Lieb-Robinson bounds, the spectral flow, and stability of the spectral gap for lattice fermion systems

Abstract

We prove Lieb-Robinson bounds for a general class of lattice fermion systems. By making use of a suitable conditional expectation onto subalgebras of the CAR algebra, we can apply the Lieb-Robinson bounds much in the same way as for quantum spin systems. We preview how to obtain the spectral flow automorphisms and to prove stability of the spectral gap for frustration-free gapped systems satisfying a Local Topological Quantum Order condition.

Contribution for the proceedings of QMath13: Mathematical Results in Quantum Physics, Atlanta, October 8-11, 2016. Version 2 contains additional references as well as discussions of those references. Typos corrected in Version 3

References in corpus (8)

• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Propagation of Correlations in Quantum Lattice Systems
• Fermionic Matrix Product States and One-Dimensional Topological Phases
• Adiabatic Theorem for Quantum Spin Systems
• The adiabatic theorem and linear response theory for extended quantum systems
• Energy and Vorticity in Fast Rotating Bose-Einstein Condensates
• Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory

Cited by in corpus (10)

• Chiral central charge from a single bulk wave function
• Maximal speed for macroscopic particle transport in the Bose-Hubbard model
• The classification of symmetry protected topological phases of one-dimensional fermion systems
• Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap
• From decay of correlations to locality and stability of the Gibbs state
• Strong coupling asymptotics for $\delta$-interactions supported by curves with cusps
• Dynamical Phase Error in Interacting Topological Quantum Memories
• Topology vs localization in synthetic dimensions
• Exploiting $\vartheta -$functions for the identification of topological materials
• Uniqueness of purifications is equivalent to Haag duality