Single-hole dynamics in thet−Jmodel on a square lattice

Abstract

We present quantum Monte Carlo (QMC) simulations for a single hole in a t-J model from J = 0.4t to J = 4t on square lattices with up to 24 × 24 sites. The lower edge of the spectrum is directly extracted from the imaginary time Green's function. In agreement with earlier calculations, we find flat bands around (0, ±π), (±π, 0) and the minimum of the dispersion at (±π/2, ±π/2). For small J both self-consistent Born approximation and series expansions give a bandwidth for the lower edge of the spectrum in agreement with the simulations, whereas for J/t > 1, only series expansions agree quantitatively with our QMC results. This band corresponds to a coherent quasiparticle. This is shown by a finite size scaling of the quasiparticle weight Z( k) that leads to a finite result in the thermodynamic limit for the considered values of J/t. The spectral function A( k, ω) is obtained from the imaginary time Green's function via the maximum entropy method. Resonances above the lowest edge of the spectrum are identified, whose J-dependence is quantitatively described by string excitations up to J/t = 2.

Single-hole dynamics in the half-filled two-dimensional Kondo-Hubbard model

“…Monte Carlo results for the latter model at J /t < 1 show the existence of a quasiparticle band of width ∼ J [15]. This should be compared to an identical spectral feature which can be observed in our QMC data for the Hubbard model upon enhancing U/t in fig.…”

Plaquette boson-fermion model of cuprates

“…the charged bosons and fermions share a common chemical potential µ. Combining (30), (36), (37), (40) yields the complete Plaquette Boson-Fermion Hamiltonian:…”

“…9. The values t ′ ≈ J, and t ′′ ≈ 0.1J are taken from the numerical Quantum Monte Carlo data for the t-J model on a 24×24 lattice 36 and the position of the minima on the magnetic zone edge (π, 0) − (0, π) were explained by theories of holes in the short range antiferromagnetic environment 37 . The semiclassical theory 29 finds that holes are highly dressed local spin polarons, which effectively hop on one sublattice.…”

Loop-cluster simulation of the zero- and one-hole sectors of thet−Jmodel on the honeycomb lattice

“…Here we use first principle Monte Carlo simulations to quantitatively investigate the single-hole dispersion relation and quasiparticle weight. To achieve this goal, we have implemented a technique similar to the ones used in [5,6] to simulate the one-hole sector of the t-J model. To calculate the fermion two-point functions in momentum space, one should keep in mind that the Brillouin zone of the honeycomb lattice is doubly covered.…”

“…Despite these difficulties, much effort has been devoted to understanding the properties of t-Jtype models on the square lattice. Although some controversial results have been obtained, various studies including exact diagonalization [2,3], series expansion [4], and Monte Carlo simulations [5,6] enable us to understand the hole-dynamics quantitatively, at least to some extent. In particular, these studies all obtained minima of the single-hole dispersion relation at lattice momenta (± π 2a , ± π 2a ) in the Brillouin zone of the square lattice which is in agreement with experimental results [7,8,9].…”