The nature of effective interaction in cuprate superconductors: a sign-problem-free quantum Monte-Carlo study

TL;DR

This study uses sign-problem-free quantum Monte Carlo simulations to investigate the effective interactions in cuprate superconductors, highlighting the role of nematic fluctuations in enhancing d-wave pairing and inducing charge density waves.

Contribution

It provides the first large-scale, sign-problem-free simulation of intertwined orders in cuprates, emphasizing the importance of nematic fluctuations in pairing mechanisms.

Findings

Nematic fluctuations are crucial for observed charge density wave order.

Nematic fluctuations enhance d-wave Cooper pairing.

Simulations reveal intertwined antiferromagnetic, superconducting, and charge orders.

Abstract

Superconductivity is an emergent phenomena in the sense that the energy scale associated with Cooper pairing is generically much lower than the typical kinetic energy of electrons. Addressing the mechanism of Cooper pairing amounts to determine the effective interaction that operates at low energies. Deriving such an interaction from a bottom-up approach has not been possible for any superconductor, especially strongly correlated ones. Top-down approaches, where one assumes an effective interaction, is plagued with the difficulty of extracting the implied electronic instabilities without uncontrolled approximations. These facts severely hinder our ability to determine the pairing mechanism for high temperature superconductors. Here we perform large-scale sign-problem-free quantum Monte-Carlo simulations on an effective theory, featured with antiferromagnetic and nematic fluctuations, to study the intertwined antiferromagnetic, superconducting, and charge density wave instabilities of the cuprates. Our results suggest the inclusion of nematic fluctuations is essential in order to produce the observed type of charge density wave ordering. Interestingly we find that the d-wave Cooper pairing is enhanced by nematic fluctuations.