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Physical Review Letters

Self-consistent renormalized hole motion in a quantum antiferromagnet

Zhixun Su, Y. M. Li, W. Y. Lai, Yu Li

Published Sep 18, 1989• 56 citations
Publisher

Abstract

A new quantum Bogoliubov--De Gennes (BdeG) formalism is developed to study the self-consistent motion of holes on an antiferromagnetic background within the generalized t-J model. The local distortion of spin configurations and the renormalization of the hole motion due to virtual excitations of the distorted spin background are treated on an equal footing. The hole wave function and its spectrum, as well as the effective mass for a propagating hole are calculated explicitly.

DOI
10.1103/physrevlett.63.1318

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A new quantum Bogoliubov--De Gennes (BdeG) formalism is developed to study the self-consistent motion of holes on an antiferromagnetic background within the generalized t-J model. The local distortion of spin configurations and the renormalization of the hole motion due to virtual excitations of the distorted spin background are treated on an equal footing. The hole wave function and its spectrum, as well as the effective mass for a propagating hole are calculated explicitly.
A new quantum Bogoliubov-de Gennes (BdeG) formalism is developed to study the self-consistent motion of holes and spin excitations in a quantum antiferromagnet within the generalized t-J model. On the one hand, the effects of local distortion of spin configurations and the renormalization of the hole motion due to virtual excitations of the distorted spin background are treated on an equal footing to obtain the hole wave function and its spectrum, as well as the effective mass for a propagating hole. On the other hand, the change of the spin excitation spectrum and the spin correlations due to the presence of dynamical holes are studied within the same adiabatic approximation. The stability of the hole states with respect to such changes justifies the self-consistency of the proposed formalism.
Within the Schwinger-boson approach for the t-J model, the single hole problem in a two-dimensional quantum antiferromagnet is studied by using the quantum Bogoliubovde Gennes formalism which treats the distortion of the spin background and quantum spin fluctuations on an equal footing. Several self-trapped localized hole states are found in the distorted spin-background as in the case of an anisotropic Heisenberg model. These localized hole states survive at finite temperatures when the antiferromagnetic order becomes short-ranged. The energy separation between the two lowest states is reduced by considering the spin-background distortion, but it remains finite.
We study a single quasihole excitation in a quantum antiferromagnet using a variational wave function that includes spin-spin as well as spin-hole correlations. The wave function can be cast in the form of a complex correlation operator acting on a Marshall-type wave function for the spin background. Such a correlation operator, featuring momentum-dependent spin-hole correlations, is shown to correspond to a coherent local rotation of the spins, which can be also interpreted as a ``spin-backflow'' current, analogous to the Feynman-Cohen backflow current in helium liquids. The variational Monte Carlo method is used to calculate the hole excitation spectrum on a square lattice for the t-J model with this wave function. Comparing our results with available exact results on a 4\ifmmode\times\else\texttimes\fi{}4 square lattice, we find qualitative and semiquantitative agreement. We provide results obtained on much larger lattices. We find that the quasihole energy band attains its minimum at k=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2) while the hole mass is strongly anisotropic in different directions of k space. The quasihole excitation creates both a planar long-range distortion of the antiferromagnetic (AF) moment of the background \ensuremath{\delta}${\mathit{m}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$(r\ensuremath{\rightarrow}\ensuremath{\infty})\ensuremath{\sim}(k\ensuremath{\cdot}r)/r2{\mathit{r}}^{2}r2 and a ferromagnetic moment localized in the immediate neighborhood of the hole, pointing in the perpendicular direction. The magnitude of the ferromagnetic moment depends on the momentum of the excitation, and at the minimum of the hole band only the long-range AF planar distortion is present.