perfect Néel state in a periodically driven repulsive Hubbard model. The dynamics is calculated for a Bethe lattice in infinite dimensions with non‐equilibrium dynamical mean‐field theory. In the absence of driving melting proceeds differently depending on the quench of the interactions to hopping ratio from the atomic limit. For decay occurs due to mobile charge‐excitations transferring energy to the spin sector, while for it is governed by the dynamics of residual quasi‐particles. Here we explore the rich effects that strong periodic driving has on this relaxation process spanning three frequency ω regimes: (i) high‐frequency , (ii) resonant with integer l, and (iii) in‐gap away from resonance. In case (i) we can quickly switch the decay from quasi‐particle to charge‐excitation mechanism through the suppression of ν₀. For (ii) the interaction can be engineered, even allowing an effective regime to be reached, giving the reverse switch from a charge‐excitation to quasi‐particle decay mechanism. For (iii) the exchange interaction can be controlled with little effect on the decay. By combining these regimes we show how periodic driving could be a potential pathway for controlling magnetism in antiferromagnetic materials. Finally, our numerical results demonstrate the accuracy and applicability of matrix product state techniques to the Hamiltonian DMFT impurity problem subjected to strong periodic driving.     

自旋为1的三粒子Heisenberg XXX链中杂质对热纠缠的影响

采用纠缠的度量方法Negativity研究了匀强磁场下自旋为l的含杂质三粒子HeisellhergXXX链的热纠缠特性.通过计算系统的杂质位与其余部分间的两体纠缠N1-23及正常位与其余部分间的两体纠缠N12-3,发现纠缠存在的临界温度T.的改变来自杂质参数J1的变化,随杂质参数J1,的增加而增加,外界磁场B的存在会降低纠缠值,但并不会改变临界温度.可以通过调节杂质参数J1和外界磁场B来控制两体纠缠N1-23,和N12-3的大小.     

Drift and Diffusion in Periodically Driven Renewal Processes

We consider the drift and diffusion properties of periodically driven renewal processes. These processes are defined by a periodically time dependent waiting time distribution, which governs the interval between subsequent events. We show that the growth of the cumulants of the number of events is asymptotically periodic and develop a theory which relates these periodic growth coefficients to the waiting time distribution defining the periodic renewal process. The first two coefficients, which are the mean frequency and effective diffusion coefficient of the number of events are considered in greater detail. They may be used to quantify stochastic synchronization.     

Quantum Heat Engine Based on Working Substance of Two Particles Heisenberg XXX Model with the Dzyaloshinskii-Moriya Interaction

A quantum heat engine (QHE) with a working substance of two-particle \( \left(\frac{1}{2},1\right) \) Heisenberg XXX model with Dzyaloshinskii–Moriya (DM) interaction in the external magnetic field B is studied, and the influences of the DM interaction on the efficiency, work are examined under different coupling strengths. The results show that the QHE can operate and produce positive work and the efficiency on the two magnetic field conditions B₁ < B₂ and B₁ > B₂. Moreover, the efficiency can achieve the large value and several interesting effects of the DM interaction on the local work are obtained.

     

含杂质三量子位Heisenberg XXX链的全局两体纠缠

研究了含杂质三量子位Heisenberg XXX链的全局两体纠缠, 通过计算N_12-3和N_1-23, 发现两体纠缠存在的临界温度T_c随杂质参数J₁的增加而升高. 给定温度T, 相应的纠缠存在的临界杂质 参数J_1c随磁场的增加而增加, 而且可以通过调节杂质参数J₁和磁场B来控制N_12-3和N_1-23的取值. 此外, 随着温度的增加, N_12-3的最大值将由0.5减小到0.3727, 而N_1-23的最大值保持0.4714不变.     

Analytical Solution of Weak-Coupling Periodically Driven Two-Level System

We present an approximate analytical solution to periodically driven two-level system in the weak-coupling regime. The analytical solution is in good agreement with the exact numerical solution in resonance and near resonance cases when Ω≤0.3ω_a with Ω and ω_a denoting the Rabi and transition frequencies respectively.     

Multiple Quantum Coherences (MQ) NMR and Entanglement Dynamics in the Mixed-Three-Spin XXX Heisenberg Model with Single-Ion Anisotropy

We analytically investigate Multiple Quantum (MQ) NMR dynamics in a mixed-three-spin (1/2,1,1/2) system with XXX Heisenberg model at the front of an external homogeneous magnetic field B. A single-ion anisotropy property ζ is considered for the spin-1. The intensities dependence of MQ NMR coherences on their orders (zeroth and second orders) for two pairs of spins (1,1/2) and (1/2,1/2) of the favorite tripartite system are obtained. It is also investigated dynamics of the pairwise quantum entanglement for the bipartite (sub)systems (1,1/2) and (1/2,1/2) permanently coupled by, respectively, coupling constants J₁ and J₂, by means of concurrence and fidelity. Then, some straightforward comparisons are done between these quantities and the intensities of MQ NMR coherences and ultimately some interesting results are reported. We also show that the time evolution of MQ coherences based on the reduced density matrix of the pair spins (1,1/2) is closely connected with the dynamics of the pairwise entanglement. Finally, we prove that one can introduce MQ coherence of the zeroth order corresponds to the pair spins (1,1/2) as an entanglement witness at some special time intervals.     

