电荷转移型Hubbard模型的相图

用玻色化技术和高斯波泛函变分理论研究了电荷转移型Hubbard模型.通过自旋密度波和电荷密度波的位相结构的变化，并结合其相应能隙的变化，得到以下结论：系统的Ising相变与Mott相变不重合，中间有一个SDI(spontaneouslydimerizedinsulating)的过渡相.在BI(band-insulator)相，自旋密度波与电荷密度波都具有能隙，而在MI(Mott-insulator)相，电荷密度波具有能隙，自旋密度波没有能隙. 关键词： Hubbard模型 电荷密度波 自旋密度波 相图     

一维扩展t-J模型中密度-自旋相互作用诱导的相分离

t-J模型是研究高温超导电性的重要理论模型之一. 最近的冷分子实验表明可用极性分子模拟t-J模型. 实验模拟的t-J模型除了引进长程的偶极相互作用外, 还引进了密度-自旋相互作用. 本文使用密度矩阵重整化群方法研究了密度-自旋相互作用对一维t-J 模型基态性质的影响. 选取了t-J模型基态相图中不同相区的三个点, 计算了不同密度-自旋相互作用强度下的粒子数和自旋的实空间分布,以及密度-密度关联函数和自旋-自旋关联函数与相应的结构因子. 计算结果表明, 密度-自旋相互作用强度较弱时, 对系统的性质不会产生定性影响;当其强度足够大时, 系统会进入相分离, 该相分离与传统t-J模型的相分离有很大区别.     

光学腔中一维玻色-哈伯德模型的奇异超固相

利用密度矩阵重整化群计算了光学腔中一维无自旋玻色-哈伯德模型的基态.通过研究超流序、局域密度分布、二阶和三阶关联函数,发现该系统出现了超越平均场理论的两个奇异超固相.这两个超固相同时具备对角和非对角长程序,其中一个展现出包络形式的密度调制振荡,另一个展现出均匀的密度分布.另外,结合光场的超辐射序参量和腔内的平均光子数,...     

应用约化密度保真度确定自旋为1的一维量子Blume—Capel模型的基态相图

约化密度保真度（reducedensityfidelity）可以用来描述量子多体系统的量子相变,其是两个约化密度矩阵距离的度量．本文应用MERA（multi—scaleentanglementreorganizationansatz）算法,模拟自旋为1的一维量子Blume-Capel模型,并通过对约化密度保真度的计算,确定出其基态相图．单点和两点约化密度矩阵所包含的至关重要的信息的量是不同的,其会体现在约化密度保真度上．另外,本文还从局域序参量和系统能隙的角度,来探讨量子多体系统的相变．     

二维半充满Hubbard模型有限温度下绝缘体──金属相变的研究

二维半充满条件下的Ｈｕｂｂａｒｄ模型，在有限温度下，是否经历一绝缘体—金属相变？在现有的文献中，这一直是一个有争议而又重要的问题。本文采用巨正则量子Ｍｏｎｔｅ Ｃａｒｌｏ方法，计算了二维半充满条件下Ｈｕｂｂａｒｄ模型的比热和电导率。对不同的库仑排斥势Ｕ（２ｔ－８ｔ），比热曲线在高温区出现一个峰，同时电导率在相应温区呈现一突然上升。因此，计算结果支持存在这样一个相变。 关键词：     

带有三体相互作用的S=1自旋链中的保真率和纠缠熵

研究了带有次近邻和三体相互作用的S=1自旋链的保真率和纠缠熵.通过密度矩阵重整化群数值方法计算了三体相互作用对保真率的影响,并分析了其与量子相变的关系.研究表明保真率可以探测Haldane相与二聚物相之间的相变.此外还研究了该相变与量子纠缠熵的关系.通过保真率和量子纠缠熵这两个信息观测量得到的结果和弦序参量得到的结果一致.在此基础之上给出了相图.     

双轨道Hubbard模型的动力学平均场理论研究

基于以Lanczos方法为杂质求解器的动力学平均场理论,研究了非局域轨道间跃迁对于双轨道强关联体系中轨道选择Mott相变的影响.计算了轨道间跃迁系数不同的双轨道Hubbard模型的准粒子权重和态密度,并构建了它们在相互作用强度U和轨道带宽比t₂/t₁影响下的相图.通过正则变换引入两个有效的退耦和轨道,在一定条件下轨道间跃迁会有利于轨道选择Mott相变的发生.还比较了Bethe晶格和正方晶格的相图,虽然基于两种不同晶格能带结构得到的轨道选择Mott相变的相变点存在一定的差异,但其中关于轨道选择Mott相变的基本物理图像具有一致性.并将方法拓展到半满的Ba₂CuO_4–δ材料的研究中,与根据密度泛函理论得到的能带对比,我们发现各向同性的轨道间跃迁对能带结构影响较大,进一步采用动量空间各向异性的非局域轨道间跃迁项,得到了材料的相图,在半满条件下Ba₂CuO_4–δ应为轨道选择Mott材料.     

