Session H45: Theoretical Methods in Strongly Correlated Electron Systems

Analytic derivation of the equivalence between the Gutzwiller-projected BCS Hamiltonian and the t-J model at half filling

A connection between quantum antiferromagnetism and high $T_C$ superconductivity is theoretically investigated by analyzing the $t$-$J$ model and its relationships to the Gutzwiller- projected BCS Hamiltonian. In particular, it is analytically shown that the ground state of the $t$-$J$ model at half filling (i.e., the 2D antiferromagnetic Heisenberg model) is entirely equivalent to the ground state of the Gutzwiller- projected BCS Hamiltonian with strong pairing. The relationship between the ground state of the projected BCS Hamiltonian and Anderson's resonating valence bond state (i.e., the projected BCS ground state) is discussed.   

Implications of the Low-Temperature Instability of Dynamical Mean Theory for Double Exchange Systems

The single-site dynamical mean field theory approximation to the double exchange model is found to exhibit a previously unnoticed instability, in which a well-defined ground state which is stable against small perturbations is found to be unstable to large-amplitude but purely local fluctuations. The instability is shown to arise either from phase separation or, in a narrow parameter regime, from the presence of a competing phase. The instability is therefore suggested as a computationally inexpensive means of locating regimes of parameter space in which phase separation occurs.   

A continuous-time impurity solver for dynamical mean field theory

We present a new continuous-time impurity solver for dynamical mean field theory. The method is based on a diagramatic expansion in the quadratic part of the effective action, in contrast to a previous approach [A. N. Rubtsov et al., cond-mat/0411344], which uses an expansion in the interaction part. Interactions and chemical potentials are taken into account during the Monte Carlo sampling of certain collections of diagrams. Comparison to Hirsch-Fye QMC simulations shows that the new approach allows an efficient calculation of the Greens function even at very low temperatures.   

Correlated hybridization in transition metal complexes

We apply local orbital basis density functional theory (using SIESTA) coupled with a mapping to the Anderson impurity model to estimate the Coulomb assisted or correlated hybridization between transition metal d-orbitals and ligand sp-orbitals for a number of molecular complexes. We find remarkably high values which can have several physical implications including: (i) renormalization of effective single band or multiband Hubbard model parameters for the cuprates and, potentially, elemental iron, and (ii) spin polarizing molecular transistors.   

Exactly solvable Hamiltonian for the chiral spin liquid

An exact spin Hamiltonian for the chiral spin liquid will be presented. The model starts with the quantum Hall wave function on a lattice of N sites in a toroidal geometry, a state that describes a spin liquid that violates the symmetries of parity and time reversal. A parent Hamiltonian for which the state is the exact ground state is constructed out of vector operators that annihilate the ground state. This model avoids the subtle error that has been identified [D. F. Schroeter, Ann. Phys. \textbf {310}, 155 (2004)] in Laughlin's original solution to the problem [R. B. Laughlin, Ann. Phys. \textbf{191}, 163 (1989)]. The construction of the model and its numerical verification will be presented.   

Spin Glass Solution to the Double-Exchange Model in Infinite Dimensions

Using dynamical mean-field theory, we have evaluated the magnetic instabilities and T=0 phase diagram of the double-exchange model on a Bethe lattice in infinite dimensions. In addition to ferromagnetic (FM) and antiferromagnetic (AF) phases, we also study a broad class of spin-glass (SG) solutions with extensive entropy and short-range magnetic order. In the weak-coupling limit, a SG has a higher transition temperature than the AF phase for all fillings p below 1 and can even have a higher transition temperature than the FM phase. At T=0 and for small Hund's coupling, a SG has lower energy than either the FM or AF phases for 0.26 $<$ p $<$ 1. Phase separation is absent as the Hund's coupling vanishes but appears for any non-zero value. Our T=0 phase diagram agrees remarkably well with Monte-Carlo results in two and three dimensions. The stability of a SG at T=0 can be understood by examining the interacting density-of-states, which is gapped for any nonzero Hund's coupling in an AF but only when the Hund's coupling exceeds a critical value in a SG.   

