arXiv subjects

Ilya Gruzberg

Publications and source records attributed to Ilya Gruzberg.

3 recordsLinked to original sources

arXiv2026

The integer quantum Hall transition: an $S$-matrix approach to random networks

In this paper we propose a new $S$-matrix approach to numerical simulations of network models and apply it to random networks that we proposed in a previous work 10.1103/PhysRevB.95.125414. Random networks are modifications of the Chalker-Coddington (CC) model for the integer quantum Hall transition that more faithfully capture the physics of electrons moving in a strong magnetic field and a smooth disorder potential. The new method has considerable advantages compared to the transfer matrix approach, and gives the value $ν\approx 2.4$ for the critical exponent of the localization length in a random network. This finding confirms our previous result and is surprisingly close to the experimental value $ν_{\text{exp}} \approx 2.38$ observed at the integer quantum Hall transition but substantially different from the CC value $ν_\text{CC} \approx 2.6$.

cond-mat.dis-nn↗

arXiv2026

Spin quantum Hall transition on random networks: exact critical exponents via quantum gravity

We solve the problem of the spin quantum Hall transition on random networks using a mapping to classical percolation that focuses on the boundary of percolating clusters. Using tools of two-dimensional quantum gravity, we compute critical exponents that characterize this transition and confirm that these are related to the exponents for the regular (square) network through the KPZ relation. Our results demonstrate the relevance of the geometric randomness of the networks and support conclusions of numerical simulations of random networks for the integer quantum Hall transition.

cond-mat.mes-hall↗

arXiv2016

Geometrically disordered network models, quenched quantum gravity, and critical behavior at quantum Hall plateau transitions

Recent high-precision results for the critical exponent of the localization length at the integer quantum Hall (IQH) transition differ considerably between experimental ($ν_\text{exp} \approx 2.38$) and numerical ($ν_\text{CC} \approx 2.6$) values obtained in simulations of the Chalker-Coddington (CC) network model. We revisit the arguments leading to the CC model and consider a more general network with geometric (structural) disorder. Numerical simulations of this new model lead to the value $ν\approx 2.37$ in very close agreement with experiments. We argue that in a continuum limit the geometrically disordered model maps to the free Dirac fermion coupled to various random potentials (similar to the CC model) but also to quenched two-dimensional quantum gravity. This explains the possible reason for the considerable difference between critical exponents for the CC model and the geometrically disordered model and may shed more light on the analytical theory of the IQH transition. We extend our results to network models in other symmetry classes.

cond-mat.dis-nn↗