Adiabatic currents for interacting fermions on a lattice

DOI10.1142/S0129055X19500090zbMath1410.81037arXiv1707.01852OpenAlexW3100253484WikidataQ129047693 ScholiaQ129047693MaRDI QIDQ4629209

Domenico Monaco, Stefan Teufel

Publication date: 20 March 2019

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.01852

zbMATH Keywords

adiabatic theoreminteracting fermionsquantum Hall conductanceadiabatic currentadiabatic responsequantum Hall conductivity

Mathematics Subject Classification ID

Perturbation theories for operators and differential equations in quantum theory (81Q15) Many-body theory; quantum Hall effect (81V70) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Adiabatic invariants for problems in Hamiltonian and Lagrangian mechanics (70H11)

Related Items (24)

On adiabatic theory for extended fermionic lattice systems ⋮ From charge to spin: Analogies and differences in quantum transport coefficients ⋮ Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap ⋮ A new approach to transport coefficients in the quantum spin Hall effect ⋮ Exactness of linear response in the quantum Hall effect ⋮ A many-body index for quantum charge transport ⋮ Local stability of ground states in locally gapped and weakly interacting quantum spin systems ⋮ Quantization of the interacting Hall conductivity in the critical regime ⋮ Derivation of Kubo's formula for disordered systems at zero temperature ⋮ Adiabatic evolution of low-temperature many-body systems ⋮ Localization of generalized Wannier bases implies Chern triviality in non-periodic insulators ⋮ Persistence of exponential decay and spectral gaps for interacting fermions ⋮ The adiabatic theorem in a quantum many-body setting ⋮ On ℤ2-indices for ground states of fermionic chains ⋮ Quantization of conductance in gapped interacting systems ⋮ Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results ⋮ Canonical Drude weight for non-integrable quantum spin chains ⋮ Non-equilibrium almost-stationary states and linear response for gapped quantum systems ⋮ Local commuting projector Hamiltonians and the quantum Hall effect ⋮ Coherent electronic transport in periodic crystals ⋮ Quasi-locality bounds for quantum lattice systems. I. Lieb-Robinson bounds, quasi-local maps, and spectral flow automorphisms ⋮ Purely linear response of the quantum Hall current to space-adiabatic perturbations ⋮ Trotter product formulae for \(\ast\)-automorphisms of quantum lattice systems ⋮ Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk

Cites Work

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