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

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 non-linear 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 around the Brillouin zone diagonals.

Figures (7)

• Figure 1: Feynman diagrams representing the RPA contributions to the gauge kernel: bare paramagnetic contribution, interaction correction, diamagnetic contribution.
• Figure 2: Effective interaction $\bar{U}$ as a function of density for $t'=-0.15t$ and $t'=-0.3t$. The polynomial fit is used for $\bar{U}(n)$ in all subsequent results. The bare interaction is $U=5t$ in all plots.
• Figure 3: $x$ coordinates of the dominant charge and spin ordering wave vectors as a function of the electron density $n$ for $U=5t$ and $T=0.02t$. Left: $t'=-0.15$, right: $t'=-0.3t$.
• Figure 4: Quasi-particle Fermi surfaces (red lines) of two stripe states with periodicities $p=5$ (left) and $p=14$ (right), presented in the full Brillouin zone (repeated zone scheme). The Fermi surface of the corresponding non-interacting system (blue lines) is shown in the same repeated zone scheme for comparison. The black box in the center indicates the (reduced) magnetic Brillouin zones corresponding to the reduced translation invariance of the stripe ordered state. Parameters: $t'=-0.15t$, $n=0.83$, $T=0.02t$ (left), $t'=-0.3t$, $n=0.799$, $T=0.02t$ (right).
• Figure 5: Spatial stiffness in $x$ direction $J_{xx}$ and temporal stiffness $Z$ as functions of density in the stripe ordered regime for $t'=-0.15t$ and various low temperatures $T = 0.02t, 0.03t, 0.04t, 0.05t$. The periodicities $p$ of the stripe order, which minimize the free energy within the restricted set $p \in \{ 1,2,\dots,16 \}$, are indicated by different colors. Larger stiffnesses (at a given density) correspond to lower temperatures.