Martin P. Gelfand

High-order convergent expansions for quantum many particle systems

We review recent advances in the calculations of high-order convergent expansions for quantum many-particle systems. Calculations for ground state properties, including correlation functions and static susceptibilities, for spin models as well as for models of many fermions, such as Hubbard and Kondo models, are discussed. A historical perspective to the subject is provided. Recently important technical advances have been made in perturbative calculations of the excitation spectra of quantum many-particle systems, which enable the calculation of these spectra to high orders. The method, along with its applications, are explained. Fairly comprehensive, though simplified, algorithms for generating lists of relevant clusters, their lattice embeddings and subclusters are presented. The perturbative recursion relations and their computer implementation are also discussed in detail. A compilation is made of various series expansion studies that have been carried out for condensed matter problems. The scope and limitations of these methods are explained, and several open problems are noted.

Convergent Expansions for Properties of the Heisenberg Model for CaV{sub {bold 4}} O{sub {bold 9}}

We have constructed high-order {ital T}=0 expansions for the elementary excitation spectra, and high-temperature expansions for the susceptibility, for the {ital S}=1/2 Heisenberg antiferromagnet believed to describe the spin-gap system CaV{sub 4}O{sub 9}. Existing susceptibility data are analyzed using these theoretical results. If nearest- and second-neighbor interactions are in the ratio 2:1, there should be clear indications in both neutron and Raman scattering. {copyright} {ital 1996 The American Physical Society.}

Series expansions for excited states of quantum lattice models

We show that by means of connected-graph expansions one can effectively generate exact high-order series expansions which are informative of low-lying excited states for quantum many-body systems defined on a lattice. In particular, the Fourier series coefficients of elementary excitation spectra are directly obtained. The numerical calculations involved are straightforward extensions of those which have already been used to calculate series expansions for ground-state correlations and T = 0 susceptibilities in a wide variety of models.

Spin-wave excitation spectra and spectral weights in square lattice antiferromagnets

Using a recently developed method for calculating series expansions of the excitation spectra of quantum lattice models, we obtain the spin-wave spectra for square lattice, S=1/2 Heisenberg-Ising antiferromagnets. The calculated spin-wave spectrum for the Heisenberg model is close to but noticeably different from a uniformly renormalized classical (large-S) spectrum with the renormalization for the spin-wave velocity of approximately 1.18. The relative weights of the single-magnon and multiple-magnon contributions to neutron-scattering spectra are obtained for wave vectors throughout the Brillouin zone.

Phase Transitions in Bilayer Heisenberg Model with General Couplings

The ground state properties and phase diagram of bilayer Heisenberg model on the square lattice are studied in a wide range of parameter space of intralayer exchange couplings, assuming an antiferromagnetic coupling between constituent layers. In the classical limit, the model exhibits three phases: two of these are ordered phases specified by the ordering wave vectors (π,π;π) and (0,0;π), where the third component of each indecates the antiferromagnetic orientation between layers, and another one is “canted” phase, stabilized by competing interactions. The effects of quantum fluctuations in the model with S =1/2 have been explored in terms of dimer mean-field theory, exact diagonalization of \(2\sqrt2\times2\sqrt2\times2\) clusters, and higher-order perturbation expansions about the interlayer dimer limit.

Phase transitions in the symmetric Kondo-lattice model in two and three dimensions

We present an application of high-order series expansion in the coupling constants for the ground-state properties of correlated lattice fermion systems. Expansions have been generated up to order ({ital t}/{ital J}){sup 14} for {ital d}=1 and ({ital t}/{ital J}){sup 8} for {ital d}=2,3 for certain properties of the symmetric Kondo-lattice model. Analyzing the susceptibility series, we find evidence for a continuous phase transition from the spin-liquid phase characteristic of a Kondo insulator to an antiferromagnetically ordered phase in dimensions {ital d}{ge}2 as the antiferromagnetic Kondo coupling is decreased. The critical point is estimated to be at ({ital t}/{ital J}){sub {ital c}}{approx}0.7 for a square lattice and ({ital t}/{ital J}){sub {ital c}}{approx}0.5 for a simple-cubic lattice.

Bond-Operator Mean Field Theory for the Bilayer Heisenberg Model

Bond-operator mean field equations for the square-lattice, S =1/2 bilayer Heisenberg model are developed and solved numerically. In the vicinity of both the zero-field critical point and the field-induced transitions, comparisons are made with T =0 and finite-temperature strong coupling expansions. The mean-field theory suggests that the quantum critical region for the field-induced transitions is restricted to significantly lower temperatures than one might have concluded based on strong-coupling expansions or other numerical studies.

Off-diagonal interactions, Hund's rules, and pair binding in C60.

We have studied the effect of including nearest-neighbor electron-electron interactions, in particular the off-diagonal (non-density-density) terms, on the spectra of truncated tetrahedral and icosahedral Hubbard molecules, focusing on the relevance of these systems to the physics of doped C[sub 60]. Our perturbation theoretic and exact diagonalization results agree with previous work in that the density-density term suppresses pair binding. However, we find that for the parameter values of interest for C[sub 60], the off-diagonal terms [ital enhance] pair binding, though not enough to offset the suppression due to the density-density term. We also find that the critical interaction strengths for the Hunds rules violating level crossings in C[sub 60][sup [minus]2], C[sub 60][sup [minus]3], and C[sub 60][sup [minus]4] are quite insensitive to the inclusion of these additional interactions.

Photon Antibunching in Small Clusters of CdSe/ZnS Core/Shell Quantum Dots.

Coincident photon histogram measurements of fluorescence antibunching via confocal microscopy correlated with atomic force microscopy were carried out on (i) individual CdSe/ZnS core/shell quantum dots (QDs), (ii) several well separated QDs, and (iii) clusters of QDs. Individual QDs and well separated QDs showed the expected degree of antibunching for a single emitter and several independent emitters, respectively. The degree of antibunching in small, compact clusters was more characteristic of a single emitter than multiple emitters. The antibunching in clusters provides strong evidence of nonradiative energy transfer between QDs in a cluster. A minimal phenomenological model of energy transfer gives reasonable quantitative agreement with the experimental results.

Correction to “Artifact-Free and Detection-Profile-Independent Higher-Order Fluorescence Correlation Spectroscopy for Microsecond-Resolved Kinetics. 2. Mixtures and Reactions”

Fluorescence correlation spectroscopy (FCS) is a primary tool in the time-resolved analysis of nonreacting or reacting molecules in solution, based on fluorescence intensity fluctuations. However, conventional FCS alone is insufficient for a complete determination of reaction or mixture parameters. In an accompanying article, a technique for the computation of artifact-free higher-order correlations with microsecond time resolution was described. Here, we demonstrate the applications of the technique to analyze the systems of fast and slow reactions. As an example of non- or slow-reacting systems, the technique is applied to resolve two-component mixtures of labeled oligonucleotides. Next, the protonation reaction of fluorescein isothiocyanate in phosphate buffer is analyzed as an example of fast reactions (relaxation time <1 μs). By reference to an (apparent) nonreacting system, the simple factorized form of cumulant-based higher-order correlations is exploited to remove the dependence on the molecular d...