Universal magnetic energy scale in the doped Fermi-Hubbard model

TL;DR

Recent experiments on doped Fermi-Hubbard systems reveal a universal magnetic energy scale, $J^*$, governing static and dynamic magnetic properties, pseudogap onset, and magnetic phase stability.

Contribution

The paper introduces a theoretical framework showing that a single doping-dependent energy scale $J^*$ explains various magnetic phenomena in doped Mott insulators.

Findings

A universal magnetic energy scale $J^*$ emerges at finite doping.

The bimagnon peak in lattice spectroscopy is set by $J^*$.

The pseudogap temperature $T^*$ is proportional to $J^*$.

Abstract

Magnetic correlations of doped Mott insulators hold the key to the unusual characteristics of many quantum materials. Recent experiments with ultracold atoms in optical lattices have provided new information about the magnetic properties of the Fermi-Hubbard model on a square lattice. We demonstrate that recent measurements indicate that a single doping-dependent energy scale determines both static correlations and dynamical response of these systems. To understand these experimental findings, we employ a self-consistent formalism to describe the coupling between antiferromagnetic magnons and doped holes, and we uncover the emergence of a universal magnetic energy scale at finite doping, which we denote by $J^*$. We present the single- and two-magnon spectral properties at finite doping and discuss the appearance of a bimagnon peak in lattice-modulation spectroscopy, at frequencies set by $J^*$. Furthermore, we argue that this same energy scale sets the onset of pseudogap phenomena, leading to the hypothesis $k_BT^* = c J^*$, with $c$ an order one number. We identify another low-energy scale emerging from our analysis of magnetic excitations, and argue that it controls the stability of N\'{e}el order at the lowest temperatures, ultimately driving a transition to an incommensurate spin-density-wave at finite doping. We discuss the relation between this low-energy scale and the nature of fermionic quasiparticles. Our analysis suggests that stability of the commensurate antiferromagentic phase at finite doping can be controlled experimentally by introducing additional quasiparticle broadening via disorder or low-frequency noise.