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S Bachmann1, W De Roeck2, M Fraas2

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Summary
This summary is machine-generated.

This study proves a quantum adiabatic theorem for interacting spin systems, applicable to the thermodynamic limit. It shows nonadiabatic excitations are exponentially small, validating Kubo

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Area of Science:

  • Quantum Physics
  • Condensed Matter Theory

Background:

  • The quantum adiabatic theorem, proven in 1928, is crucial for quantum annealing and topological matter studies.
  • Existing proofs do not cover many-body systems where the total Hamiltonian varies rapidly, unlike local terms.

Purpose of the Study:

  • To prove a version of the adiabatic theorem for gapped ground states of interacting quantum spin systems.
  • To address limitations in current literature regarding the adiabatic theorem's application to many-body systems.

Main Methods:

  • Developing a novel proof of the adiabatic theorem tailored for interacting quantum spin systems.
  • Analyzing systems under conditions valid in the thermodynamic limit.

Main Results:

  • A rigorous proof of the adiabatic theorem for gapped interacting quantum spin systems in the thermodynamic limit.
  • Mathematical proof of Kubo's linear response formula for a wide range of gapped interacting systems.
  • Prediction of exponentially small nonadiabatic excitation density with dimension-dependent exponent scaling.

Conclusions:

  • The developed adiabatic theorem proof extends applicability to complex many-body systems.
  • The findings provide a theoretical foundation for quantum annealing and topological property investigations.
  • The results offer insights into the behavior of interacting quantum systems under adiabatic driving.