Low energy and dynamical properties of a single hole in the t-Jz model

TL;DR

This paper introduces a technique to analyze dynamical correlation functions in many-body Hamiltonians, applying it to the t-Jz model to reveal low energy properties and spectral weights of a single hole in quantum antiferromagnets.

Contribution

The paper presents a new method for extracting dynamical properties without finite size limitations and applies it to the t-Jz model, providing insights into the ground state and spectral weight behavior.

Findings

Ground state connects continuously with Nagaoka state as J_z approaches zero.

Spectral weight vanishes faster than any power law at the Nagaoka energy for J_z=0.

Spin-charge decoupling is exact on the Bethe lattice but not on more realistic lattices.

Abstract

We review in details a recently proposed technique to extract information about dynamical correlation functions of many-body hamiltonians with a few Lanczos iterations and without the limitation of finite size. We apply this technique to understand the low energy properties and the dynamical spectral weight of a simple model describing the motion of a single hole in a quantum antiferromagnet: the $t-J_z$ model in two spatial dimension and for a double chain lattice. The simplicity of the model allows us a well controlled numerical solution, especially for the two chain case. Contrary to previous approximations we have found that the single hole ground state in the infinite system is continuously connected with the Nagaoka fully polarized state for $J_z \to 0$. Analogously we have obtained an accurate determination of the dynamical spectral weight relevant for photoemission experiments. For $J_z=0$ an argument is given that the spectral weight vanishes at the Nagaoka energy faster than any power law, as supported also by a clear numerical evidence. It is also shown that spin charge decoupling is an exact property for a single hole in the Bethe lattice but does not apply to the more realistic lattices where the hole can describe closed loop paths.