Local Ward identities for collective excitations in fermionic systems with spontaneously broken symmetries

Abstract

We derive Ward identities for fermionic systems exhibiting a gauge symmetry that gets globally broken. In particular, we focus on the relation that connects the gauge field response functions to the transverse susceptibilities of the order parameter. We find that the long-wavelength and zero energy limit of the former are related to the coefficients of a low-energy expansion of the latter. We examine three physical cases: the superconductor, the Néel antiferromagnet and the spiral magnet. In the case of a metallic spiral magnet that completely breaks the SU(2) spin symmetry we explicitly show that the Ward identities are fulfilled within the random phase approximation. We subsequently derive microscopic expressions for the spin stiffnesses and spin wave velocities, which can be plugged into low energy models to study the effect of long-wavelength bosonic fluctuations on top of mean-field solutions.

References in corpus (21)

• Superconductors are topologically ordered
• On the fulfillment of Ward identities in the functional renormalization group approach
• Crossover and scaling in a nearly antiferromagnetic Fermi liquid in two dimensions
• Universal Magnetic Properties of Frustrated Quantum Antiferromagnets in Two Dimensions
• Quantum Phase Transition in Frustrated Two-Dimensional Antiferromagnets
• Incommensurate magnetic order and phase separation in the two-dimensional Hubbard model with nearest and next-nearest neighbor hopping
• Topological order in the pseudogap metal
• Antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model: a non-linear sigma model approach
• A Renormalization Group Study of Helimagnets in D=2+EPSILON Dimensions
• Magnetic Phases of the 2D Hubbard Model at Low Doping
• Coexistence of incommensurate magnetism and superconductivity in the two-dimensional Hubbard model
• Theory of plasmonic effects in nonlinear optics: the case of graphene
• Fermi surface reconstruction and drop of Hall number due to spiral antiferromagnetism in high-$T_c$ cuprates
• Conservation in two-particle self-consistent extensions of dynamical-mean-field-theory
• Stability of the spiral phase in the 2D extended t-J model
• The massive $C{P}^{N-1}$ model for frustrated spin systems
• Gauge invariance and Ward identities in nonlinear response theory
• Longitudinal conductivity and Hall coefficient in two-dimensional metals with spiral magnetic order
• Charge carrier drop at the onset of pseudogap behavior in the two-dimensional Hubbard model
• Phase stiffness in an antiferromagnetic superconductor
• Analog spacetimes from nonrelativistic Goldstone modes in spinor condensates

Cited by in corpus (7)

• Comprehensive mean-field analysis of magnetic and charge orders in the two-dimensional Hubbard model
• SU(2) gauge theory of the pseudogap phase in the two-dimensional Hubbard model
• Spiral to stripe transition in the two-dimensional Hubbard model
• Antiferromagnetic and spin spiral correlations in the doped two-dimensional Hubbard model: gauge symmetry, Ward identities, and dynamical mean-field theory analysis
• Spin susceptibility in a pseudogap state with fluctuating spiral magnetic order
• Frequency dependence of temporal spin stiffness and short-range magnetic order in the doped two-dimensional Hubbard model
• Non-perturbative effects of short-range spatial correlations at the two-particle level