Tensor coupling effect on relativistic symmetries

The similarity renormalization group is used to transform the Dirac Hamiltonian with tensor coupling into a diagonal form. The upper(lower) diagonal element becomes a Schr¨odinger-like operator with the tensor component separated from the original Hamiltonian.Based on the operator, the tensor effect of the relativistic symmetries is explored with a focus on the single-particle energy contributed by the tensor coupling. The results show that the tensor coupling destroying(improving) the spin(pseudospin) symmetry is mainly attributed to the coupling of the spin-orbit and the tensor term, which plays an opposite role in the single-particle energy for the(pseudo-) spin-aligned and spin-unaligned states and has an important influence on the shell structure and its evolution.     

Detecting some three-qubit MUB diagonal entangled states via nonlinear optimal entanglement witnesses

The three qubits mutually unbiased bases (MUB) diagonal density matrices with maximally entanglement in Greenberger-Horne-Zeilinger (GHZ) basis are studied. These are a natural generalization of Bell-state diagonal density matrices. The linearity of positive partial transpose (PPT) conditions allows one to specify completely PPT states or feasible region (FR) which form a polygon, where the projection of the feasible region to some two dimensional planes has lead to better visualization. To reveal the PPT entangled regions of these density matrices, we manipulate some appropriate optimal non-decomposable linear entanglement witnesses (EWs) as the envelope of family of linear optimal non-decomposable EWs. These nonlinear EWs are nonlinear functional of MUB diagonal states, so that they are nonnegative valued over all separable, but they are negative valued over some PPT entangled MUB diagonal states. Even though, these nonlinear EWs can not separate completely, the PPT entanglement region from separable one, but however in special cases they lead to necessary and sufficient condition for separability. To support the evidence, we study three categories for special choices of parameters in density matrices, and using the nonlinear EWs we can distinguish the region of PPT entangled states and separable states, completely. At the end some numerical simulations are provided to show the practical applicability of these nonlinear EWs in detecting some PPT entangled MUB diagonal states.     

Majorana's stellar representation for the quantum geometric tensor of symmetric states

Majorana's stellar representation provides an intuitive picture in which quantum states in high-dimensional Hilbert space can be observed using the trajectory of Majorana stars. We consider the Majorana's stellar representation of the quantum geometric tensor for a spin state up to spin-3/2. The real and imaginary parts of the quantum geometric tensor, corresponding to the quantum metric tensor and Berry curvature, are therefore obtained in terms of the Majorana stars. Moreover, we work out the expressions of quantum geometric tensor for arbitrary spin in some important cases. Our results will benefit the comprehension of the quantum geometric tensor and provide interesting relations between the quantum geometric tensor and Majorana's stars.     

Indirect optical cooperative excitation of two-particle electronic excitations in doped organic molecular crystals

A theory on the indirect optical cooperative excitation of a two-particle electronic excitation composed of one host exciton and one guest-molecule one-particle electronic excitation through one electric dipole-moment active singlet guest molecule one-particle electronic excitation is developed by considering the nonradiative coupling bstween one- and two-particle electronic excitations.The complex dielectric tensor and the corresponding absorption coefficient are found out, which are expressed in terms of the Fourier-transform of the retarded Green function: The derived formulas are discussed in an explicit form for the one-dimensional model of the doped organic molecular crystal. Within the framework of ths one-dimensional model also the conditions for the existence of the host exciton-guest molecule one-particle electronic excitation bound states are established and discussed.     

Decay of correlations in spin systems

We investigate the decay of initial correlations in a spin system where each spin relaxes independently by an intramolecular mechanism. The equation of motion for the spin density matrix is assumed to be the Redfield equation, which is of the form of a quantum mechanical master equation. Our analysis of this problem is based on the techniques of Shuler, Oppenheim, and coworkers, who have studied the decay of correlations in systems which can be described by classical stochastic master equations. We find that the off-diagonal elements of the reduced spin density matrices approach their equilibrium values faster than the diagonal elements. The Ursell functions, which are a measure of the correlations in the system, decay to their zero equilibrium values faster than the spin density matrix except for the furthest off-diagonal elements. Far off-diagonal matrix elements of the spin density matrix approach equilibrium at the same rate as the Ursell functions, which is the important difference between the quantum mechanical model studied here and the classical models studied earlier.Supported in part by the National Science Foundation.     

Alternative approaches to the construction of the Poincare-invariant spin operators of the Dirac particles

At present a number of methods of constructing the Poincare-invariant spin operators for relativistic particles with half-integer spin in the one-particle theory are well known. The method of odd operator constructing, the Lorentz method of bilinear covariant form transformation, and the method with the Foldy–Wouthuysen representation belong to them. New approaches to the construction of spin operators are developed in the present work, namely, a method of separating space-like component directly from the spin matrices of bilinear covariant forms, including the method of multiplication of the covariant Hamiltonian of the Dirac equation by these matrices. By this means we succeeded in constructing the Poincare-invariant spin operators by simpler and mathematically faultless methods. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 10–15, November, 2008.     