Hubbard模型中的相位弦效应与交互Chern-Simons理论

费米子符号在费米液体理论中至关重要. 然而, 在Mott绝缘体中, 很强的电子Coulomb相互作用抑制了体系的电荷涨落并消除了电子交换带来的费米子符号问题. 本文首先回顾二分晶格上Hubbard模型的相位弦理论, 从弱关联的费米液体到强关联的反铁磁Mott绝缘体的转变可以由此得到统一理解. 在任意Coulomb作用强度U下, 我们首先导出Hubbard模型的严格的符号结构. 在小U极限下, 它回到通常的费米子符号; 在大U极限下, 它给出了t-J模型的相位弦符号. 在半满情形下, 我们构造了一种电子分数化的表象, 其中, 电荷子与自旋子通过演生的交互Chern-Simons规范场相互耦合. 由此导出的基态波函数拟设与低能有效理论可以定性刻画Hubbard模型的基态相图. 在弱关联区域, 费米液体的准粒子由电荷子与自旋子的束缚态构成, 其长程相位相干性取决于背景自旋的关联性质. 体系的Mott转变可以通过电荷子打开能隙或是通过自旋子玻色凝聚来实现.     

有限温度下一维Hubbard模型的化学势泛函理论研究

通过数值方法求解了有限温度下一维均匀Hubbard模型的热力学Bethe-ansatz方程组,得到了在给定温度和相互作用强度情况下,比热c、磁化率χ和压缩比κ随化学势μ的变化图像.基于有限温度下一维均匀Hubbard模型的精确解,利用化学势(μ)-泛函理论研究了一维谐振势下的非均匀Hubbard模型,给出了金属态和Mott绝缘态下不同温度情况时局域粒子密度n_i和局域压缩比_κi随格点的变化情况.     

周期性Hubbard模型密度矩阵函数的研究

在晶格密度泛函理论(LDFT)的框架内研究了哈巴德(Hubbard)模型,当考虑晶格内位置的单粒子密度矩阵γij、自旋S时,这个模型的相互作用能w[γij,S]为密度矩阵γij、总自旋S的函数.且当所有最近邻的γij=γ12时,对环状系统的w[γij,S]可获得精确的数值计算结果;文中同时还讨论了w[γij,S]函数在弱电子关联(γ102)和强电子关联(γi∞j)以及在γ1∞2<γ12<γ012区域限制下的性质.以非关联能w0[γ0ij,S]为单位标度的w[γij,S]表明的赝普适行为与g12=(γ12-γ1∞2)/(γ012-γ1∞2)函数一样.另外,w[γij,S]函数对不同总自旋S有一定的依赖.     

Phase diagram of the one-dimensional half-filled extended Hubbard model

We determine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site (nearest-neighbor) repulsive interaction U (V) and nearest-neighbor hopping t using the density-matrix renormalization group technique. Based on the results of the excitation gaps, Luttinger-liquid exponents, and bond-order-wave (BOW) order parameter, we confirm that the BOW phase appears in a substantial region between the charge-density-wave (CDW) and spin-density-wave phases. Each phase boundary is determined by multiple means and it allows us to make a cross-check on the validity of our estimations. We also find that the BOW-CDW transition changes from continuous to first order at the tricritical point (U(t),V(t)) approximately (5.89 t,3.10 t) and the BOW phase shrinks to zero at the critical end point (U(c),V(c)) approximately (9.25 t,4.76 t).     

Phase diagram of the one-dimensional extended Hubbard model at half filling

We reexamine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site and nearest-neighbor repulsive interactions. We calculate second-order corrections to coupling constants in the weak-coupling renormalization-group approach ( g-ology) to show that the bond-charge-density-wave (BCDW) phase exists for weak couplings in between the charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons destabilizes the BCDW state and gives rise to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line.     

