arXiv subjects

R. J. Gooding

Publications and source records attributed to R. J. Gooding.

At least 19 recordsLinked to original sources

arXiv2013

Incorporating the Hayflick Limit into a model of Telomere Dynamics

A model of telomere dynamics is proposed and examined. Our model, which extends a previously introduced two-compartment model that incorporates stem cells as progenitors of new cells, imposes the Hayflick Limit, the maximum number of cell divisions that are possible. This new model leads to cell populations for which the average telomere length is not necessarily a monotonically decreasing function of time, in contrast to previously published models. We provide a phase diagram indicating where such results would be expected. In addition, qualitatively different results are obtained for the evolution of the total cell population. Last, in comparison to available leukocyte baboon data, this new model is shown to provide a better fit to biological data.

physics.bio-ph↗

arXiv2012

Multi-site mean-field theory for cold bosonic atoms in optical lattices

We present a detailed derivation of a multi-site mean-field theory (MSMFT) used to describe the Mott-insulator to superfluid transition of bosonic atoms in optical lattices. The approach is based on partitioning the lattice into small clusters which are decoupled by means of a mean field approximation. This approximation invokes local superfluid order parameters defined for each of the boundary sites of the cluster. The resulting MSMFT grand potential has a non-trivial topology as a function of the various order parameters. An understanding of this topology provides two different criteria for the determination of the Mott insulator superfluid phase boundaries. We apply this formalism to $d$-dimensional hypercubic lattices in one, two and three dimensions, and demonstrate the improvement in the estimation of the phase boundaries when MSMFT is utilized for increasingly larger clusters, with the best quantitative agreement found for $d=3$. The MSMFT is then used to examine a linear dimer chain in which the on-site energies within the dimer have an energy separation of $Δ$. This system has a complicated phase diagram within the parameter space of the model, with many distinct Mott phases separated by superfluid regions.

cond-mat.quant-gas↗

arXiv2012

The BCS Pairing Instability in the Thermodynamic Limit

The superconducting pairing instability---as determined by a divergence of the two-particle susceptibility---is obtained in the mean field (BCS) approximation in the thermodynamic limit. The usual practice is to examine this property for a finite lattice. We illustrate that, while the conclusions remain unchanged, the technical features are very different in the thermodynamic limit and conform more closely with the usual treatment of phase transitions encountered in, for example, the mean-field paramagnetic-ferromagnetic transition. Furthermore, by going to the extreme dilute limit, one can distinguish three dimensions from one and two dimensions, in which a pairing instability occurs even for two particles.

cond-mat.supr-con↗

arXiv2011

Variational Monte Carlo Study of Anderson Localization in the Hubbard Model

We have studied the effects of interactions on persistent currents in half-filled and quarter-filled Hubbard models with weak and intermediate strength disorder. Calculations are performed using a variational Gutzwiller ansatz that describes short range correlations near the Mott transition. We apply an Aharonov-Bohm magnetic flux, which generates a persistent current that can be related to the Thouless conductance. The magnitude of the current depends on both the strength of the screened disorder potential and the strength of electron-electron correlations, and the Anderson localization length can be extracted from the scaling of the current with system size. At half filling, the persistent current is reduced by strong correlations when the interaction strength is large. Surprisingly, we find that the disorder potential is strongly screened in the large interaction limit, so that the localization length grows with increasing interaction strength even as the magnitude of the current is suppressed. This supports earlier dynamical mean field theory predictions that the elastic scattering rate is suppressed near the Mott transition.

cond-mat.str-el↗

arXiv2011

Analyzing the success of T-matrix diagrammatic theories in representing a modified Hubbard model

We present a systematic study of various forms of renormalization that can be applied in the calculation of the self-energy of the Hubbard model within the T-matrix approximation. We compare the exact solutions of the attractive and repulsive Hubbard models, for linear chains of lengths up to eight sites, with all possible taxonomies of the T-matrix approximation. For the attractive Hubbard model, the success of a minimally self-consistent theory found earlier in the atomic limit (Phys. Rev. B 71, 155111 (2005)) is not maintained for finite clusters unless one is in the very strong correlation limit. For the repulsive model, in the weak correlation limit at low electronic densities -- that is, where one would expect a self-consistent T-matrix theory to be adequate -- we find the fully renormalized theory to be most successful. In our studies we employ a modified Hubbard interaction that eliminates all Hartree diagrams, an idea which was proposed earlier (Phys. Rev. B 63, 035104 (2000)).

cond-mat.str-el↗

arXiv2011

Application of a multi-site mean-field theory to the disordered Bose-Hubbard model

