New insights into the problem of a single hole in an antiferromagnet

While undoped cuprates are in general very well understood as Mott or charge-transfer insulators, the doped cuprates are still enigmatic in many ways posing a great challenge for modern physicists who study them. Probably "the easiest from the hardest" is the problem of a single hole introduced to the undoped Mott insulator (antiferromagnet). An example of models, often studied in connection to the single-hole physics in undoped cuprates, are for example Hubbard model or the t-J model. Here we study the t-J model and its strongly anisotropic (Ising) limit, the t-Jz model. We cover four cases: (a) 1D t-Jz model, t-Jz model on a Bethe lattice with coordination z = 4, (c) 2D t-Jz model on a square lattice, and (d) 1D t-J model. We study each case by going to magnon-holon basis by means of slave-fermion and Holstein-Primakoff transformations. This allows us to directly systems of different dimensionality and to investigate the role of the magnon-magnon interactions in all the cases.

In each case, we provide new insights into the problem of a single hole introduced to the undoped system. Often neglected in the broad literature magnon-magnon interactions turn out to be crucial in determining properties of the single-hole ground state and spectral function. Moreover, an infinitesimal perturbation of the magnon-magnon interactions breaks the spin-charge separation in 1D in favor of the spin polaron ground state. This may have important consequences for the interpretation of angle-resolved photoemission spectroscopy on quasi-1D cuprates where a small but finite interchain coupling can be approximately modeled by rescaled magnon-magnon interactions. Studying the expansion coefficients of the ground state wave function in magnon-holon basis we discover that the superexponential decay of the cloud of magnons around the hole is a fingerprint of a discrete linear potential acting on that hole. When the hole feels only a point potential the decay is exponential. We also discover new two types of states present in the spectral function of a single hole in a 2D t-Jz model on a square lattice. Besides well-known vibrational modes ~(J/t)^(2/3) a substantial part of the spectral function is incoherent with energy states densely packed. This stands in contradiction to the general belief that the spectral function of a single hole in the 2D t-Jz model is ladder-like. Additionally, a symmetry of the square lattice allows for the hybridization of the vibrational modes with rotational modes, which results in the appearance of states linear in J/t. We explain in detail the origin of linear behavior as well as the reasons for hybridization.