Charge and Spin Structures of a $d_{x^2 - y^2}$ Superconductor in the Proximity of an Antiferromagnetic Mott Insulator

TL;DR

This study uses quantum Monte Carlo simulations to explore how an added interaction in the Hubbard model induces a transition from an antiferromagnetic Mott insulator to a $d_{x^2 - y^2}$ superconductor, revealing finite-temperature Kosterlitz-Thouless behavior.

Contribution

It demonstrates that a specific interaction term can drive a quantum phase transition and characterizes the finite-temperature superconducting transition in the Hubbard model.

Findings

Interaction $W$ induces a transition to $d_{x^2 - y^2}$ superconductivity.

Evidence of a Kosterlitz-Thouless transition at finite temperature.

Development of a pseudogap and spin susceptibility features near $T_{KT}$.

Abstract

To the Hubbard model on a square lattice we add an interaction, $W$, which depends upon the square of a near-neighbor hopping. We use zero temperature quantum Monte Carlo simulations on lattice sizes up to $16 \times 16$, to show that at half-filling and constant value of the Hubbard repulsion, the interaction $W$ triggers a quantum transition between an antiferromagnetic Mott insulator and a $d_{x^2 -y^2}$ superconductor. With a combination of finite temperature quantum Monte Carlo simulations and the Maximum Entropy method, we study spin and charge degrees of freedom in the superconducting state. We give numerical evidence for the occurrence of a finite temperature Kosterlitz-Thouless transition to the $d_{x^2 -y^2}$ superconducting state. Above and below the Kosterlitz-Thouless transition temperature, $T_{KT}$, we compute the one-electron density of states, $N(\omega)$, the spin relaxation rate $1/T_1$, as well as the imaginary and real part of the spin susceptibility $\chi(\vec{q},\omega)$. The spin dynamics are characterized by the vanishing of $1/T_1$ and divergence of $Re \chi(\vec{q} = (\pi,\pi), \omega = 0)$ in the low temperature limit. As $T_{KT}$ is approached $N(\omega)$ develops a pseudo-gap feature and below $T_{KT}$ $Im \chi(\vec{q} = (\pi,\pi), \omega)$ shows a peak at finite frequency.