From "weak" to "strong" hole confinement in a Mott insulator

Abstract

We study the problem of a single hole in a Néel antiferromagnet and, using the magnon expansion and analytical methods, determine the expansion coefficients of its wave function in the magnon basis. In the 1D case, the hole is "weakly" localized in a potential well and the magnon coefficients decay exponentially in the absence of a string potential. This behavior is in sharp contrast to the 2D case for which the hole is confined by a string potential and is "strongly" localized with the coefficients decaying superexponentially. The latter is identified here to be a fingerprint of the strings in doped antiferromagnets that can be recognized in the numerical or cold atom simulations of the 2D doped Hubbard model. Finally, we attribute the differences between these cases to the peculiarities of the magnon-magnon interactions.

Hole in the 2D Ising Antiferromagnet: Origin of the Incoherent Spectrum

“…it consists of the well-separated quasiparticle-like peaks with the lowlying ones split by a gap ∝ (J z /t) 2/3 . [2][3][4] The above picture was qualitatively confirmed by a number of works, for example by applying the retraceable path approximation 6 to this problem 2,7 , using the self-consistent Born approximation 3,4,8 whose equations can be analytically written using a closed form 9 , extending the latter one to include the magnon-magnon interactions 10,11 , or designing the so-called magnon expansion method 11 .…”

“…we express the (constrained) electron and spin operators in terms of the (fermionic) hole h † i and (bosonic) magnon a † i operators, cf. 3,4,[9][10][11] . To this end, we first split the lattice into two sublattices A and B, each consisting respectively of spins up and down in the ground state.…”

“…Let us stress that the above slave-fermion transformation is very common to the 'single hole in the antiferromagnet' problems 3,4,[9][10][11] , although note that, unlike e.g. in 3,4 , below magnons are not subject to the linear spin wave approximation.…”

“…1. It turned out that such a process lead to a momentumdependence of the spectral function, though for instance its contribution to the ground state energy is estimated to be relatively small [10][11][12] . Indeed the magnon expansion results 11 , which include the Trugman loops, advocate that the ladder-like spectrum should not be substantially affected by the closed loop processes.…”

“…It turned out that such a process lead to a momentumdependence of the spectral function, though for instance its contribution to the ground state energy is estimated to be relatively small [10][11][12] . Indeed the magnon expansion results 11 , which include the Trugman loops, advocate that the ladder-like spectrum should not be substantially affected by the closed loop processes. Interestingly, Macready and Jacobs 13 consider the t-J z model in the hopping basis and obtain a result that could suggest a breakdown of the ladder spectrum in the t-J z model on a square lattice.…”