Bound states, symmetry breaking, and memory effects in doped $t-J$ $Y$-junctions

The effect of strong electronic correlations on the properties of the weakly doped $Y$-junctions is studied within the $t-J$ and $t-J_z$ models using an analytical Green's function approach and DMRG. It is shown that the bound state at the junction depends counter-intuitively on the strength of the correlation: the bound state exists for the range of\ $0 [Preview Abstract]

Quasiparticle self-consistent GW method applied to f systems

We have applied the recently-developed quasi-particle self-consistent $GW$ method (QPsc$GW$) to several f systems, Gd, GdN, GdAs, ErAs, and CeO2. The QPsc$GW$ is desigened to determine the best independent particle picture; it can cover rather wide-range of materials, semiconductor to transion metal oxides with acceptable accuracy [1] [2] without any parameters. We found that QPsc$GW$ gives reasonable description of the f level positions and exchange splitting, though it predicts unoccupied f levels a little too high. In addition, the Fermi surface analysis shows that SdH frequencies and carrier concentration are in good agreement with available experimental data. [1] Mark van Schilfgaarde, Takao Kotani, and Sergey V. Faleev, cond-mat/0510408 [2] A. N. Chantis, Mark van Schilfgaarde, Takao Kotani, cond-mat/0508274   

Fermi arcs and hidden zeros of the Green function in the pseudogap state

We investigate the evolution of the low energy properties of a correlated metal in the proximity of a Mott insulator within the planar Hubbard model. We use a generalized version of the Cellular Dynamical Mean Field Theory having cumulants as the basic irreducible objects for re-constructing the lattice quantities from their cluster counterparts. We find that the zero temperature one particle Green function is characterized by the appearance of lines of zeros, in addition to a Fermi surface which changes topology as a function of doping. We show that these features are directly related to the opening of a pseudogap in the one particle spectrum and provide a simple picture for the appearance of Fermi arcs.   

Incompressible Quantum Liquids and New Conservation Laws

We discuss a class of Hamiltonians which, in addition to the usual center-of-mass (CM) momentum conservation, also have center-of-mass position conservation. We find that regardless of the particle statistics, the energy spectrum is at least $q$-fold degenerate when the filling factor is $p/q$, where $p$ and $q$ are coprime integers. Interestingly, the simplest form of Hamiltonian respecting this type of symmetry encapsulates two prominent examples of novel states of matter, namely the fractional quantum Hall liquid and the quantum dimer liquid. We explore the connection to the Hall liquid in some detail, and also discuss the possible relevance of this class of Hamiltonian to the search for featureless Mott insulators.   

High-Temperature Criticality in Strongly Constrained Quantum Systems

The exotic nature of many strongly correlated materials at reasonably high temperatures, for instance cuprate superconductors in their normal state, has lead to the suggestion that such behavior occurs within a quantum critical region where the physics is controlled by the influence of a phase transition down at zero temperature. Such a scenario can be thought of as a bottom-up approach, with the zero temperature mechanisms finding a way to manifest critical behavior at high temperatures. Here we propose an alternative, top-down, mechanism by which strong kinematic constraints that can only be broken at extremely high temperatures are responsible for critical behavior at intermediate but still high temperatures. This critical behavior may extend all the way down to zero temperature, but this outcome is not one of necessity, and the system may actually order at low temperatures. We provide explicit examples of such high-temperature criticality when extra strong interactions are added to quantum Heisenberg, transverse field Ising, and some lattice bosonic models.   

Search for ferromagnetism in a generalized Hubbard model with disorder

While the Hubbard model on a hypercubic lattice in two and three dimensions is believed to have a ferromagnetic phase away from half filling, its extent and precise location has remained controversial. With the introduction of positional disorder, a random singlet/valence-bond glass state is stabilized at half filling over the conventional antiferromagnetic phase, which could lead to a considerable reduction in the regime of ferromagnetism. In this study, we have used a variety of numerical techniques, including exact diagonalization of small systems and numerical mean field methods to search for the possibility of ferromagnetism in a generalized Hubbard model with and without positional disorder, aimed at the system of hydrogenic centers in semiconductors. We will present our results showing the effects of positional disorder, of electron-hole asymmetry, and other properties applicable to real experimental systems of doped semiconductors. The possibility of setting up a renormalization scheme as for the half-filled case will be discussed.   

Quantum Phase Transitions of Hard-Core Bosons on the Kagome Lattice

We study hard-core bosons with nearest-neighbor repulsion on the kagome lattice at different filling factors using quantum Monte Carlo simulations and a dual vortex theory. At half-filling, the ground state of the system is always a uniform superfluid in contrast to the case of the triangular lattice. There exists a quantum phase transition from a superfluid to a valence bond solid phase away from half-filling. The possibility of unusual quantum criticality is investigated.