Two Holes in the t–J Model Form a Bound State for Any Nonzero J/t

Abstract

Determination of the parameter regime in which two holes in the t-J model form a bound state represents a long standing open problem in the field of strongly correlated systems. By applying and systematically improving the exact diagonalization method defined over a limited functional space (EDLFS), we show that the average distance between two holes scales as d ∼ 2(J/t) −1/4 for J/t < 0.15, therefore providing strong evidence that two holes in the t-J model form the bound state for any nonzero J/t. However, the symmetry of such bound pair in the ground state is p-wave. This state is consistent with phase separation at finite hole filling, as observed in a recent study [Maska et al, Phys. Rev. B 85, 245113 (2012)].

Local properties of the t-J model in a two-pole approximation within COM

“…This clearly shows that our solution correctly captures the behavior in this regime, consistently with the well-established AF Nï¿oeel state at half filling. The FM phase in the t-J model has been predicted in the literature [28,29,[33][34][35][36][37][38][39][40][41]: mobile holes can form Nagaoka polarons which results in a FM ordering [38,40]. We witness a similar behavior here, i.e., once enough holes are present in the system, FM correlations clearly emerge and they overcome the AF ones, whose correlation lengths decrease rapidly with doping [35].…”

“…Yet, Nagaoka proved that in the infinite-U regime of the Hubbard model, which corresponds to vanishing exchange integral in the t-J model, if we introduce one hole into the system the ground state becomes ferromagnetic (FM) [30][31][32]. This idea got generalized in the t-J model by so many successive studies which showed transition to FM phase for finite hole dopings [33][34][35][36][37][38][39][40][41].…”

Exploration of doped quantum magnets with ultracold atoms

“…However, at low doping a strong pairing mechanism of holes into molecular pairs, which would be required deep in a BEC regime, remains elusive. Theoretically it has become clear that pairing is possible at low doping in the t − J model [206,134,200,21], but it is not very robust to parameter changes. Recently broad numerical analysis by the Simons Collaboration has produced mounting evidence that the clean 2D Hubbard model may not support a superconducting ground state in the relevant regime, although the addition of next-nearest neighbor hopping terms t may support it [161].…”

Strong pairing in mixed dimensional bilayer antiferromagnetic Mott insulators

“…We demonstrate that the interplay of potential energy, arising from the string tension, and kinetic energy of the partons leads to large binding energies for mesonic pairs of chargons. Our work goes beyond earlier analysis [28][29][30][31][32] by including adverse effect that suppress pairing in a generic system. Effects detrimental to pairing will be suppressed in the mixed dimensional bilayer model we propose, featuring overwhelmingly attractive emerging parton interactions.…”