The conductivity matrix at the topological phase transition
Abstract
For a general class of two-dimensional non-interacting semi-metallic electron systems on a lattice, we derive an explicit formula for the whole conductivity matrix, by using Euclidean many-body formalism. The semi-metallic phase takes place whenever two Bloch bands touch at the Fermi energy with conical intersections and generally occurs at the transition between distinct integer quantum Hall phases. Unlike the longitudinal conductivity (which depends solely on the shape of the cones at the Fermi level), the transverse conductivity is remarkably determined both by the conical structures of the bands and by the nature of the two nearby topological phases. Generically, in the semi-metallic state, neither the longitudinal nor the transverse conductivities are quantized in integer multiples of a universal conductivity quantum; however, universality of the conductivity matrix is restored under the assumption of emergent rotational symmetry of the linearized Hamiltonian at the Fermi points. Using our formula, we compute the conductivity matrix for several physically relevant models of quantum Hall fluids at the topological phase transition, exhibiting cases where the transverse conductivity is quantized in half-integer multiples of e2/h and cases where it depends continuously on an external strain parameter, thus shedding light on its universality or non-universality features.
Related
- Estimation of the Label-Noise Transition Matrix with Performance Guarantees via Selective Classification
- Non-negative Matrix Factorisation with Topological Regularisation
- Impact of matrix topological properties on the convergence of the conjugate gradient method
- Phase transition of random non-uniform hypergraphs
- Analytic description of the phase transition of inhomogeneous multigraphs
BibTeX
@misc{fabbri2026conductivity,
title = {{The conductivity matrix at the topological phase transition}},
author = {Simone Fabbri and Giovanna Marcelli and Alessandro Giuliani},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03832},
eprint = {2609.03832},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03832},
}
RIS
TY - UNPB
TI - The conductivity matrix at the topological phase transition
AU - Simone Fabbri
AU - Giovanna Marcelli
AU - Alessandro Giuliani
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03832
UR - https://arxiv.org/abs/2609.03832
AB - For a general class of two-dimensional non-interacting semi-metallic electron systems on a lattice, we derive an explicit formula for the whole conductivity matrix, by using Euclidean many-body formalism. The semi-metallic phase takes place whenever two Bloch bands touch at the Fermi energy with conical intersections and generally occurs at the transition between distinct integer quantum Hall phases. Unlike the longitudinal conductivity (which depends solely on the shape of the cones at the Fermi level), the transverse conductivity is remarkably determined both by the conical structures of the bands and by the nature of the two nearby topological phases. Generically, in the semi-metallic state, neither the longitudinal nor the transverse conductivities are quantized in integer multiples of a universal conductivity quantum; however, universality of the conductivity matrix is restored under the assumption of emergent rotational symmetry of the linearized Hamiltonian at the Fermi points. Using our formula, we compute the conductivity matrix for several physically relevant models of quantum Hall fluids at the topological phase transition, exhibiting cases where the transverse conductivity is quantized in half-integer multiples of e^2/h and cases where it depends continuously on an external strain parameter, thus shedding light on its universality or non-universality features.
ER -