海森堡J1-J2自旋链的量子关联与量子纠缠

文章计算了海森堡J1-J2自旋链的任意两格点间的量子失谐与相对熵纠缠,不仅给出了量子失谐、相对熵纠缠与两格点自旋关联函数的解析关系,而且给出了精确对角化的数值结果.解析结果指出了两格点的量子失谐与纠缠非零的条件,并为用两格点的量子失谐与纠缠探测该模型的相变点提供了理论依据.数值结果表明,在该模型中,量子失谐比纠缠具有较长程的关联,近邻和远距离两格点间的量子失谐在基态时能标度一级相变点J2/J1 =0.5,在第一激发态时,除了能标度相变点J2/J1=0.5外,还能标度无穷级相变点J2/J1 =0.241 1;而纠缠仅存在最近邻与次近邻两格点间,且只有最近邻两格点的纠缠能标度相变点.     

次近邻相互作用对Heisenberg XX链纠缠影响的研究

研究了存在次近邻相互作用(耦合)时Heisenberg XX链的纠缠特性. 结果表明对近邻格点, 随着耦合常数J的变化, 次近邻相互作用的存在可能使其纠缠度增大或者减小; 而对次近邻格点, 引进次近邻相互作用却可以产生纠缠, 并且使其随着|J|的增大而增大. 近邻格点间纠缠存在的临界温度T_c随着J的增大而降低, 次近邻格点间纠缠存在的临界温度T_c随着|J|的增大而升高. 此外对纠缠W态的制备, 次近邻相互作用的存在还使得三量子位情形时W态产生的时刻改变, 而对于四量子位情形却没有影响.     

多体关联Green函数动力学Ⅰ多体关联Green函数的运动方程

从多体系统的哈密顿量及海森堡方程出发,通过引进非线性变换,完成了体系的多体Green函数的关联分离,并建立起非相对论性的多体关联Green函数的动力学方程组.这个方程组为描述多体系统提供了一种完整的、系统的非微扰计算方法.     

含复杂近邻的二维正方格子键渗流的蒙特卡罗模拟

基于高效的单团簇生长算法,采用蒙特卡罗方法模拟了考虑最近邻、次近邻,直至第五近邻格点的二维正方格子的键渗流.计算得到了二十余种格点模型高精度的键渗流阈值,并深入探讨了渗流阈值p_c与格点结构之间的关联.通过引入参数ξ=∑_i z_ir2~2/i(其中z_i和r_i分别为第i近邻格点的配位数及到中心格点的距离)来消除“简并”,研究发现p_c随ξ的变化较好地满足幂律关系p_c∝ξ^-γ,数值拟合得γ≈1.     

多体关联动力学中的自洽平均场

本文仔细地讨论了量子多体关联动力学中的广义自洽平均场,证明无论动态还是定态自洽平均场都是存在的。多体关联通过两体关联c₂及其相应的碰撞项I进入平均场。I的作用是双重的:对单粒子运动量子态的动力学效应和对单粒子态填充数的影响。多体关联还在多体系统的能量表达式中表现出来,使得该表达式不同于通常的HF-Brueckner理论中的表达式。 关键词：     

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.     

多体关联Green函数动力学Ⅲ截断近似

从多体关联Green函数的基本动力学方程组出发,通过对多体关联Green函数作低阶截断近似,得到了通常Green函数理论中所有主要的非微扰结果.而且二体关联Green函数动力学把梯形图对应的短程关联与环形图对应的长程关联统一在同一个动力学方程组中,这是通常的Green函数理论所没有得到的新结果.     

镶嵌正方晶格上Ising模型的近似解

采用格点自旋消约方法,将具有最近邻和次近邻耦合作用的镶嵌正方Ising晶格变换成等效的具有最近邻、次近邻和四体耦合作用的正方Ising晶格,得到系统近似解的临界点在K′C=0.4406868.结果表明:在相变点最近邻耦合作用K1和次近邻耦合作用K2之间满足一定关系.如果只计及镶嵌正方Ising晶格的最近邻耦合作用K1,则其严格解的临界点在K1C=0.7635.由此可以推断在正方格点间安放两个自旋的双镶嵌正方Ising晶格,在只计及最近邻耦合作用情况下,也是严格可解的.     

镶嵌正方晶格上具有次近邻耦合作用Ising模型的临界性质

采用部分格点自旋消约变换,将镶嵌正方晶格上具有最近邻耦合作用K1和次近邻耦合作用K2的Ising模型变换成等效的具有最近邻、次近邻和四体耦合作用的正方Ising晶格.发现系统的临界点在(K1C,K2C)=(0.5125,0.2134),由此决定系统的临界温度,幷讨论了系统的普适性.     

多体关联Green函数动力学——Ⅲ.截断近似

从多体关联Green函数的基本动力学方程组出发,通过对多体关联Green函数作低阶截断近似,得到了通常Green函数理论中所有主要的非微扰结果。而且二体关联Green函数动力学把梯形图对应的短程关联与环形图对应的长程关联统一在同一个动力学方程组中,这是通常的Green函数理论所没有得到的新结果。     

Iterated Fully Coordinated Percolation on a Square Lattice

We study, on a square lattice, an extension to fully coordinated percolation which we call iterated fully coordinated percolation. In fully coordinated percolation, sites become occupied if all four of its nearest neighbors are also occupied. Repeating this site selection process again yields the iterated fully coordinated percolation model. Our results show a large enhancement in the size of highly connected regions after each iteration (from ordinary to fully coordinated and then to iterated fully coordinated percolation); enhancements that are much larger than an extension of correlations by an extra lattice constant might suggest. We also study the universality among the three problems by determining the corresponding static and dynamic critical exponents. Specifically, a new method to directly calculate the walk dimension, d _w , using finite size scaling applied to normal mode analysis is used. This method is applicable to any geometry and requires significantly less computation than previously known calculations to determine d _w .     