Multiple Quantum Coherences(MQ) NMR and Entanglement Dynamics in the Mixed-Three-Spin XXX Heisenberg Model with Single-Ion Anisotropy

We analytically investigate Multiple Quantum(MQ) NMR dynamics in a mixed-three-spin(1/2,1,1/2)system with XXX Heisenberg model at the front of an external homogeneous magnetic field B. A single-ion anisotropy property ζ is considered for the spin-1. The intensities dependence of MQ NMR coherences on their orders(zeroth and second orders) for two pairs of spins(1,1/2) and(1/2,1/2) of the favorite tripartite system are obtained. It is also investigated dynamics of the pairwise quantum entanglement for the bipartite(sub)systems(1,1/2) and(1/2,1/2)permanently coupled by, respectively, coupling constants J_1 and J_2, by means of concurrence and fidelity. Then, some straightforward comparisons are done between these quantities and the intensities of MQ NMR coherences and ultimately some interesting results are reported. We also show that the time evolution of MQ coherences based on the reduced density matrix of the pair spins(1,1/2) is closely connected with the dynamics of the pairwise entanglement. Finally, we prove that one can introduce MQ coherence of the zeroth order corresponds to the pair spins(1,1/2) as an entanglement witness at some special time intervals.     

Effects of impurity on the entanglement of the three-qubit Heisenberg XXX spin chain

We investigate the entanglement of the three-qubit Heisenberg XXX chain in the presence of impurity and obtain the analytical expressions of the concurrence C. It is found that for impurity entanglement, C appears only when J1 > J for J > 0, and J1 > 0 for J < 0, and in these two regions C increases with the increase of J1, so is the critical temperature Tc. When J1 >>|J| , C reaches its maximum value 0.5 and Tc reaches the asymptotic value Tc = 3.41448J1. For entanglement between the normal lattices, C appears only when J > 0 and 2J < J1 < J, and initially increases with the increase of J1 and arrives at the maximum value Cmax = (e4JIT-3)/(e4JIT+3) before it decays to zero gradually, so is the critical temperature Tc with, however, the maximum value Tcmax = 4J/ln3.     

Many-Body Localization Transition in the Heisenberg Ising Chain

In this paper, we use exact matrix diagonalization to explore the many-body localization (MBL) transition of the Heisenberg Ising spin-1/2 chain with nearest neighbor couplings and disordered external fields. It demonstrates that the fidelity, magnetization and spin-spin space correlation can be used to characterize the many-body localization transition in this closed spin system which is also in agreement with previous analytical and numerical results. We test the properties for the middle third many-body eigenstates. It shows that for this model with random-field, the excited-state fidelity exhibits a pronounced drop at the transition and then gradually tends to be stable in the localized phase, the critical point and the final value of averaged fidelity are all size dependent. It demonstrates that disordered external fields drive the occurrence of the MBL transition. Moreover, we investigate the magnetization and spin-spin space correlation in this model to verify the conclusion we got and further explore the properties of ergodic phase and localized phase.

     

Quantum Discord Behavior about Two-Qubit Heisenberg XYZ Model with Decoherence

We investigate the properties of quantum discord dynamics of a two-qubit Heisenberg XYZ system which is influenced by the environmental decoherence under an external nonuniform magnetic field. It shows that the influence of the parameters on the system heavily rely on the selection of the initial states. One point shows that the environmental decoherence cannot entirely destroy the quantum correlation, and properly controlling the parameters can inhibit the decoherence. Moreover, it presents that the inhomogeneous magnetic field cannot affect the steady quantum discord （QD）, while the uniform magnetic field and the anisotropy coupling constant will change the steady QD. These investigations imply that one can obtain larger steady QD values by reasonably adjusting parameters on quantum correlation in solid state systems.     

Exponential Bound for the Heating Rate of Periodically Driven Spin Systems

Journal of Experimental and Theoretical Physics - For the nuclear spin system of a solid in the presence of an inhomogeneous magnetic field, we have found a rigorous bound for the heating rate of...     