We present a multi-site formulation of mean-field theory applied to the disordered Bose-Hubbard model. In this approach the lattice is partitioned into clusters, each isolated cluster being treated exactly, with inter-cluster hopping being treated approximately. The theory allows for the possibility of a different superfluid order parameter at every site in the lattice, such as what has been used in previously published site-decoupled mean-field theories, but a multi-site formulation also allows for the inclusion of spatial correlations allowing us, e.g., to calculate the correlation length (over the length scale of each cluster). We present our numerical results for a two-dimensional system. This theory is shown to produce a phase diagram in which the stability of the Mott insulator phase is larger than that predicted by site-decoupled single-site mean-field theory. Two different methods are given for the identification of the Bose glass-to-superfluid transition, one an approximation based on the behaviour of the condensate fraction, and one of which relies on obtaining the spatial variation of the order parameter correlation. The relation of our results to a recent proposal that both transitions are non self-averaging is discussed.

cond-mat.dis-nn↗

arXiv2009

Optical conductivity of a metal-insulator transition for the Anderson-Hubbard model in 3 dimensions away from 1/2 filling

We have completed a numerical investigation of the Anderson-Hubbard model for three-dimensional simple cubic lattices using a real-space self-consistent Hartree-Fock decoupling approximation for the Hubbard interaction. In this formulation we treat the spatial disorder exactly, and therefore we account for effects arising from localization physics. We have examined the model for electronic densities well away 1/2 filling, thereby avoiding the physics of a Mott insulator. Several recent studies have made clear that the combined effects of electronic interactions and spatial disorder can give rise to a suppression of the electronic density of states, and a subsequent metal-insulator transition can occur. We augment such studies by calculating the ac conductivity for such systems. Our numerical results show that weak interactions enhance the density of states at the Fermi level and the low-frequency conductivity, there are no local magnetic moments, and the ac conductivity is Drude-like. However, with a large enough disorder strength and larger interactions the density of states at the Fermi level and the low-frequency conductivity are both suppressed, the conductivity becomes non-Drude-like, and these phenomena are accompanied by the presence of local magnetic moments. The low-frequency conductivity changes from a sigma-sigma_dc omega^{1/2} behaviour in the metallic phase, to a sigma omega^2 behaviour in the nonmetallic regime. Our numerical results show that the formation of magnetic moments is essential to the suppression of the density of states at the Fermi level, and therefore essential to the metal-insulator transition.

cond-mat.str-el↗

arXiv2009

Real-space variational Gutzwiller wave functions for the Anderson-Hubbard model

Partially-projected Gutzwiller variational wavefunctions are used to describe the ground state of disordered interacting systems of fermions. We compare several different variational ground states with the exact ground state for disordered one-dimensional chains, with the goal of determining a minimal set of variational parameters required to accurately describe the spatially-inhomogeneous charge densities and spin correlations. We find that, for weak and intermediate disorder, it is sufficient to include spatial variations of the charge densities in the product state alone, provided that screening of the disorder potential is accounted for. For strong disorder, this prescription is insufficient and it is necessary to include spatially inhomogeneous variational parameters as well.

cond-mat.str-el↗

arXiv2008

Critiquing Variational Theories of the Anderson-Hubbard Model: Real-Space Self-Consistent Hartree-Fock Solutions

A simple and commonly employed approximate technique with which one can examine spatially disordered systems when strong electronic correlations are present is based on the use of real-space unrestricted self-consistent Hartree-Fock wave functions. In such an approach the disorder is treated exactly while the correlations are treated approximately. In this report we critique the success of this approximation by making comparisons between such solutions and the exact wave functions for the Anderson-Hubbard model. Due to the sizes of the complete Hilbert spaces for these problems, the comparisons are restricted to small one-dimensional chains, up to ten sites, and a 4x4 two-dimensional cluster, and at 1/2 filling these Hilbert spaces contain about 63,500 and 166 million states, respectively. We have completed these calculations both at and away from 1/2 filling. This approximation is based on a variational approach which minimizes the Hartree-Fock energy, and we have completed comparisons of the exact and Hartree-Fock energies. However, in order to assess the success of this approximation in reproducing ground-state correlations we have completed comparisons of the local charge and spin correlations, including the calculation of the overlap of the Hartree-Fock wave functions with those of the exact solutions. We find that this approximation reproduces the local charge densities to quite a high accuracy, but that the local spin correlations, as represented by < S_i . S_j >, are not as well represented. In addition to these comparisons, we discuss the properties of the spin degrees of freedom in the HF approximation, and where in the disorder-interaction phase diagram such physics may be important.

