PreprintarXiv licencearXiv
Logarithmic transport at topological phase transitions of one-dimensional chiral quantum systems
Abstract
The random hopping Hamiltonian is a toy model for a disorder-driven topological phase transitions in one-dimensional chiral Hamiltonians. It has a vanishing Lyapunov exponent and a Dyson peak in the density of states at zero energy. This work shows how the quantum dynamics leads to a logarithmic growth of the moments of the position operator, similar as in classical Sinai diffusion. The mechanism at the origin of this phenomenon is that the eigenfunction of the smallest eigenvalue is well-approximated by the exponential of a classical random walk, leading to two essentially independent subexponential localization centers.
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BibTeX
@misc{markovic2026logarithmic,
title = {{Logarithmic transport at topological phase transitions of one-dimensional chiral quantum systems}},
author = {Dragan Markovic and Hermann Schulz-Baldes},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28688},
eprint = {2609.28688},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28688},
}
RIS
TY - UNPB
TI - Logarithmic transport at topological phase transitions of one-dimensional chiral quantum systems
AU - Dragan Markovic
AU - Hermann Schulz-Baldes
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28688
UR - https://arxiv.org/abs/2609.28688
AB - The random hopping Hamiltonian is a toy model for a disorder-driven topological phase transitions in one-dimensional chiral Hamiltonians. It has a vanishing Lyapunov exponent and a Dyson peak in the density of states at zero energy. This work shows how the quantum dynamics leads to a logarithmic growth of the moments of the position operator, similar as in classical Sinai diffusion. The mechanism at the origin of this phenomenon is that the eigenfunction of the smallest eigenvalue is well-approximated by the exponential of a classical random walk, leading to two essentially independent subexponential localization centers.
ER -