Exact Diagonalization Study of Strongly Correlated Electron Models: Hole pockets and shadow bands in the doped t-J model

TL;DR

This study uses exact diagonalization to analyze the doped t-J model, revealing small hole pockets and shadow bands, supporting a Fermi-liquid picture with non-Luttinger Fermi surface in doped cuprates.

Contribution

It demonstrates the rigid-band behavior, identifies small hole pockets, and constructs spin-bag operators to describe doped holes in the t-J model, linking numerical results with experimental observations.

Findings

Rigid-band behavior observed in spectral functions

Identification of small hole pockets as Fermi surface

Elementary excitations well described by weakly-interacting quasiparticles

Abstract

A detailed exact-diagonalization study is made for the doping dependence of the single-particle spectral function $A({\bf k},\omega)$ and momentum distribution function $n({\bf k})$ of the two-dimensional $t$$-$$J$ model as a representative model for doped Mott insulators. The results for $A({\bf k},\omega)$ show unambiguously that the rigid-band behavior is realized in the small-cluster $t$$-$$J$ model: upon doping, the uppermost states of the quasiparticle band observed at half filling simply cross the Fermi level and reappear as the lowermost states of the inverse photoemission spectrum, while the photoemission side of the band remains essentially unaffected. We discuss problems in directly determining the Fermi surface from $n({\bf k})$ and make a situation where they are largely avoided; we then find clear signatures of a Fermi surface which takes the form of small hole pockets. The identical scaling with $t/J$ of the quasiparticle weight $Z_h$ and difference in $n({\bf k})$ between neighboring ${\bf k}$-points suggests the existence of such a Fermi surface in the physical regime of parameters. We construct spin-bag operators which describe the holes dressed by the antiferromagnetic spin fluctuations and find that elementary electronic excitations of the system can be described well in terms of weakly-interacting spin-1/2 Fermionic quasiparticles corresponding to the doped holes. We make a comparison with other numerical calculations and recent angle-resolved photoemission experiment and argue that, adopting this rather conventional Fermi-liquid scenario with non-Luttinger Fermi surface, one would explain many quasiparticle-relating properties of doped cuprates in a very simple and natural way. We also show that the dynamical spin and charge excitations deviate from the particle-hole excitations of this Fermi liquid: e.g., the dominant low-energy spin excitation at momentum transfer $(\pi,\pi)$ reflects excitations of the incoherent spin background and is identified as a collective mode comparable to spin waves in the Heisenberg antiferromagnet.