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Published on: August 2, 2019
Large Scale Response of Gapless 1d and Quasi-1d Systems
Marcello Porta1, Harman Preet Singh1
1Mathematics Area, SISSA, Via Bonomea 265, 34136 Trieste, Italy.
Annales Henri Poincare
|August 13, 2026
Summary
This study validates the Kubo formula for quantum systems under specific time-dependent perturbations. It demonstrates that linear response accurately predicts transport properties in one-dimensional systems and topological insulators at zero temperature.
Area of Science:
- Condensed Matter Physics
- Quantum Field Theory
- Mesoscopic Physics
Background:
- Understanding transport properties in quantum systems is crucial for developing novel electronic devices.
- The Kubo formula is a cornerstone for calculating linear response transport coefficients.
- Investigating edge states in topological insulators and one-dimensional systems reveals unique quantum phenomena.
Purpose of the Study:
- To rigorously prove the validity of the Kubo formula for non-interacting, gapless one-dimensional quantum systems and edge modes of two-dimensional topological insulators.
- To analyze the linear response of these systems under weak, slowly varying, time-dependent perturbations in an Euler-like scaling limit.
- To establish a quantum dynamical approach for proving the quantization of edge conductance in quantum Hall systems.
Main Methods:
- The study employs a novel approach by representing the real-time Duhamel series in imaginary time.
- Convergence of the series is proven uniformly in the scaling parameter and system size at low temperatures.
- A key cancellation mechanism, linked to anomalous chiral gauge symmetry, is exploited for the scaling limit.
Main Results:
- The validity of the Kubo formula is established for a specific class of perturbations in the zero-temperature, infinite-volume limit.
- It is shown that linear response is the dominant contribution to the system's full response as temperature and scaling parameter approach zero.
- The method successfully proves the quantization of edge conductance in two-dimensional quantum Hall systems from fundamental quantum dynamics.
Conclusions:
- The research provides a rigorous dynamical foundation for the Kubo formula in relevant quantum systems.
- The findings highlight the importance of emergent symmetries and cancellations in determining transport properties.
- This work offers a pathway to understand quantum transport phenomena from first principles, particularly in topological systems.
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