cond-mat.str-el↗

arXiv2007

Exact diagonalization analysis of the Anderson-Hubbard model and comparison to real-space self-consistent Hartree-Fock solutions

We have obtained the exact ground state wave functions of the Anderson-Hubbard model for different electron fillings on a 4x4 lattice with periodic boundary conditions - for 1/2 filling such ground states have roughly 166 million states. When compared to the uncorrelated ground states (Hubbard interaction set to zero) we have found strong evidence of the very effective screening of the charge homogeneities due to the Hubbard interaction. We have successfully modelled these local charge densities using a non-interacting model with a static screening of the impurity potentials. In addition, we have compared such wave functions to self-consistent real-space unrestricted Hartree-Fock solutions and have found that these approximate ground state wave functions are remarkably successful at reproducing the local charge densities, and may indicate the role of dipolar backflow in producing a novel metallic state in two dimensions.

cond-mat.str-el↗

arXiv2007

Two-electron bound state formation in the t-J-U model for exchange-coupled planes

An anisotropic t-J-U model Hamiltonian is used to model electron behaviour in quasi-2d materials in the dilute limit, and as a highly simplified representation of the weakly coupled CuO2 planes of the high-Tc cuprates we model the very poor out-of-plane conductivity via the complete suppression of interplanar hopping. However, we do include the very weak interplanar superexchange, and are thus considering a model of exchange-coupled planes. For an isotropic three-dimensional system in the dilute limit, we find that the formation of two-particle bound states requires Jc/t ~ 5.9. Also, it is known that Jc/t = 2 for a 2d square lattice. However, for our model of exchange-coupled planes any infinitesimal interplanar exchange (Jc = 0) is adequate to form bound states.

cond-mat.str-el↗

arXiv2006

The role of strong electronic correlations in the metal-to-insulator transition in disordered LiAl_yTi_(2-y)O_4

The compound LiAl_yTi_(2-y)O_4 undergoes a metal-to-insulator transition for y_c ~0 .33. This system, in the absence of strong electronic correlations, is a prototypical example of quantum site percolation. However, it is known that the effects of disorder produced by such a percolating lattice are insufficient to explain this transition: a quantum site percolation model predicts y_c ~ 0.8, well above the experimental value. We have included an on-site Hubbard interaction into a model of this compound, using a real-space Hartree-Fock approach, and have found that for a Hubbard energy equal to 1.5 times the non-interacting bandwidth one obtains y_c~0.35. Further, as a function of increasing Hubbard energy, we find that an Altshuler-Aronov suppression of the density of states, delta N(E) ~ sqrt(| E-E_F |), reduces the density of states at the Fermi energy to zero at the critical Hubbard interaction. Using this ratio of correlation to hopping energy one is led to a prediction for the value of near-neighbour superexchange J/t~1/3 which is similar to that for the cuprate superconductors.

cond-mat.str-el↗

arXiv2006

Electronic properties of disordered corner-sharing tetrahedral lattices

We have examined the behaviour of noninteracting electrons moving on a corner-sharing tetrahedral lattice into which we introduce a uniform (box) distribution, of width W, of random on-site energies. We have used both the relative localization length and the spectral rigidity to analyze the nature of the eigenstates, and have determined both the mobility edge trajectories as a function of W, and the critical disorder, Wc, beyond which all states are localized. We find (i) that the mobility edge trajectories (energies Ec vs. disorder W) are qualitatively different from those found for a simple cubic lattice, and (ii) that the spectral rigidity is scale invariant at Wc and thus provides a reliable method of estimating this quantity -- we find Wc/t=14.5. We discuss our results in the context of the metal-to-insulator transition undergone by LiAlyTi{2-y}O4 in a quantum site percolation model that also includes the above-mentioned Anderson disorder, and show that the effects produced by Anderson disorder are far less important than those produced by quantum site percolation, at least in the determination of the doping concentration at which the metal-to-insulator transition is predicted to occur.

cond-mat.str-el↗

arXiv2005

Magnetic susceptibility of a CuO2 plane in the La2CuO4 system: I. RPA treatment of the Dzyaloshinskii-Moriya Interactions

Motivated by recent experiments on undoped La2CuO4, which found pronounced temperature-dependent anisotropies in the low-field magnetic susceptibility, we have investigated a two-dimensional square lattice of S=1/2 spins that interact via Heisenberg exchange plus the symmetric and anti-symmetric Dzyaloshinskii-Moriya anisotropies. We describe the transition to a state with long-ranged order, and find the spin-wave excitations, with a mean-field theory, linear spin-wave analysis, and using Tyablikov's RPA decoupling scheme. We find the different components of the susceptibility within all of these approximations, both below and above the N'eel temperature, and obtain evidence of strong quantum fluctuations and spin-wave interactions in a broad temperature region near the transition.

