# Multifractality and conformal invariance at 2D metal-insulator transition in the spin-orbit symmetry class.

@article{Obuse2006MultifractalityAC, title={Multifractality and conformal invariance at 2D metal-insulator transition in the spin-orbit symmetry class.}, author={Hideaki Obuse and Arvind Rasi Subramaniam and Akira Furusaki and Ilya A. Gruzberg and Andreas W. W. Ludwig}, journal={Physical review letters}, year={2006}, volume={98 15}, pages={ 156802 } }

We study the multifractality (MF) of critical wave functions at boundaries and corners at the metal-insulator transition (MIT) for noninteracting electrons in the two-dimensional (2D) spin-orbit (symplectic) universality class. We find that the MF exponents near a boundary are different from those in the bulk. The exponents at a corner are found to be directly related to those at a straight boundary through a relation arising from conformal invariance. This provides direct numerical evidence…

## 25 Citations

### Boundary criticality and multifractality at the two-dimensional spin quantum Hall transition

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- 2008

Multifractal scaling of critical wave functions at a disorder-driven Anderson localization transition is modified near boundaries of a sample. Here this effect is studied for the example of the spin…

### Conformal invariance, multifractality, and finite-size scaling at Anderson localization transitions in two dimensions

- Physics
- 2010

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### Generalized multifractality at metal-insulator transitions and in metallic phases of two-dimensional disordered systems

- PhysicsPhysical Review B
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We study generalized multifractality characterizing ﬂuctuations and correlations of eigenstates in disordered systems of symmetry classes AII, D, and DIII. Both metallic phases and…

### Generalized multifractality at metal-insulator transitions and in metallic phases of 2D disordered systems

- Physics
- 2022

We study generalized multifractality characterizing ﬂuctuations and correlations of eigenstates in disordered systems of symmetry classes AII, D, and DIII. Both metallic phases and…

### Symmetries of multifractal spectra and field theories of Anderson localization.

- Mathematics, PhysicsPhysical review letters
- 2011

The field-theoretical origin of symmetry relations for multifractal spectra at Anderson transitions and at critical points of other disordered systems are uncovered and it is demonstrated that for the Anderson localization problem the entire probability distribution for the local density of states possesses a symmetry arising from the invariance of correlation functions of the underlying nonlinear σ model.

### Multifractal analysis of the metal-insulator transition in the three-dimensional Anderson model. I. Symmetry relation under typical averaging

- Physics
- 2008

The multifractality of the critical eigenstate at the metal to insulator transition (MIT) in the three-dimensional Anderson model of localization is characterized by its associated singularity…

### Quartic multifractality and finite-size corrections at the spin quantum Hall transition

- PhysicsPhysical Review B
- 2021

The spin-quantum Hall transition (or class C transition in two dimensions) represents one of the few localization-delocalization transitions for which some of the critical exponents are known…

### Generalized multifractality at the spin quantum Hall transition: Percolation mapping and pure-scaling observables

- PhysicsPhysical Review B
- 2022

(Dated: This work extends the analysis of the generalized multifractality of critical eigenstates at the spin quantum Hall transition in two-dimensional disordered superconductors [J. F. Karcher et…

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