Fractional Fermi liquid in a generalized $t-J$ model

TL;DR

This paper introduces a fractional Fermi liquid phase in a generalized $t-J$ model inspired by nickelate superconductors, revealing a small Fermi pocket on a spin liquid that violates Luttinger’s theorem, supported by mean field and DMRG analyses.

Contribution

It identifies a robust FL* phase in a generalized $t-J$ model and connects it to a 1D fractional Luttinger liquid, providing new insights into nickelate superconductors.

Findings

Discovery of a stable FL* phase across doping levels.

Verification of the FL* state using DMRG simulations.

Connection between FL* and Luttinger liquids via a quantum phase transition.

Abstract

Inspired by the recent discovery of superconductivity in the nickelate Nd$_{1-x}$Sr$_x$NiO$_2$, we study a generalized $t-J$ model to investigate the correlated phases induced by doping spin-one Ni$^{2+}$ into a spin $1/2$ Mott insulator formed by Ni$^{1+}$. Based on a three-fermion parton mean field analysis, we identify a robust fractional Fermi liquid (FL*) phase for almost every doping level. The FL* state is characterized by a small Fermi pocket on top of a spin liquid, which violates the Luttinger theorem of a conventional Fermi liquid and is an example of a symmetric pseudogap metal. Furthermore, we verify our theory in one dimension through density matrix renormalization group (DMRG) simulations on both the generalized $t-J$ model and a two-orbital Hubbard model. The fractional Fermi liquid reduces to fractional Luttinger liquid (LL*) in one dimension, which is connected to the conventional Luttinger liquid through a continuous quantum phase transition by tuning interaction strength. Our findings offer new insights into correlated electron phenomena in nickelate superconductors and other multi-orbital transition metal oxide with spin-triplet $d^8$ state.