Auto- versus Cross-Correlation Noise in Periodically Driven Quantum Coherent Conductors

Expressing currents and their fluctuations at the terminals of a multi-probe conductor in terms of the wave functions of carriers injected into the Fermi sea provides new insight into the physics of electric currents. This approach helps us to identify two physically different contributions to shot noise. In the quantum coherent regime, when current is carried by non-overlapping wave packets, the product of current fluctuations in different leads, the cross-correlation noise, is determined solely by the duration of the wave packet. In contrast, the square of the current fluctuations in one lead, the autocorrelation noise, is additionally determined by the coherence of the wave packet, which is associated with the spread of the wave packet in energy. The two contributions can be addressed separately in the weak back-scattering regime, when the autocorrelation noise depends only on the coherence. Analysis of shot noise in terms of these contributions allows us, in particular, to predict that no individual traveling particles with a real wave function, such as Majorana fermions, can be created in the Fermi sea in a clean manner, that is, without accompanying electron–hole pairs.     

匀强及非匀强磁场中Heisenberg XXX链的纠缠研究

研究了匀强及非匀强磁场中反铁磁体Heisenberg XXX链的近邻和次近邻纠缠.结果表明对基态情形,纠缠随磁场B变化呈现阶梯型结构,这可用来构建量子纠缠"放大器"或量子纠缠"开关".对有限温度情形,引进一非匀强磁场Bi=(-1)iB可以使近邻格点间纠缠在某些区域明显增大,而次近邻格点间纠缠则完全消失;同时引进非匀强磁场Bi=(-1)iB还可以使近邻格点纠缠的临界温度Tcn增大,且Tcn随B的增大而升高,这意味着我们可以通过调节B的大小而在任意温度下得到纠缠.     

The Heisenberg Model of the He Atom Revisited

The present work is devoted to a study of the Heisenberg model of the He atom. We consider the subset of the singlet states, in which one of the electron is kept on its 1s orbital. This spectrum is treated as a pseudo two-body problem. Use is made of a method designed to solve the inverse problem from bound states to determine the local equivalent potential seen by the second electron. The problem is simplified by the use of parametric expressions instead of a full numerical determination of the local equivalent potential. It keeps the numerical effort to a reasonable level. By construction, the local equivalent potential should fit the experimental eigenvalues, which is well achieved with the proposed simplified expressions. It shows the validity of the Heisenberg model for the excited states. It yields also a value for the mean square radius of the He atom. This one is in good qualitative agreement with the value derived from large basis calculations of the He ground state.     

Many-body Green's function theory for thin ferromagnetic anisotropic Heisenberg films: treatment of the exchange anisotropy

The many-body Green's function theory developed in our previous work for treating the reorientation of the magnetization of thin ferromagnetic films is extended to include the exchange anisotropy. This leads to additional momentum dependencies which require some non-trivial changes in the formalism. The theory is developed for arbitrary spin values S and for multilayers. The effects of the exchange anisotropy and the single-ion anisotropy, which was treated in our earlier work, on the magnetic properties of thin ferromagnetic films are compared. Received 31 October 2002 Published online 7 May 2003     

Dynamical Behavior of the Quant um Periodically Kicked Harmonic Oscillator

We explore the properties of the quantum kicked harmonic osciUation governed by the Hamiltonian H=1/2p²+1/2ω₀²x²-K cos x∑_n=-∞^∞δ(t/T - n): The classical version of this model is known to exhibit certain type of stochastic behavior. We reduce the quantum equation of the model td quantum mapping equations. Numerical results of the mappings show that the behavior of the average energy as a function of time depends on the ration of the frequency of the external (2π/T) and that of the unperturbed system wo. The energy increases first very rapidly and then the energy growth saturates for irrational ω₀T/2π. The break time is independent of the strength of the external force, but is roughly proportional to 1/ω₀T.For a fixed rational ω₀T/2πt,h e energy is damped oscillation for smaller T , a nd it is seemingly recurrent with time in the sense of Hogg and Huberman. In both cases, these behaviors of energy are independent of the strength of the external force and differ from the behavior of the quantum kicked rotator.     

Asymptotics of the Mean-Field Heisenberg Model

We consider the mean-field classical Heisenberg model and obtain detailed information about the total spin of the system by studying the model on a complete graph and sending the number of vertices to infinity. In particular, we obtain Cramér- and Sanov-type large deviations principles for the total spin and the empirical spin distribution and demonstrate a second-order phase transition in the Gibbs measures. We also study the asymptotics of the total spin throughout the phase transition using Stein’s method, proving central limit theorems in the sub- and supercritical phases and a nonnormal limit theorem at the critical temperature.     

The Heisenberg Model after an Interaction Quench

In accordance with the recent experimental progress of the controllable spin-spin interactions, the Heisenberg model after an interaction quench is discussed. The Hamiltonian of the system out of equilibrium is introduced and treated by the flow equation method. As a result, the spectrum and zero-point spin deviation are obtained with the help of time-evolved operators. Additionally, other methods are applied to verify the results in mathematics. It is found that the observables show an oscillating behavior. The feasible experimental scheme of the concerned scenario is also mentioned.