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Physical review. B, Condensed matter

Hole motion in a coupled-chain model: Some exact results

Indrani Bose, Saurabh Gayen

Published Oct 1, 1993• 60 citations
Publisher

Abstract

Some exact results on single-hole dynamics in a coupled-chain model are derived. The hole moves in the background of a dimer state which is the exact ground state of the model in the absence of the hole. Three different types of exact eigenfunctions have been determined describing (1) the motion of a bound object of the hole and a free spin 1/2 in a sea of singlets, (2) a state in which the bound object of hole and free spin 1/2 stays close to a localized triplet excitation, and (3) a state in which the bound object moves away from the triplet excitation. The energy eigenvalues corresponding to the three eigenfunctions have been exactly determined.

DOI
10.1103/physrevb.48.10653

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Some exact results on single-hole dynamics in a coupled-chain model are derived. The hole moves in the background of a dimer state which is the exact ground state of the model in the absence of the hole. Three different types of exact eigenfunctions have been determined describing (1) the motion of a bound object of the hole and a free spin 1/2 in a sea of singlets, (2) a state in which the bound object of hole and free spin 1/2 stays close to a localized triplet excitation, and (3) a state in which the bound object moves away from the triplet excitation. The energy eigenvalues corresponding to the three eigenfunctions have been exactly determined.
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.
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 state. We start with the t-J Hamiltonian for this model describing two holes in the same octahedron, one in the base and the other at one of the vertex sites of the octahedron. The t-J Hamiltonian consists of three parts: Ht1{\mathit{H}}_{\mathit{t}1}Ht1​, describing the motion of holes along the chain, Ht2{\mathit{H}}_{\mathit{t}2}Ht2​, describing the motion of holes in the bases of the octahedra, and HJ{\mathit{H}}_{\mathit{J}}HJ​, describing the antiferromagnetic spin-spin interaction. Some exact eigenstates of Ht2{\mathit{H}}_{\mathit{t}2}Ht2​ and HJ{\mathit{H}}_{\mathit{J}}HJ​ are constructed. Successive applications of Ht1{\mathit{H}}_{\mathit{t}1}Ht1​ on some of these states show two types of localization for one of the holes. In one type of localization one of the holes is localized at its original location while the other hole moves. In the other type of localization, a hole, located in the base of an octahedron, cannot move away from the other hole sitting at a vertex site of the same octahedron. The localization in both cases is produced by the topology of the lattice on which the t-J model is defined.
We compare ground-state properties as well as spin and single-particle excitation spectra of a single dopant-induced hole carrier in strong-coupling-limit single-orbital and three-orbital Hubbard model lattices with up to 16 square lattice sites. Our results indicate that there is a close correspondence in their ground-state and low-lying excited-state properties, consistent with the recent proposal by Zhang and Rice (ZR). For the three-orbital model, we also find direct spectroscopic evidence for the singlet-triplet excitation gap associated with the dopant-induced ZR Cu-O spin-hole singlet state.