Density of states of the two-dimensional Hubbard model on a 4×4 lattice

Leung, Pak Wo; Liu, Zhiping; Manousakis, Efstratios; Novotny, M. A.; Oppenheimer, Paul

doi:10.1103/physrevb.46.11779

Cited by 44 publications

(31 citation statements)

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“…where E is calculated using a continued fraction expansion [8] with 300 iterations and an artificial broadening factor ǫ = 0.05. We obtain A(k, ω) that are well converged using these quantities.…”

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Dynamical properties of the single-holet-Jmodel on a 32-site square lattice

1995

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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 ...

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Dynamical properties of the single-holet-Jmodel on a 32-site square lattice

1995

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“…By contrast, the dimension of the Hilbert space of the Heisenberg model -which is equivalent to the Hubbard model for large U/t -in the 4 × 4 cluster is only 12870, in the 18-site cluster it is 48620. The Heisenberg model -and in the doped case the t-J model -thus are much easier to study numerically and in fact the largest cluster for which exact diagonalization studies for the Hubbard model have been performed [36,37] is 4 × 4, whereas larger clusters are possible for the t-J model. For a study of the self energy, however, the t-J model cannot be used due to its 'projected' nature which for example implies the absence of the upper Hubbard band.…”

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confidence: 99%

Self-energy and Fermi surface of the two-dimensional Hubbard model

2011

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We present an exact diagonalization study of the self-energy of the two-dimensional Hubbard model. To increase the range of available cluster sizes we use a corrected t-J model to compute approximate Greens functions for the Hubbard model. This allows to obtain spectra for clusters with 18 and 20 sites. The self-energy has several 'bands' of poles with strong dispersion and extended incoherent continua with k-dependent intensity. We fit the self-energy by a minimal model and use this to extrapolate the cluster results to the infinite lattice. The resulting Fermi surface shows a transition from hole pockets in the underdoped regime to a large Fermi surface in the overdoped regime. We demonstrate that hole pockets can be completely consistent with the Luttinger theorem. Introduction of next-nearest neighbor hopping changes the self-energy stronlgy and the spectral function with nonvanishing next-nearest-neighbor hopping in the underdoped region is in good agreement with angle resolved photoelectron spectroscopy.

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“…In order to calculate DOS, we used the spectral functions [12] for adding an electron of spin σ, momentum k and energy ω to the ground state e e e e 1 1 ( )…”

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Reentrant superconductivity in the strong coupling limit

Gorczyca

Mierzejewski

2007

Physica Status Solidi (b)

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The usual approaches to the reentrant superconductivity are based on the mean field approximation. Here, we investigate this effect carrying out exact diagonalization of finite systems. We have found a nonmonotonic field dependence of the pair susceptibility both in the weak and strong coupling limit. This result strongly supports the possible onset of the reentrant superconductivity in the presence of strong magnetic field.

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Density of states of the two-dimensional Hubbard model on a 4×4 lattice

Cited by 44 publications

References 11 publications

Dynamical properties of the single-holet-Jmodel on a 32-site square lattice

Dynamical properties of the single-holet-Jmodel on a 32-site square lattice

Self-energy and Fermi surface of the two-dimensional Hubbard model

Reentrant superconductivity in the strong coupling limit

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