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Journal of Physics Condensed Matter

Single-hole dynamics in a coupled-chain model

Indrani Bose, Saurabh Gayen

Published Jul 18, 1994• 6 citations
Publisher

Abstract

The single-hole dynamics in a coupled-chain model described by the t-t'-J model is studied. The excitation spectrum is obtained exactly and analytically and shows a structure consisting of bound, antibound and extended states. Based on the exact results obtained, the possibility of a localization-to-delocalization transition for the hole is conjectured.

DOI
10.1088/0953-8984/6/29/001

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The single-hole dynamics in a coupled-chain model described by the t-t'-J model is studied. The excitation spectrum is obtained exactly and analytically and shows a structure consisting of bound, antibound and extended states. Based on the exact results obtained, the possibility of a localization-to-delocalization transition for the hole is conjectured.
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We present a unified account for the coupled single-hole and spin dynamics in the spin-gap phase of dimerized and frustrated spin chains and two-leg spin ladders. Based on the strong dimer limit of a one-dimensional t1,2,3{t}_{1,2,3}t1,2,3​-J1,2,3{J}_{1,2,3}J1,2,3​ model a diagrammatic approach is presented that employs a mapping of the spin Hamiltonian onto a pseudofermion bond-boson model. Results for the single-hole spectrum are detailed. A finite quasiparticle weight is observed and studied for a variety of system parameters. A comparison with existing exact-diagonalization data is performed and good agreement is found.
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An antiferromagnetic spin model (S=1/2) consisting of a chain of octahedra is considered. In a certain parameter regime of the Hamiltonian the exact ground state is a local resonating-valence-bond (RVB) state. We start with the t-J Hamiltonian for this model describing a single hole in the system and derive exact ground and excited states of the Hamiltonian when the hole is static. The local spin distortion around a hole is termed a spin polaron. The dynamics of the hole is studied through construction of exact eigenstates describing spin polarons in extended states. Coherent states for all momentum wave vectors in the chain direction exist for certain spin polarons. In the Nagaoka limit, the RVB polaronic states have energy greater than that of the ferromagnetic state. For exchange interaction J\ensuremath{\ne}0, the RVB states have lower energy. Other exact states obtained include states in which the hole motion is localized. Structural similarity of the present model to the arrangement of Cu spins in La2{\mathrm{La}}_{2}La2​CuO4{\mathrm{CuO}}_{4}CuO4​ is also highlighted.
We study the dynamics of one hole in the polarized t-J model. The model describes the physics of holes in polarized antiferromagnetic systems and the one-particle excitations in strong-coupling superconductors as well. The spectral densities of a single hole are calculated numerically using exact diagonalization of small clusters with toroidal boundary conditions. The quasiparticle spectrum is analyzed in detail. We show that a coherent quasiparticle peak is well defined for J/t>0.2. The dispersion relation of the quasiparticle is obtained for different magnetizations. The results are used to discuss the characteristics of one-particle excitations in small-coherence-length superconductors.