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We present results of an exact diagonalization calculation of the spectral function A(k, ω) for a single hole described by the t-J model propagating on a 32-site square cluster. The minimum energy state is found at a crystal momentum k = ( π 2 , π 2 ), consistent with theory, and our measured dispersion relation agrees well with that determined using the self-consistent Born approximation. In contrast to smaller cluster studies, our spectra show no evidence of string resonances. We also make a qualitative comparison of the variation of the spectral weight in various regions of the first Brillouin zone with recent ARPES data. PACS: 71.27.+a, 74.25.Jb, 75.10.Jm Typeset using REVT E X 1The t-J model has received a lot of attention in recent years. It is believed to be the simplest strong-coupling model of the low energy physics of the anomalous metallic state of high-temperature superconductors [1,2]. The Hamiltonian of the model iswhere ij denotes nearest neighbor sites, andc † iσ ,c iσ are the constrained operators,c iσ = In this paper we report the first exact diagonalization results, found using the Lanczos algorithm, for a single hole described by the t-J model on a 32-site square lattice. We use t as the unit of energy, i.e., t = 1. Figure 1 shows the distinct k points in the reciprocal space of the 32-site square lattice. Previous calculations for this model were mostly done on the 16-site (4 × 4) square lattice, where the k points along the antiferromagnetic Brillouin zone (ABZ) edge (from (0, π) to (π, 0)) are degenerate. Other square lattices that have been studied (18-, 20-, and 26-site) do not have the important k points along the ABZ edge, viz., the single-hole ground state wavevector () nor many points along the (1, 1) direction (from (0, 0) to (π, π)). The 32-site square lattice is the smallest one which has these high symmetry points, and does not have the spurious degeneracy of the 4 × 4 square lattice.2 Thus, this paper represents a major advance in the exact, unbiased, numerical treatment of an important strong-coupling Hamiltonian.In order for us to complete the exact diagonalization on such a large lattice, we use translation and one reflection symmetry to reduce the total number of basis states to about), no reflection symmetry can be used and the total number of basis states is about 300 million. To study the effect of finite system sizes, we will supplement our results with data obtained from smaller systems: the N = 16 (4 × 4) cluster, as well as a 24-site ( √ 18 × √ 32) cluster that includes many of the important wave vectors [7].The electron spectral function is defined bywhere E [8] with 300 iterations and an artificial broadening factor ǫ = 0.05. We obtain A(k, ω) that are well converged using these quantities.Figure 2(a) shows A(k, ω) at J = 0.3 from (0, 0) to (π, π). At (0, 0), the spectrum has a quasiparticle peak at ω ∼ 1.34 and a broad feature at lower energies. As k moves away from (0, 0) along the (1, 1) direction towards (π, π), spectral weight shifts from the broad ...

We critique a Padé analytic continuation method whereby a rational polynomial function is fit to a set of input points by means of a single matrix inversion. This procedure is accomplished to an extremely high accuracy using a novel symbolic computation algorithm. As an example of this method in action, it is applied to the problem of determining the spectral function of a single-particle thermal Green's function known only at a finite number of Matsubara frequencies with two example self energies drawn from the Tmatrix theory of the Hubbard model. We present a systematic analysis of the effects of error in the input points on the analytic continuation, and this leads us to propose a procedure to test quantitatively the reliability of the resulting continuation, thus eliminating the black magic label frequently attached to this procedure.

BackgroundResistance to platinum-based chemotherapy remains a major impediment in the treatment of serous epithelial ovarian cancer. The objective of this study was to use gene expression profiling to delineate major deregulated pathways and biomarkers associated with the development of intrinsic chemotherapy resistance upon exposure to standard first-line therapy for ovarian cancer.MethodsThe study cohort comprised 28 patients divided into two groups based on their varying sensitivity to first-line chemotherapy using progression free survival (PFS) as a surrogate of response. All 28 patients had advanced stage, high-grade serous ovarian cancer, and were treated with standard platinum-based chemotherapy. Twelve patient tumours demonstrating relative resistance to platinum chemotherapy corresponding to shorter PFS (< eight months) were compared to sixteen tumours from platinum-sensitive patients (PFS > eighteen months). Whole transcriptome profiling was performed using an Affymetrix high-resolution microarray platform to permit global comparisons of gene expression profiles between tumours from the resistant group and the sensitive group.ResultsMicroarray data analysis revealed a set of 204 discriminating genes possessing expression levels which could influence differential chemotherapy response between the two groups. Robust statistical testing was then performed which eliminated a dependence on the normalization algorithm employed, producing a restricted list of differentially regulated genes, and which found IGF1 to be the most strongly differentially expressed gene. Pathway analysis, based on the list of 204 genes, revealed enrichment in genes primarily involved in the IGF1/PI3K/NF κB/ERK gene signalling networks.ConclusionsThis study has identified pathway specific prognostic biomarkers possibly underlying a differential chemotherapy response in patients undergoing standard platinum-based treatment of serous epithelial ovarian cancer. In addition, our results provide a pathway context for further experimental validations, and the findings are a significant step towards future therapeutic interventions.