Extremum of the percolation cluster surface

The internal and external surfaces of a percolation cluster, as well as the total surface of the entire percolation system, are investigated numerically and analytically. Numerical simulation is carried out using the Monte Carlo method for problems of percolation over lattice sites and bonds on square and simple cubic lattices. Analytic expressions derived by using the probabilistic approach describe the behavior of such surfaces to a high degree of accuracy. It is shown that both the external and total surface areas of a percolation cluster, as well as the total area of the surface of the entire percolation system, have a peak for a certain (different in the general case) fraction of occupied sites (in the site problem) or bonds (in the bond problem). Two examples of technological processes (current generation in a fuel cell and self-propagating high-temperature synthesis in heterogeneous condensed systems) in which the surface of a percolation cluster plays a significant role are discussed.     

Bootstrap percolation in a polluted environment

Let a low densityp of sites on the lattice Z² be occupied, remove a proportionq of them, and call the remaining sites empty. Then update this configuration in discrete time by iteration of the following synchronous rule: an empty site becomes occupied by contact with at least two occupied nearest neighbors, while occupied and removed sites nerver change their states. Ifq/p ² is large most sites remain unoccupied forever, while ifq/p ² is small, this dynamics eventually makes most sites occupied. This demonstrates how sensitive the usual bootstrap percolation rule (theq=0 case) is to the pollution of space.     

Percolation with nearest neighbour interaction

A Monte Carlo technique is used to investigate site percolation in a three dimensional lattice in which the presence of occupied sites influences the selection of the next site for occupation. Results are given for a simple cubic geometry.     

感染生长模型的逾渗模拟

在规则格子点阵中，活跃点逐步动态地以可变概率感染附近空缺点而生成系综.利用感染概率替代系综温度，给粒子划分能级，可以用巨正则系综配分函数表征体系.蒙特卡洛方法模拟验证了该体系在逾渗阈值处的相变行为.提出了一种新的较为普适的估算规则点阵逾渗阈值的方法.对介质基底上金属薄膜的实验研究验证了该感染生长模型的合理性.由此给出了格子点阵的固有属性(逾渗)如何在粒子聚集成团簇这一动态过程中体现出来的物理模型. 关键词： 逾渗 系综 蒙特卡洛方法 生长模型     

Percolation clusters above criticality form Kardar-Parisi-Zhang surfaces

This study is concerned with the characteristics of regular (isotropic) percolation clusters above the critical threshold p{c}. Analytic arguments for the general dimension case, and numerical results for the two-dimensional case, lead to the conclusion that the characteristics of the shortest paths (defined as the chemical distance l) between given two sites on a percolation cluster are similar to the characteristics of optimal paths in the directed polymer model. A corollary which should be valid for the general dimension case, and verified by numerical results for the two-dimensional case, is that a cluster whose sites are at chemical distance l from a given site forms a Kardar-Parisi-Zhang surface.     

High-density percolation: Exact solution on a Bethe lattice

A new percolation problem is posed where the sites on a lattice are randomly occupied but where only those occupied sites with at least a given numberm of occupied neighbors are included in the clusters. This problem, which has applications in magnetic and other systems, is solved exactly on a Bethe lattice. The classical percolation critical exponents=gg=1 are found. The percolation thresholds vary between the ordinary percolation thresholdp _c (m=1)=l/(z – 1) andp _c(m=z) =[l/(z – 1)]¹/(z–1). The cluster size distribution asymptotically decays exponentially withn, for largen, p p _c .Supported in part by National Science Foundation grant DMR78-10813.     

On the universality of geometrical and transport exponents of rigidity percolation

We develop a three-parameter position-space renormalization group method and investigate the universality of geometrical and transport exponents of rigidity (vector) percolation in two dimensions. To do this, we study site-bond percolation in which sites and bonds are randomly and independently occupied with probabilitiess andb, respectively. The global flow diagram of the renormalization transformation is obtained which shows that thegeometrical exponents of the rigid clusters in both site and bond percolation belong to the same universality class, and possibly that of random (scalar) percolation. However, if we use the same renormalization transformation to calculate the critical exponents of the elastic moduli of the system in bond and site percolation, we find them to be very different (although the corresponding values of the correlation length exponent are the same). This indicates that the critical exponent of the elastic moduli of rigidity percolation may not be universal, which is consistent with some of the recent numerical simulations.     

Probing nearest-neighbor correlations of ultracold fermions in an optical lattice

We demonstrate a probe for nearest-neighbor correlations of fermionic quantum gases in optical lattices. It gives access to spin and density configurations of adjacent sites and relies on creating additional doubly occupied sites by perturbative lattice modulation. The measured correlations for different lattice temperatures are in good agreement with an ab initio calculation without any fitting parameters. This probe opens new prospects for studying the approach to magnetically ordered phases.     

Percolation in Media with Columnar Disorder

We study a generalization of site percolation on a simple cubic lattice, where not only single sites are removed randomly, but also entire parallel columns of sites. We show that typical clusters near the percolation transition are very anisotropic, with different scaling exponents for the sizes parallel and perpendicular to the columns. Below the critical point there is a Griffiths phase where cluster size distributions and spanning probabilities in the direction parallel to the columns have power-law tails with continuously varying non-universal powers. This region is very similar to the Griffiths phase in subcritical directed percolation with frozen disorder in the preferred direction, and the proof follows essentially the same arguments as in that case. But in contrast to directed percolation in disordered media, the number of active (“growth”) sites in a growing cluster at criticality shows a power law, while the probability of a cluster to continue to grow shows logarithmic behavior.