Spin susceptibility in a pseudogap state with fluctuating spiral magnetic order

We compute the electron spin susceptibility in the pseudogap regime of the two-dimensional Hubbard model in the framework of a SU(2) gauge theory of fluctuating magnetic order. The electrons are fractionalized in fermionic chargons with a pseudospin degree of freedom and bosonic spinons. The chargons are treated in a renormalized mean-field theory and order in a Néel or spiral magnetic state in a broad range around half-filling below a transition temperature $T^$. Fluctuations of the spin orientation are captured by the spinons. Their dynamics is governed by a non-linear sigma model, with spin stiffnesses computed microscopically from the pseudospin susceptibility of the chargons. The SU(2) gauge group is higgsed in the chargon sector, and the spinon fluctuations prevent breaking of the physical spin symmetry at any finite temperature. The electron spin susceptibility obtained from the gauge theory shares many features with experimental observations in the pseudogap regime of cuprate superconductors: the dynamical spin susceptibility $S(\mathbf{q},ω)$ has a spin gap, the static uniform spin susceptibility $κ_s$ decreases strongly with temperature below $T^$, and the NMR relaxation rate $T_1^{-1}$ vanishes exponentially in the low temperature limit if the ground state is quantum disordered. At low hole doping, $S(\mathbf{q},ω)$ exhibits nematicity below a transition temperature $T_{\rm nem} < T^$, and at larger hole doping in the entire pseudogap regime below $T^$.

💡 Research Summary

In this paper the authors develop a comprehensive theory of the spin response in the pseudogap regime of the two‑dimensional Hubbard model by employing an SU(2) gauge formulation of fluctuating magnetic order. The central idea is to fractionalize the physical electron operator into a fermionic “chargon” ψ that carries charge and a pseudospin index, and a bosonic SU(2) matrix field R (the spinon) that encodes the local orientation of the spin quantization axis. This decomposition introduces a redundant SU(2) gauge symmetry, which is treated explicitly throughout the work.

The chargons are handled within a renormalized mean‑field framework. The authors first obtain momentum‑dependent effective interactions from a functional renormalization‑group (FRG) flow, then replace the bare Hubbard U by a static renormalized coupling (\bar U) evaluated at the wave vector where the magnetic susceptibility is maximal. Solving the mean‑field equations yields self‑consistent magnetic order parameters Δm and ordering wave vectors Q. In a broad region of the phase diagram the lowest‑energy solution is a planar spiral with Q = (π−2π η, π) (or symmetry‑related equivalents), while near half‑filling a Néel state (Q = (π, π)) also appears. The quasiparticle spectrum consists of two bands (E_{\pm}(\mathbf{k})) split by the magnetic gap Δm.

Fluctuations of the spin orientation are captured by the spinon field. Integrating out the chargons to quadratic order in the SU(2) gauge fields generates an effective action for the gauge fields of the form
(S