Quasiparticle structure and coherent propagation in thet-Jz-J⊥

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 − Jz model. Based on this observation, we attempt to visualize the quasiparticle formation and subsequent coherent propagation at low energy by studying the generalized t − Jz − J ⊥ model in which we first diagonalize the t − Jz model and then perform a degenerate perturbation in J ⊥ . 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 ⊥ from the anisotropic J ⊥ < Jz to the isotropic J ⊥ = Jz limit, despite the fact that the spin wave excitations change from gapful to gapless. Extrapolating to J ⊥ = Jz, our quasiparticle dispersion and spectral weight compare well with the exact numerical results for small clusters.

Composite quasiparticle formation and the low-energy effective Hamiltonians for the one- and two-dimensional Hubbard model

“…We expect that the results for the coefficients α(r) and λ(r) calculated in Ref. 20 remain a good estimate so long as the correlation length (or time) of the antiferromagnetic order remains long. The two parameters, α( √ 2) and α(2), describe a quasiparticle band of a width of order 2J, with the minimum at (π/2, π/2) and extended van Hove regions around (π, 0) and (0, π).…”

“…9,11,20 As the soliton moves, it leaves behind a string of overturned spins which cost antiferromagnetic energy. This energy cost inhibits the motion of the soliton and mimics the effects of a linearly confining potential.…”

“…The bound state of the soliton in this potential is the quasiparticle. 20 It is important to point out that spin flipping processes in principle can erase the string of frustrated bonds behind the soliton and enable it to escape the potential. If that happens the quasiparticle is no longer well defined.…”

“…To find the effective action for the quasiparticle propagation, we need to generalize the quasiparticle construction in Ref. 20 to allow a smoothly fluctuating spin background. Since the dressing envisioned in Ref.…”

Spectral Properties of the Generalized Spin-Fermion Models

“…For the explicit approximate calculation of the elements of the mass operator it is convenient to write down the GFs in (44) in terms of correlation functions by using the well-known spectral theorem [26]:…”