Quasiparticle structure and coherent propagation in the $t-J_z-J_{\perp }$ model

Abstract

Numerical studies, from variational calculation to exact diagonalization, all indicate that the quasiparticle generated by introducing one hole into a two-dimensional quantum antiferromagnet has the same nature as a string state in the $t-J_z$ model. Based on this observation, we attempt to visualize the quasiparticle formation and subsequent coherent propagation at low energy by studying the generalized $t-J_z-J_{\perp }$ model in which we first diagonalize the $t-J_z$ model and then perform a {\em degenerate} perturbation in $J_{\perp }$. We construct the quasiparticle state and derive an effective Hamiltonian describing the coherent propagation of the quasiparticle and its interaction with the spin wave excitations in the presence of the Néel order. We expect that qualitative properties of the quasiparticle remain intact when analytically continuing $J_{\perp }$ from the anisotropic $J_{\perp }<J_z$ to the isotropic $J_{\perp }=J_z$ limit, despite the fact that the spin wave excitations change from gapful to gapless. Extrapolating to $J_{\perp }=J_z$, our quasiparticle dispersion and spectral weight compare well with the exact numerical results for small clusters.

Revised with minor changes and references updated. To appear in Phys. Rev. B., Jan. 1996. 10 pages, The complete PostScript file including figures can be obtained via ftp at ftp://serval.berkeley.edu/tjzjp.ps . It is also posted in the WEB site of Niels Bohr Institute at http://roemer.fys.ku.dk/recent.htm

References in corpus (12)

• Correlated Electrons in High Temperature Superconductors
• Theory of Two-Dimensional Quantum Heisenberg Antiferromagnets with a Nearly Critical Ground State
• Universal quantum critical dynamics of two-dimensional antiferromagnets
• Toward a Unified Magnetic Phase Diagram of the Cuprate Superconductors
• Quasiparticle Dispersion of the 2D Hubbard Model: From an Insulator to a Metal
• Universal Magnetic Properties of $L{a}_{2-\delta }S{r}_{\delta }Cu{O}_4$ at Intermediate Temperatures
• Quasiparticle dispersion of the t-J and Hubbard models
• Dynamical Properties of a Single Hole in an Antiferromagnet
• Quantum Critical Scaling in a Moderately Doped Antiferromagnet
• Validity of the rigid band picture for the t-J model
• Spin bags in the doped t-J model
• Hole Pockets in the Doped 2D Hubbard Model

Cited by in corpus (4)

• Spectral Properties of the Generalized Spin-Fermion Models
• Excitations in antiferromagnetic cores of superconducting vortices
• Optical conductivity of strongly correlated electron systems
• Composite quasiparticle formation and the low-energy effective Hamiltonians of the one- and two-dimensional Hubbard Model