We present series-expansion investigations of the square-lattice spin-~Heisenberg antiferromagnet with nearest-neighbor (J&},second-neighbor (J2},and third-neighbor (J3) exchanges. Expansions for ground-state properties around dimerized Hamiltonians in conjunction with finite-size studies and cluster mean-field theories allow us to map out the magnetically ordered phase boundaries. The magnetically disordered phase of the square-lattice Heisenberg model, which is accessible to the dimer expansions, appears to be spontaneously dimerized in the "columnar" pattern predicted by Read and Sachdev. Estimates for the dimerization order parameter in this phase are a substantial fraction of that of the fully dimerized state.

A theory of the electronic properties of doped fullerenes is proposed in which electronic correlation effects within single fullerene molecules play a central role, and qualitative predictions are made which, if verified, would support this hypothesis. Depending on the effective intrafulllerene electron-electron repulsion and the interfullerene hopping amplitudes (which should depend on the dopant species, among other things), the calculations indicate the possibilities of singlet superconductivity and ferromagnetism.

We have developed a general scheme for carrying out systematic perturbation expansions for groundstate properties of quantum lattice models. As an application, we study the onset of spontaneous Neel order in S = j Heisenberg antiferromagnets by expanding around dimerized Hamiltonians. In one dimension (ID) we recover accurately the known exact results. On the square lattice we find novel critical points separating Neel ordered and disordered phases; the estimated critical exponents are consistent with those of the 3D classical Heisenberg model. PACS numbers: 75.10.Jm, 71.10.+X, 75.40.Cx The zero-temperature properties of quantum manybody systems and the location and character of groundstate instabilities (critical points) under changes of parameters in the Hamiltonian represent fundamental problems in condensed matter theory. Unlike classical statistical mechanics, where our understanding of critical phenomena and phase transitions is quite extensive, there have been few concrete developments in quantum critically. ! A notable exception is the case of onedimensional systems. 2 Recent experimental 3 and theoretical 4 advances in high-temperature superconductivity have led to a resurgence of interest in some of these problems, in particular, to the question of long-range order in 2D Heisenberg antiferromagnets. We discuss here a general calculational scheme that addresses the topic of zero-temperature quantum criticality, and apply it to low-dimensional Heisenberg antiferromagnets. For ID, we recover accurately the known exact results for alternating spin chains. In 2D we find that introducing bond alternation in the square lattice Heisenberg antiferromagnet leads to novel quantum critical points. These critical points, which separate Neel ordered and disordered phases, have critical exponents consistent with those of the 3D classical Heisenberg model, given proper interpretation of the 2D-3D correspondence.The basic idea behind our work is that there are well defined phases in the parameter space of quantum Hamiltonians. Within a given phase the ground-state properties of one Hamiltonian can be accessed from that of another by adiabatic continuation, i.e., by following the evolution of the ground state under continuous variation in parameters. Adiabatic continuity of the ground state breaks down at phase boundaries, where singularities or crossings of energy levels occur. In order to implement this idea of adiabatic continuation in a concrete manner and investigate these quantum phase transitions, we shall borrow tools and techniques from classical critical phenomena, namely, series expansions and analysis.We consider, specifically, spin-y Heisenberg models on the linear chain and the square lattice with nearestneighbor antiferromagnetic exchange /. Let us partition the infinite lattice into nearest-neighbor dimers and let Ho be the part of the Hamiltonian containing the exchanges within dimers, while H\ contains the remainder of the exchanges. We then consider the one-parameter family of models with Hamiltonia...

A systematic method for developing high-order, zero-temperature perturbation expansions for quantum many-body systems is presented. The models discussed explicitly are spin models with a variety of interactions, in one and two dimensions. The wide applicability of the method is illustrated by expansions around Hamiltonians with ordered and disordered ground states, namely Ising and dimerized models. Computer implementation of this method is discussed in great detail. Some previously unpublished series are tabulated.

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