The Renormalization Group Treatment of the Hubbard Model

The article presents the renormalization group treatment to the Hubbard model. To begin with, the bosonization of Hubbard model Hamiltonian is performed. We have obtained the sine-Gordon Hamiltonian. We have further approximated this Hamiltonian by the Hamiltonian of ⁴-theory. Then we utilized Wilson's results of the renormalization group method and obtained the recursion formula for the Hubbard model. Having solved these formulas we have obtained the critical indices for the Hubbard model.     

Magnetism in the single-band Hubbard model

A self-consistent spectral density approach (SDA) is applied to the Hubbard model to investigate the possibility of spontaneous ferro- and antiferromagnetism. The starting point is a two-pole ansatz for the single-electron spectral density, the free parameter of which can be interpreted as energies and spectral weights of respective quasiparticle excitations. They are determined by fitting exactly calculated spectral moments. The resulting self-energy consists of a local and a non-local part. The higher correlation functions entering the spin-dependent local part can be expressed as functionals of the single-electron spectral density. Under certain conditions for the decisive model parameters (Coulomb interaction U, Bloch bandwidth W, band occupation n, temperature T) the local part of the self-energy gives rise to a spin-dependent band shift, thus allowing for spontaneous band magnetism. As a function of temperature, second-order phase transitions are found away from half-filling, but close to half-filling, the system exhibits a tendency towards first-order transitions. The non-local self-energy part is determined by use of proper two-particle spectral densities. Its main influence concerns a (possibly spin-dependent) narrowing of the quasiparticle bands with the tendency to stabilize magnetic solutions. The non-local self-energy part disappears in the limit of infinite dimensions. We present a full evaluation of the Hubbard model in terms of quasiparticle densities of states, quasiparticle dispersions, magnetic phase diagram, critical temperatures (T_c, T_N) as well as spin and particle correlation functions. Special attention is focused on the non-locality of the electronic self-energy, for which some rigorous limiting cases are worked out.     

Quantum coherence and ground-state phase transition in a four-chain Bose–Hubbard model

We study the quantum coherence and ground-state phase transition of a four-chain Bose–Hubbard model with the long-range interaction. In a special four-chain Bose–Hubbard model,i.e., each chain only has one optical potential, four types of the ground-state phases are discovered. The effects of the disorder, the on-site interaction and the long-range interaction on the quantum coherence are studied. For the system without the long-range interaction, the quantum coherence changes from one periodic oscillation to two periodic oscillations as the onsite interaction increases. By considering the long-range interaction, the quantum coherence goes back to one periodic oscillation again. The on-site interaction itself suppresses the quantum coherence, both the on-site interaction and long-range interaction together enhance the quantum coherence with the weak disorder. If the disorder strength is increased beyond a critical value,they start to suppress the quantum coherence. In a regular four-chain Bose–Hubbard model, i.e.,each chain has many optical potentials, the ground-state phase transitions are obtained by using the cluster Gutzwiller mean-field method. Exotic ground-state phases are found, i.e., superfluid phase, integer Mott insulator phase, supersolid phase and loophole insulator phase. The combination of the loophole insulator phase and the supersolid phase expands the lobes with the half-integer filling per site for the small ratio β = t_■/t_⊥.     

Phase diagram of the three-dimensional Hubbard model at half filling

We investigate the phase diagram of the three-dimensional Hubbard model at half filling using quantum Monte Carlo (QMC) simulations. The antiferromagnetic Néel temperature is determined from the specific heat maximum in combination with finite-size scaling of the magnetic structure factor. Our results interpolate smoothly between the asymptotic solutions for weak and strong coupling, respectively, in contrast to previous QMC simulations. The location of the metal-insulator transition in the paramagnetic phase above is determined using the electronic compressibility as criterion. Received 11 April 2000 and Revised in final form 29 June 2000     

Ground-state phase diagram of the dimerizedspin-1/2 two-leg ladder

Dimerized spin-1/2 ladders exhibit a variety of phase structures, which depend on the intra-chain and inter-chain spin exchange energies as well as on the dimerization pattern of the ladder. Using the density matrix renormalization group (DMRG) algorithm, we study critical properties of the bond-alternating two-leg Heisenberg spin ladder with diagonal interaction J_×. Two types of spin systems, staggered dimerized antiferromagnetic ladder and columnar dimerized ferro-antiferromagnetic couplings ladder, are investigated. To clarify the phase transition behaviors, we simultaneously analyze the string order parameter (SOP), the twisted order parameter (TOP), as well as a measurement of the quantum information analysis. Based on measuring this different observables, we establish the phase diagram accurately and give the fitting functions of the phase boundaries. In addition, the phase transition of cross-coupled spin ladder (in the absence of intrinsic dimerization) is also discussed.