Two-hole bound states from a systematic low-energy effective field theory for magnons and holes in an antiferromagnet

Abstract

Identifying the correct low-energy effective theory for magnons and holes in an antiferromagnet has remained an open problem for a long time. In analogy to the effective theory for pions and nucleons in QCD, based on a symmetry analysis of Hubbard and t-J-type models, we construct a systematic low-energy effective field theory for magnons and holes located inside pockets centered at lattice momenta (±). The effective theory is based on a nonlinear realization of the spontaneously broken spin symmetry and makes model-independent universal predictions for the entire class of lightly doped antiferromagnetic precursors of high-temperature superconductors. The predictions of the effective theory are exact, order by order in a systematic low-energy expansion. We derive the one-magnon exchange potentials between two holes in an otherwise undoped system. Remarkably, in some cases the corresponding two-hole Schrödinger equations can even be solved analytically. The resulting bound states have d-wave characteristics. The ground state wave function of two holes residing in different hole pockets has a d x 2 −y 2 -like symmetry, while for two holes in the same pocket the symmetry resembles d xy .

Loop-cluster simulation of the zero- and one-hole sectors of thet−Jmodel on the honeycomb lattice

“…This powerful method was used to systematically construct the effective theory for t-Jtype models on the square lattice in [15,16,36]. The effective theories were used to investigate the one-magnon exchange potential and the resulting bound states between two holes and two electrons as well as the possible existence of spiral phases [16,36,37]. Using the information about the location of the pockets and based on the symmetry properties of the underlying microscopic theory, we have constructed a systematic low-energy effective theory for the t-J model on the honeycomb lattice.…”

“…The physics of the undoped systems is quantitatively described by magnon chiral perturbation theory [10,11,12,13,14], while the interactions of magnons and holes are described by a low-energy effective theory for hole-doped antiferromagnets [15,16]. Predictions of the effective theory only depend on a small number of low-energy constants which can be determined from either experiments or Monte Carlo data.…”

Spiral phases and two-particle bound states from a systematic low-energy effective theory for magnons, electrons, and holes in an antiferromagnet

“…In the pure magnon sector, due to the spin stiffness ρ s , a spiral costs more energy than the homogeneous configuration. However, due to the hole-one-magnon vertex in the effective action [1], some of the fermions can gain energy in the spiral background, which provides a mechanism for stabilizing a spiral. Based on analytical calculations, in [3], we work out how the hole pockets are populated and whether a homogeneous or a spiral phase in the staggered magnetization is realized depending on the low-energy parameters ρ s , Λ and the hole mass.…”

“…We have systematically constructed a low-energy effective field theory for hole-and electron-doped antiferromagnets [1,2]. The construction relies on basic principles of quantum field theory as well as on a symmetry analysis of the Hubbard or t-J model.…”

“…For reasons of space limitations, here we are not going to show the terms in the effective action. The reader will find all terms properly constructed and listed in [1] for hole doping and in [2] for electron doping.…”