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We study a model for the metal-insulator (M-I) transition in the rare-earth-element nickelates RNiO3, based upon a negative charge transfer energy and coupling to a rocksaltlike lattice distortion of the NiO6 octahedra. Using exact diagonalization and the Hartree-Fock approximation we demonstrate that electrons couple strongly to these distortions. For small distortions the system is metallic, with a ground state of predominantly d8L character, where L_ denotes a ligand hole. For sufficiently large distortions (δdNi-O∼0.05-0.10  Å), however, a gap opens at the Fermi energy as the system enters a periodically distorted state alternating along the three crystallographic axes, with (d8L_2)S=0(d8)S=1 character, where S is the total spin. Thus the M-I transition may be viewed as being driven by an internal volume "collapse" where the NiO6 octahedra with two ligand holes shrink around their central Ni, while the remaining octahedra expand accordingly, resulting in the (1/2, 1/2, 1/2) superstructure observed in x-ray diffraction in the insulating phase. This insulating state is an example of charge ordering achieved without any actual movement of the charge.

We present a new, highly efficient yet accurate approximation for the Green's functions of dressed particles, using the Holstein polaron as an example. Instead of summing a subclass of diagrams (e.g. the non-crossed ones, in the self-consistent Born approximation (SCBA)), we sum all the diagrams, but with each diagram averaged over its free propagators' momenta. The resulting Green's function satisfies exactly the first six spectral weight sum rules. All higher sum rules are satisfied with great accuracy, becoming asymptotically exact for coupling both much larger and much smaller than the free particle bandwidth. Possible generalizations to other models are also discussed.PACS numbers: 72.10.Di, 63.20.Kr One of the most fundamental problems in both highenergy and condensed matter physics is to understand what happens when a particle couples to an environment, in particular what are the properties of the resulting object, consisting of the bare particle dressed by a cloud of excitations. This type of problem arises again and again as couplings to new kinds of environments are studied.The most desirable quantity to know is the Green's function G( k, ω) of the dressed particle -its poles mark the eigenspectrum, while the associated residues contain information on the eigenfunctions. Moreover, the spectral weight A( k, ω) = − 1 π ImG( k, ω) can be directly measured experimentally using Angle-Resolved Photoemission Spectroscopy [1]. Recently, such work has reignited a debate on whether the carriers in high-T c cuprates are polarons, that is, electrons dressed by phonons [2].G( k, ω) is the sum of an infinite number of diagrams corresponding to an expansion to all orders in the coupling strength [3]. Diagrammatic Monte Carlo (DMC) can perform the numerical summation of all diagrams [4]. Other ways to find G( k, ω) are from exact diagonalizations (ED) of small systems, variational methods, Density Matrix Renormalization Group in one-dimension, etc [5,6,7,8]. However, these methods require considerable computational resources, are time consuming, and often limit themselves to finding only the low-energy properties, such as the ground-state energy.To our knowledge, there are only two easy-to-estimate approximations for G( k, ω). One is the the SCBA which consists in summing only the non-crossed diagrams. Because the percentage of diagrams kept decreases fast with increasing order, SCBA fails badly at strong couplings. The other approximation, obtained from a modified Lang-Firsov (MLF) approach [9], is exact both for zero coupling and for zero bandwidth, however results for finite bandwidth/coupling are rather poor (see below).In this Letter we find a new approximation for G( k, ω), which is as easy to estimate as SCBA and MLF, but is highly accurate over most of the parameter space. We validate this both by comparison against numerical results, and by investigating its sum rules. Most of the discussion here is limited to the Holstein model, for which many numerical results are available. Possible generalizations for...

We present a novel, highly efficient yet accurate analytical approximation for the Green's function of a Holstein polaron. It is obtained by summing all the self-energy diagrams, but with each selfenergy diagram averaged over the momenta of its free propagators. The result becomes exact for both zero bandwidth and for zero electron-phonon coupling, and is accurate everywhere in the parameter space. The resulting Green's function satisfies exactly the first six spectral weight sum rules. All higher sum rules are satisfied with great accuracy, becoming asymptotically exact for coupling both much larger and much smaller than the free particle bandwidth. Comparison with existing numerical data also confirms this accuracy. We use this approximation to analyze in detail the redistribution of the spectral weight as the coupling strength varies.

The ferromagnetic semiconductor (Ga,Mn)As has emerged as the most studied material for prototype applications in semiconductor spintronics. Because ferromagnetism in (Ga,Mn)As is hole-mediated, the nature of the hole states has direct and crucial bearing on its Curie temperature T(C). It is vigorously debated, however, whether holes in (Ga,Mn)As reside in the valence band or in an impurity band. Here we combine results of channelling experiments, which measure the concentrations both of Mn ions and of holes relevant to the ferromagnetic order, with magnetization, transport, and magneto-optical data to address this issue. Taken together, these measurements provide strong evidence that it is the location of the Fermi level within the impurity band that determines T(C) through determining the degree of hole localization. This finding differs drastically from the often accepted view that T(C) is controlled by valence band holes, thus opening new avenues for achieving higher values of T(C).

Antiferromagnetic Hamiltonians with short-range, non-frustrating interactions are well-known to exhibit long range magnetic order in dimensions, d ≥ 2 but exhibit only quasi long range order, with power law decay of correlations, in d = 1 (for half-integer spin). On the other hand, non-frustrating long range interactions can induce long range order in d = 1. We study Hamiltonians in which the long range interactions have an adjustable amplitude λ, as well as an adjustable power-law 1/|x| α , using a combination of quantum Monte Carlo and analytic methods: spin-wave, large-N non-linear σ model, and renormalization group methods. We map out the phase diagram in the λ-α plane and study the nature of the critical line separating the phases with long range and quasi long range order. We find that this corresponds to a novel line of critical points with continuously varying critical exponents and a dynamical exponent, z < 1.

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We study a single polaron in the Su-Schrieffer-Heeger (SSH) model using four different techniques (three numerical and one analytical). Polarons show a smooth crossover from weak to strong coupling, as a function of the electron-phonon coupling strength λ, in all models where this coupling depends only on phonon momentum q. In the SSH model the coupling also depends on the electron momentum k; we find it has a sharp transition, at a critical coupling strength λ(c), between states with zero and nonzero momentum of the ground state. All other properties of the polaron are also singular at λ=λ(c). This result is representative of all polarons with coupling depending on k and q, and will have important experimental consequences (e.g., in angle-resolved photoemission spectroscopy and conductivity experiments).