Robust fluctuating intertwined charge stripes in the Emery model

TL;DR

This study investigates the presence and characteristics of intertwined charge stripes in the Emery model using advanced numerical techniques, revealing their robustness and connection to nematicity.

Contribution

It provides the first comprehensive analysis of charge stripes in the Emery model, confirming their existence and exploring their relation to nematic fluctuations.

Findings

Oxygen-centered charge stripes confirmed in the Emery model.

Charge density modulation is stronger on p-orbitals along 'the rivers of charge'.

Emergence of unidirectional spin and charge stripes at low temperatures, linked to nematic susceptibility.

Abstract

The single-band Hubbard model is one of the most extensively studied models in condensed matter physics, giving rise to intertwined spin and charge stripes that coexist with, or lie in the vicinity of, superconductivity in the phase diagram. However, whether the low energy physics of the single-band Hubbard model is fully equivalent to the multi-band (multi-orbital) Emery model remains an unsettled question. While the intertwined stripes and nematicity have been studied in the single-band Hubbard model, a comprehensive picture in the Emery model is lacking. In this paper, we focus on the less investigated intertwined charge stripes using complementary density matrix renormalization group (DMRG) and determinant quantum Monte Carlo (DQMC) techniques. Our ground state DMRG confirms the presence of the oxygen-centered charge stripes at a reduced amplitude in the Emery model parameter regime widely used in the study of intertwined stripes. Close analysis of the oxygen orbital structure of the static charge correlation function from DQMC reveals the charge stripe pattern in real-space, showcasing stronger charge density modulation on $p$-orbitals pointing along ``the rivers of charge'', consistent with DMRG. For the parameter set with the largest fermion signs, we managed to reach a temperature where the system first demonstrated tendencies to form purely unidirectional spin and charge stripes, and the $B_{1g}$ component becomes dominant in the bond-charge nematic susceptibility. This observation correlates with the doping dependence of the kinetic energy anisotropy, suggesting a close relation between the nematicity and charge stripes in the Emery model.