Low-energy states with different symmetries in thet−Jmodel with two holes on a 32-site lattice

Abstract

We study the low-energy states of the t-J model with two holes on a 32-site lattice with periodic boundary conditions. In contrary to common belief, we find that the state with d x 2 Ϫy 2 symmetry is not always the ground state in the realistic parameter range 0.2рJ/tр0.4. There exist low-lying finite-momentum p states whose energies are lower than the d x 2 Ϫy 2 state when J/t is small enough. We compare various properties of these low-energy states at J/tϭ0.3 where they are almost degenerate and find that those properties associated with the holes ͑such as the hole-hole correlation and the electron momentum distribution function͒ are very different between the d x 2 Ϫy 2 and p states, while their spin properties are very similar. Finally, we demonstrate that by adding ''realistic'' terms to the t-J model Hamiltonian, we can easily destroy the d x 2 Ϫy 2 ground state. This casts doubt on the robustness of the d x 2 Ϫy 2 state as the ground state in a microscopic model for the hightemperature superconductors.

A phenomenological theory of the anomalous pseudogap phase in underdoped cuprates

“…An extrapolation from finite size clusters to the infinite lattice, however, suggests that the pair state is no longer the ground state at J /t = 0.3, but an excited state with an energy of approximately 0.17t [143]. The inclusion of longer range interactions and hopping in the t-J model increases the energy of the pair state further and confirms the conclusion that for parameter values relevant to cuprates the ground state of the cluster has two unbound holes in the nodal states [144]. Extending the calculations to the 32-site clusters with 4 holes, which corresponds to a doping of 1/8, shows all four holes entering into nodal states with no signs of pairing correlations [145].…”

“…However, at present there is no information on this question to the best of our knowledge. Leung and collaborators [143][144][145] concluded from these calculations that at low densities holes entered the nodal regions, consistent with nodal Fermi pockets. The low energy d-wave pair excited state is interpreted as a finite energy cooperon in the strong coupling t-J model and its extensions.…”

“…The only limitation in these calculations is the finite cluster size which currently is limited to small clusters containing up to 32 sites and 1, 2 and 4 holes. Leung and his collaborators [143][144][145] have reported a series of calculations for these clusters using the strong coupling t-J model, which describes the Hubbard model near half-filling and its extensions to include longer range hopping and interactions. The main conclusions of these cluster calculations are as follows.…”

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].…”

Magnetically mediated hole pairing in fermionic ladders of ultracold atoms

“…While the magnetic degree of freedom favours the pairing of holes, the bound state is frustrated due to Pauli blocking causing a kinetic energy cost for two holes at close distance. This intricate interplay of magnetic and kinetic energy not only complicates theoretical investigations but also also leads to small binding energies [25,26] rendering pairing challenging to observe at temperatures of state-of-the-art quantum simulators [27].…”