Quasi-Adiabatic Continuation in Gapped Spin and Fermion Systems: Goldstone's Theorem and Flux Periodicity

Abstract

We apply the technique of quasi-adiabatic continuation to study systems with continuous symmetries. We first derive a general form of Goldstone's theorem applicable to gapped nonrelativistic systems with continuous symmetries. We then show that for a fermionic system with a spin gap, it is possible to insert $\pi$-flux into a cylinder with only exponentially small change in the energy of the system, a scenario which covers several physically interesting cases such as an s-wave superconductor or a resonating valence bond state.

arXiv comment19 pages, 2 figures, final version in press at JSTAT

References in corpus (11)

• Lieb-Schultz-Mattis in Higher Dimensions
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Spectral Gap and Exponential Decay of Correlations
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
• Locality in Quantum and Markov Dynamics on Lattices and Networks
• Fractionalization, topological order, and cuprate superconductivity
• Novel approach to description of spin liquid phases in low-dimensional quantum antiferromagnets
• Extending Luttinger's theorem to Z(2) fractionalized phases of matter
• Sufficient Conditions for Topological Order in Insulators
• Impurity induced spin texture in quantum critical 2D antiferromagnets

Cited by in corpus (11)

• The Density Matrix Renormalization Group in Chemistry and Molecular Physics: Recent Developments and New Challenges
• Making Almost Commuting Matrices Commute
• Shortcuts to Adiabaticity in Krylov Space
• Quasi-adiabatic Continuation for Disordered Systems: Applications to Correlations, Lieb-Schultz-Mattis, and Hall Conductance
• Ground states of linear rotor chains via the density matrix renormalization group
• Bounds on the entanglement entropy of droplet states in the XXZ spin chain
• Topological quantum error correction in the Kitaev honeycomb model
• Local Perturbations Perturb -Exponentially- Locally
• Inaccessible entanglement in symmetry protected topological phases
• Topology of superconductors beyond mean-field theory
• Locality of gapped ground states in systems with power-law decaying interactions