cond-mat.str-el↗

arXiv2004

Pairing Fluctuations in The Attractive Hubbard Model in the Atomic Limit

BCS theory accounts for the pairing instability in the weak coupling limit, but fails to describe pairing fluctuations above $T_c$. One possibility for describing these fluctuations in the dilute limit is the T-matrix approximation. We critically examine various degrees of self-consistency in the T-matrix formalism, along with a non-diagrammatic two-particle self-consistent (TPSC) formulation, in the strong coupling regime, where an exact solution is readily available. We find that one particular degree of self-consistency is quite accurate, particularly at low temperature as evidenced by examining both static and dynamic properties.

cond-mat.supr-con↗

arXiv2004

Demonstration of a robust pseudogap in a three-dimensional correlated electronic system

We outline a partial-fractions decomposition method for determining the one-particle spectral function and single-particle density of states of a correlated electronic system on a finite lattice in the non self-consistent T-matrix approximation to arbitrary numerical accuracy, and demonstrate the application of these ideas to the attractive Hubbard model. We then demonstrate the effectiveness of a finite-size scaling ansatz which allows for the extraction of quantities of interest in the thermodynamic limit from this method. In this approximation, in one or two dimensions, for any finite lattice or in the thermodynamic limit, a pseudogap is present and its energy diverges as Tc is approached from above; this is an unphysical manifestation of using an approximation that predicts a spurious phase transition in one or two dimensions. However, in three dimensions one expects the transition predicted by this approximation to represent a true continuous phase transition, and in the thermodynamic limit any pseudogap predicted by this formulation will remain finite. We have applied our method to the attractive Hubbard model on a three-dimensional simple cubic lattice, and find that for intermediate coupling a prominent pseudogap is found in the single-particle density of states, and this gap persists over a large temperature range. In addition, we also show that for weak coupling a pseudogap is also present. The pseudogap energy at the transition temperature is almost a factor of three larger than the T=0 BCS gap for intermediate coupling, whereas for weak coupling the pseudogap and BCS gap energies are essentially equal.

cond-mat.str-el↗

arXiv2003

Examining the metal-to-insulator transitions in Li1+xTi2-xO4 and LiAlyTi2-yO4 with a Quantum Site Percolation model

We have studied the composition-induced metal-to-insulator transitions of cation substituted Lithium Titanate, in the forms Li1+xTi2-xO4 and LiAlyTi2-yO4, utilising a quantum site percolation model, and we argue that such a model provides a very reliable representation of the noninteracting electrons in this material if strong correlations are ignored. We then determine whether or not such a model of 3d electrons moving on the Ti (corner-sharing tetrahedral) sublattice describes the observed metal-to-insulator transitions, with the critical concentration defined by the matching of the mobility edge and the chemical potential. Our analysis leads to quantitative predictions that are in disagreement with those measured experimentally. For example, experimentally for the LiAlyTi2-yO4 compound an Al concentration of y_c approximately 0.33 produces a metal-to-insulator transition, whereas our analysis of a quantum site percolation model predicts y_c approximately 0.83. One hypothesis that is consistent with these results is that since strong correlations are ignored in our quantum site percolation model, which includes the effects of configurational disorder only, such strong electronic correlations are both present and important.

cond-mat.str-el↗

arXiv2002

Increasing Superconducting Tc's by a Factor of 1000 with StripeLike Hopping Anisotropies

We have studied the enhancement of the superconducting transition temperature, Tc, in a t-J-U model of electrons moving on a square lattice in which anisotropic electronic hopping is introduced. The inclusion of such hopping mimics, in a approximate fashion, a potentially important characteristic of materials possessing stripelike charge and spin correlations. For this model we have calculated Tc for singlet pairing using the non self-consistent Thouless criterion, and find a dramatic enhancement of Tc induced by hopping anisotropies. Further, the maximum increase in Tc is obtained when the system is pushed towards the extreme anisotropy limit, that is, when the hopping of electrons is confined to occur in 1+0^+ dimensions. We demonstrate that in this limit the increase in Tc, with respect to the isotropic system, can be of the order of 1000. We have also determined that in the extreme anisotropy limit the superconducting gap is an equal mixture of s and d pairing symmetries (two choices of such a combination being s + d and s + id) owing to the reduced (square to rectangular) symmetry of the system in the presence of hopping anisotropies. Thus, the presence of d-wave superconducting features in materials whose symmetry is very different from that of a two-dimensional square lattice, with the anisotropy produced by the appearance of stripes, is not unexpected.

cond-mat.supr-con↗