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arXiv:2603.13071 · Physical review. B./Physical review. B

SU(2) gauge theory of fluctuating stripe order in the two-dimensional Hubbard model

Henrik Müller-Groeling, Pietro M. Bonetti, Paulo Forni, Walter Metzner

Published Aug 13, 2026• 0 citations
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Abstract

We present an SU(2) gauge theory of fluctuating stripe order in the two-dimensional Hubbard model. The theory is based on a fractionalization of the electron operators in fermionic chargons with a pseudospin degree of freedom, and charge-neutral spinons capturing fluctuations of the spin orientation. The chargons are treated in a renormalized mean-field theory. We focus on regions of the phase diagram where they undergo stripe order. The spinons are described by a nonlinear sigma model with pseudospin stiffnesses determined by the chargons. They prevent breaking of the physical SU(2) spin symmetry at any finite temperature, resulting in a charge-ordered pseudogap phase with a reconstructed Fermi surface and a spin gap. The spectral function for single-particle excitations exhibits a collection of Fermi arcs and other structures. The arcs appear in various regions of the Brillouin zone, but never exclusively near the Brillouin zone diagonals. For a suitable choice of the bare dispersion relation, the form of the low energy spectral function resembles experimental observations from angular resolved photoemission on cuprates in which stripe fluctuations play an important role.

DOI
10.1103/tksj-ywhm

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This thesis deals with the Hubbard model as prototypical model to describe the physics of electrons in the two-dimensional copper-oxide planes of high-TcT_cTc​ cuprates. To get approximate solutions, we employ functional renormalization group (fRG) and dynamical mean-field theory (DMFT) methods. We deal with the problem of identifying bosonic fluctuations in the vertex function, exhibiting an intricate dependence on momenta and frequencies already at moderate coupling. In the normal, paramagnetic phase, the goal is achieved by employing the recently introduced single-boson exchange decomposition. In the symmetry-broken phases, we reformulate the previously introduced combination of fRG with mean-field theory by explicitly introducing a bosonic field. A widely discussed and challenging problem is the emergence of a pseudogap in the Hubbard model. In this thesis we assume this phase to be characterized by strong magnetic fluctuations. Following previous works, we fractionalize the electron in a chargon, carrying the electron's charge, and a charge neutral spinon, which represents local fluctuations of the spin orientation. The chargons undergo Néel or spiral magnetic order below a density-dependent transition temperature T∗T^*T∗. We compute DC charge transport coefficients for the chargons, and obtain a pronounced drop in the charge carrier density across the magnetic-to-paramagnetic transition. Directional fluctuations of the spin orientation are described by a non-linear sigma model and prevent long-range ordering of the electrons at any finite temperature. The phase where the chargon degrees of freedom are magnetically ordered shares many features with the pseudogap regime observed in high-TcT_cTc​ cuprates: a strong reduction of the charge carrier density, a spin gap, Fermi arcs, and electronic nematicity.
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