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HOLES IN A 2-DIMENSIONAL QUANTUM ANTIFERROMAGNET

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Published Sep 10, 2026• 0 citations
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Abstract

A brief review is presented on the studies of the hole motion in a two-dimensional quantum antiferromagnet. An extended introduction is given to cover the background of the problem. The quantum Bogoliubov-de Gennes formalism which treats the local distortion of the spin configuration and the quantum renormalization process on an equal footing, is outlined. The latest development on the central issue, whether a hole can freely propagate on an antiferromagnetic background, is overviewed.

DOI
10.82444/warw.33550075

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A brief review is presented on the studies of the hole motion in a two-dimensional quantum antiferromagnet. An extended introduction is given to cover the background of the problem. The quantum Bogoliubov-de Gennes formalism which treats the local distortion of the spin configuration and the quantum renormalization process on an equal footing, is outlined. The latest development on the central issue, whether a hole can freely propagate on an antiferromagnetic background, is overviewed.
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.
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.