Numerical study of bi-layer two-orbital model for La$_{3}$Ni$_{2}$O$_{7}$ on a plaquette ladder

TL;DR

This study uses large-scale DMRG calculations on a bi-layer two-orbital model for La$_{3}$Ni$_{2}$O$_{7}$ to explore its ground state properties, revealing quasi-long-range correlations and signs of pair density waves relevant to understanding its high-$T_c$ superconductivity.

Contribution

First large-scale DMRG analysis of the bi-layer two-orbital model on a plaquette ladder for La$_{3}$Ni$_{2}$O$_{7}$, identifying key correlation behaviors and potential pair density wave features.

Findings

Spin, charge, and pairing correlations show quasi-long-range behavior.

Sign oscillations in pairing correlations suggest possible pair density wave.

Results provide insights into the microscopic mechanisms of La$_{3}$Ni$_{2}$O$_{7}$ superconductivity.

Abstract

The recently discovered high-$T_c$ superconductivity in La$_{3}$Ni$_{2}$O$_{7}$ with $T_c \approx 80K$ provides another intriguing platform to explore the microscopic mechanism of unconventional superconductivity. In this work, we study a previously proposed bi-layer two-orbital model Hamiltonian for La$_{3}$Ni$_{2}$O$_{7}$ [Y. Shen, et al, Chinese Physics Letters 40, 127401 (2023)] on a plaquette ladder, which is a minimum setup with two-dimensional characteristic. We employ large-scale Density Matrix Renormalization Group calculations to accurately determine the ground state of the model. We determine the density, magnetic structure, and the pairing property of the model. We find that with large effective inter-layer anti-ferromagnetic exchange for the 3$d_{z^2}$ orbital, both spin, charge, and pairing correlation display quasi-long-range behavior, which could be viewed as a precursor of possible true long-range order in the two dimensional limit. Interestingly, sign oscillation for the pairing correlation are observed for both the 3$d_{x^2-y^2}$ and 3$d_{z^2}$ orbitals, indicating the presence of possible pair density wave in the system. Even though we only study the model on a quasi one-dimensional plaquette ladder geometry due to the computational difficulty, the results on the spin, charge, and pairing correlation provide valuable insight in the clarification of the properties of La$_{3}$Ni$_{2}$O$_{7}$ in the future.