SU(2) gauge theory of the pseudogap phase in the two-dimensional Hubbard model

Abstract

We present a SU(2) gauge theory of fluctuating magnetic order in the two-dimensional Hubbard model. The theory is based on a fractionalization of electrons in fermionic chargons and bosonic spinons. The chargons undergo Néel or spiral magnetic order below a density dependent transition temperature $T^{\ast }$. Fluctuations of the spin orientation are described by a non-linear sigma model obtained from a gradient expansion of the spinon action. The spin stiffnesses are computed from a renormalization group improved random phase approximation. Our approximations are applicable for a weak or moderate Hubbard interaction. The spinon fluctuations prevent magnetic long-range order of the electrons at any finite temperature. The phase with magnetic chargon order exhibits many features characterizing the pseudogap regime in high-$T_c$ cuprates: a strong reduction of charge carrier density, a spin gap, Fermi arcs, and electronic nematicity.

17 pages, 7 figures

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• Spin density wave, Fermi liquid, and fractionalized phases in a theory of antiferromagnetic metals using paramagnons and bosonic spinons
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• Commensurate and incommensurate magnetic order in the doped two-dimensional Hubbard model: dynamical mean-field theory analysis
• The foot, the fan, and the cuprate phase diagram: Fermi-volume-changing quantum phase transitions
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• Quantum oscillations in the hole-doped cuprates and the confinement of spinons
• Antiferromagnetic and spin spiral correlations in the doped two-dimensional Hubbard model: gauge symmetry, Ward identities, and dynamical mean-field theory analysis
• Electrons interacting with Goldstone modes and the rotating frame
• Fractionalized Fermi liquids and the cuprate phase diagram
• Non-Perturbative Feats in the Physics of Correlated Antiferromagnets
• Geometric orthogonal metals: Hidden antiferromagnetism and pseudogap from fluctuating stripes
• Canted magnetism and ${\mathbb{Z}}_2$ fractionalization in metallic states of the Lieb lattice Hubbard model near quarter filling
• Mean-field analysis of a Hubbard interaction on Bernal Bilayer Graphene
• Thermopower across Fermi-volume-changing quantum phase transitions without translational symmetry breaking
• Spin susceptibility in a pseudogap state with fluctuating spiral magnetic order
• Yamaji effect in models of underdoped cuprates
• Frequency dependence of temporal spin stiffness and short-range magnetic order in the doped two-dimensional Hubbard model
• Non-Fermi Liquid Behavior of the $t$-$J$ Model in the Strange Metal Phase: $U(1)$ Gauge Theory Consistent with Local Constraints