Electrons interacting with Goldstone modes and the rotating frame

Abstract

We consider electronic systems with a spontaneously broken continuous symmetry. The scattering vertex between electrons and Goldstone modes is calculated over the entire Brillouin zone using the random phase approximation. This calculation reveals two things: (1) electrons always couple to both $\varphi$ and ${\partial }_t\varphi$, where $\varphi$ is the Goldstone field, and (2) quasi-particles in a state with continuous symmetry breaking have to be defined in a rotating frame, which locally follows the fluctuations of the order parameter. The implications of these findings for electron spectral functions in both symmetry-broken and thermally disordered systems are discussed, and the examples of anti-ferromagnetism in the Hubbard model and spin spiral order in the three-band model are worked out in detail.

References in corpus (17)

• Unified Description of Nambu-Goldstone Bosons without Lorentz Invariance
• Slave-rotor mean field theories of strongly correlated systems and the Mott transition in finite dimensions
• Quantum textures of the many-body wavefunctions in magic-angle graphene
• Topological order in the pseudogap metal
• Global Phase Diagram of the Normal State of Twisted Bilayer Graphene
• Effective theory of Fermi pockets in fluctuating antiferromagnets
• Imaging inter-valley coherent order in magic-angle twisted trilayer graphene
• Gauge theory for the cuprates near optimal doping
• Antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model: a non-linear sigma model approach
• Criterion for stability of Goldstone Modes and Fermi Liquid behavior in a metal with broken symmetry
• Fermi surface reconstruction and drop of Hall number due to spiral antiferromagnetism in high-$T_c$ cuprates
• Ground-state phase diagram of the three-band Hubbard model from density matrix embedding theory
• Intertwining topological order and broken symmetry in a theory of fluctuating spin density waves
• SU(2) gauge theory of the pseudogap phase in the two-dimensional Hubbard model
• Low-energy behavior of spin-liquid electron spectral functions
• Magnetic orders in the hole doped three-band Hubbard model: spin spirals, nematicity, and ferromagnetic domain walls
• Magnetic and charge orders in the ground state of the Emery model -- accurate numerical results

Cited by in corpus (1)

• Topological Green's function zeros in an exactly solved model and beyond