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

Abstract

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 ...

Theory for Slightly Doped Antiferromagnetic Mott Insulators

“…States described by |Ψ ′ 1 have smaller Z k 's and are thus with a strong incoherent character. We also found that more quasi-particle states have lower energy below the continuum in the pure t-J model with t ′ = t ′′ = 0 [11] than in the t-t ′ -t ′′ -J model. This is consistent with what has been known in the exact results [8].…”

“…But so far most experiments do not support the coexistence. In addition, there has been not enough understanding on various properties found in the exact results of the t-J type models on finite clusters [5,6,8,9,10,11,12] in terms of the many-particle wave functions (WF's).…”

Spin-charge separation in the single-hole-doped Mott antiferromagnet

“…6. As noted before, the localization length scale of the holon is generally much larger than the maximum sample sizes (< 6 × 6) in numerical exact-diagonalization calculations [12]. Thus, numerical calculations providing a "metallic" quasiparticle picture should be irrelevant to the true picture at large length scales.…”

Spatial structure of spin polarons in thet−Jmodel

“…While the major part of investigations for the t-J model was concerned e.g. with the polaron dispersion and the spectral function using a variety of techniques such as exact diagonalization [2][3][4][5][6][7], selfconsistent Born approximation (SCBA) [8][9][10][11], string theory [12,13] and other methods [14][15][16][17], -our focus here is on the spatial structure of the spin polarization and its asymptotic behaviour. The study of the deformation of the spin system due to spin polaron formation was mainly performed by exact diagonalization techniques [3,18].…”