TL;DR
This paper develops an approximate theoretical framework for the dynamics of Heisenberg spin ladders, using a bond-Boson mapping, and extends it to analyze hole doping effects with good agreement to numerical results.
Contribution
It introduces a novel bond-Boson based approximation for spin ladder dynamics and incorporates hole coupling, providing accurate predictions aligned with Lanczos calculations.
Findings
Strong quantum fluctuation renormalization observed.
Good agreement between theoretical and Lanczos results for spin correlations.
Accurate spectral functions for hole dynamics predicted.
Abstract
We derive an approximate theory for Heisenberg spin ladders with two legs by mapping the spin dynamics onto the problem of hard-core `bond-Bosons'. The parameters of the Bosonic Hamiltonian are obtained by matching anomalous Green's functions to Lanczos results and we find evidence for a strong renormalization due to quantum fluctuations. Various dynamical spin correlation functions are calculated and found to be in good agreement with Lanczos results. We then enlarge the effective Hamiltonian to describe the coupling of the bond-Bosons to a single hole injected into the system and treat the hole-dynamics within the `rainbow-diagram' approximation by Schmidt-Rink et. al. Theoretical predictions for the single hole spectral function are obtained and found to be in good agreement with Lanczos results.
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