Bargmann–Wigner方程与高自旋场方程

在坐标表象中由Bargmann-Wigner方程导出了便于求解的高自旋场方程,并给出了相应的拉氏函数.     

基于张量网络算法的自旋梯子系统的弦序参量的研究

通过基于矩阵乘积态(MPS)的强关联电子量子自旋梯子格点系统的张量网络(TN)算法,摸索研究自旋梯子量子多体系统的弦序参量,探测系统的量子相变点,刻画系统的量子临界现象,获取系统的量子相图,这为我们提供了一个研究自旋梯子系统的量子多体物理性质强有力的工具和方法:在不知道系统是否缺乏Landau对称性破缺序或者系统是否存在相关的拓扑弦序的情况下,可以先得到系统的基态波函数,如果基态缺乏Landau对称性破缺序,或可以通过其它方式找出系统存在若干非局域的弦序参量,来完整地描述一些拓扑量子相变点,获得系统的量子相图,从而丰富和发展了传统的Landau对称性破缺的相变理论.     

有限温度张量重正化群方法及其在阻挫量子磁性研究中的应用

阻挫量子磁体中的新奇物态与效应是凝聚态物理研究的重要前沿方向,因其与高温超导、拓扑量子计算等的密切联系,近年来吸引了人们浓厚的研究兴趣。实验上,阻挫自旋液体候选材料的 新进展层出不穷,人们系统地研究了若干三角晶格、笼目晶格和六角Kitaev 阻挫磁体等材料,发 现其在一定条件下展现出自旋液体态的特征,但澄清其中的量子物态是充满挑战的量子多体问题。 作者最近的工作指出,可以从有限温度张量重正化群多体计算入手,开展热力学性质的精确计算 与分析,确定阻挫磁体的微观自旋模型,做出进一步理论预言并开展实验验证,从而建立量子磁性 系统的多体计算精确研究方案。有限温度张量重正化群方法是计算大尺寸二维阻挫量子自旋模型 有限温度性质的有力工具,在本文中作者首先介绍新近发展的系列张量重正化群方法,包括线性 和指数张量重正化群等。随后,作者讨论有限温度张量方法在三角晶格量子伊辛磁体TmMgGaO4 和六角晶格Kitaev 磁体α-RuCl3 的微观自旋模型中的具体应用：通过高精度和全面的多体计算, 揭示出其中存在演生U(1) 对称性与拓扑相变,以及高场量子自旋液体态等新颖的结论,这些理 论预言也陆续被实验所证实。通过上述实例,作者展示了有限温度张量重正化群计算方法在自旋 液体候选材料研究中的应用价值,并期待这些方法能在强关联量子物质研究中发挥重要作用。     

Analytically Computable Symmetric Quantum Correlations

One of the greatest challenges in developing the resource theory of a quantum feature is to establish an analytically computable quantifier, which directly limits the practicability of such quantifiers. Here, analytic quantifiers of both the symmetric quantum discord (SQD) and the symmetric measurement‐induced nonlocality (SMIN) in a bipartite system of qubits are studied on the basis of the quantum skew information. It is shown that the SMIN of any two‐qubit system and the SQD of bipartite “X”‐type states and block‐diagonal states can be analytically determined. In addition, the SQD and the SMIN are invariant with an attached quantum state. The validity of our analytical expressions is further illustrated numerically on the basis of several randomly generated density matrices.     

Para-Grassmann Star Product Calculation

In this Letter, we construct the star product for polynomials over the para-Grassmann variable and we present as an example a para-Grassmann version of the model of q–quantum mechanics. Moreover, using the structural relations of the q–deformed algebra generated by annihilation and creation operators, we decompose the Jacobi matrix in the product of three matrices: the diagonal matrix, the upper and lower diagonal matrices, mutually adjoint.     

一般WGHZ态和它的退纠缠与概率隐形传态

给出了一般纠缠的WGHZ态，然后利用所得一般WGHZ态导出了一般纠缠的不同的W态，得到了不同退纠缠的条件，一般WGHZ态取不同的复系数为零时，有不同的退纠缠，并可得到不同的W态和不同的一般的Bell基，以上对退纠缠的讨论结果与通常用密度矩阵的可分性得的退纠缠条件一致.通过构造一个5×5 对角投影变换矩阵,解决了使用一般纠缠量子信道并不再引入辅助态时，态畸变的恢复问题，并且这里的对角投影变换矩阵U_M也与以往文献的不同，而且还更直接，进而解决了不引入辅助态并使用一般纠缠信道纠缠的一般WGHZ态的概率隐形传态的问题,本文关于对角的投影变换矩阵U_M的变换方法等可以直接推广到任意一般纠缠信道的一般纠缠态的概率隐形传态. 关键词： 隐形传态 纠缠 W态 量子信道     

CO-ORDINATE TRANSFORMATIONS FOR SECOND ORDER SYSTEMS. PART II: ELEMENTARY STRUCTURE-PRESERVING TRANSFORMATIONS

It has been shown in a previous paper that there is a real-valued transformation from the generalN -degree-of-freedom second order system to a second order system characterized by diagonal matrices. An immediate extension of this fact is that for any second order system, there is a set of real-valued transformations (thestructure-preserving transformations) which transform this system to a different second order system having identical characteristic behaviour. There are several possible reasons why it may be very useful to achieve a particular structure in the transformed system. It is obvious that a diagonal structure is extremely useful and a method has been devised for determining the diagonalizing transformation from the solution of the usual (complex) eigenvalue-eigenvector problem.This paper begins by outlining the usefulness of some other structures. Then it defines a class of elementary structure-preserving co-ordinate transformations that transform from one N -degree-of-freedom second order system to another. The termelementary is applied because any one of these transformations is the minimum-rank modification of the identity transformation. The changes occurring in the system matrices as a result of the application of one such elementary transformation transpire to be very simple in form, they are low rank, and they can be computed very efficiently.This paper provides the fundamental tools to enable the design of structure-preserving co-ordinate transformations which transform a second order system originally characterized by three general matrices in stages into a mathematically similar second order system characterized by three diagonal matrices. The procedure by which the individual elementary transformations are obtained is still under development and it is not discussed in this paper. However, an illustration is given of a five-degree-of-freedom self-adjoint system being transformed into tridiagonal form.     

Quantum logical operations for spin 3/2 quadrupolar nuclei monitored by quantum state tomography

This article presents the realization of many self-reversible quantum logic gates using two-qubit quadrupolar spin 3/2 systems. Such operations are theoretically described using propagation matrices for the RF pulses that include the effect of the quadrupolar evolution during the pulses. Experimental demonstrations are performed using a generalized form of the recently developed method for quantum state tomography in spin 3/2 systems. By doing so, the possibility of controlling relative phases of superimposed pseudo-pure states is demonstrated. In addition, many aspects of the effect of the quadrupolar evolution, occurring during the RF pulses, on the quantum operations performance are discussed. Most of the procedures presented can be easily adapted to describe selective pulses of higher spin systems (>3/2) and for spin 1/2 under J couplings.     

Relativistic quantum field theory with fractional spin and statistics

We construct a relativistic quantum field theory in 2 + 1 dimensions whose Fock states provide a multivalued representation of the Poincaré group. We add a topological term to the action of a scalar field theory and we show that this endows the path integral of the theory with an operator-valued cocycle which modifies the transformation properties of physical states. We demonstrate that one-particle states carry (in general) fractional spin. We determine the spin of many-particle states and we prove a generalized spin-statistics relation. We propose an equation of motion for on-shell states which generalizes naturally the Dirac equation.     

The thermodynamic one-particle Green function in the renormalized spin wave approximation for isotropic cubic ferromagnets

The thermodynamic one-particle Green function in the renormalized spin wave approximation for isotropic cubic ferromagnetic insulators with Dyson's spin wave theory as a base is derived. In quantitative respect, dynamic and kinematic effects of spin waves are approximated by the graphs deficient in the energy denominators, wherefore at low temperature kinematic interaction turns out to be too strong. As against the one-particle Green function for independent spin waves, dynamic interaction of ferromagnons is shown to effect the renormalization of the spin wave energy, whereas kinematic interaction directly modifies the average ferromagnon population numbers. In the matter of magnetization, its formula based on the Green function assumes a similar form as in the spin wave theory without interactions on the understanding that it remains valid within the entire range of temperatures from absolute zero up to the critical point.     

Relativistic symmetry of position-dependent mass particle in Coulomb field including tensor interaction

The spatially-dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials including a tensor interaction under the spin and pseudospin symmetric limit. Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number κ. Some numerical results are given too. The effect of the tensor interaction on the bound states is presented. It is shown that the tensor interaction removes the degeneracy between two states in the spin doublets. We also investigate the effects of the spatially-dependent mass on the bound states under the conditions of the spin symmetric limit in the absence of tensor interaction.     

Nonrelativistic Quantum Mechanics with Spin in the Framework of a Classical Subquantum Kinetics

Recently it has been shown that the spinless one-particle quantum mechanics can be obtained in the framework of entirely classical subquantum kinetics. In the present paper we argue that, within the same scheme and without any extra assumption, it is possible to obtain both the nonrelativistic quantum mechanics with spin, in the presence of an arbitrary external electromagnetic field, as well as the nonlinear quantum mechanics.     

Specific features of the formation of phase states in a non-Heisenberg magnet with S = 2

Spin states of a non-Heisenberg magnet with a magnetic ion spin of 2 have been determined. It has been shown that the inclusion of the higher-order spin invariants leads to realization of specific phases with the tensor order parameters whose realization is impossible in magnets with S = 1. The free energy of the system in different spin states has been studied. The geometric images of the tensor phases in the spin space have been determined.     

Curvy steps for density matrix based energy minimization: tensor formulation and toy applications

A unitary transformation-based framework is explained for varying the one-particle density matrix in a non-orthogonal expansion basis while preserving both the idempotency and electron number constraints. The equations are presented in a compact tensor formulation that permits the use of any representation for the matrices. A connection with the LNV method is established. Curvy steps, which are high order line searches along a chosen descent direction, are defined. Calculations with two toy model systems are presented to illustrate the nature of the displacements in this approach.