Universal Scaling Theory of the Boundary Geometric Tensor in Disordered Metals
arXiv:1807.07085 · doi:10.1103/PhysRevLett.122.106601
Abstract
We investigate the finite-size scaling of the boundary quantum geometric tensor (QGT) numerically close to the Anderson localization transition in the presence of small external magnetic fields. The QGT exhibits universal scaling and reveals the crossover between the orthogonal and unitary critical states in weak random magnetic fields. The flow of the QGT near the critical points determines the critical exponents. Critical distributions of the QGT are universal and exhibit a remarkable isotropy even in a homogeneous magnetic field. We predict universal and isotropic Hall conductance fluctuations at the metal-insulator transition in an external magnetic field.
arXiv comment5 + 5 pages, 6 figures
References in corpus (33)
- Topological Insulators
- Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
- Imaging topological edge states in silicon photonics
- Non-Abelian statistics and topological quantum information processing in 1D wire networks
- The many-body localization phase transition
- Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
- Direct Measurement of the Zak phase in Topological Bloch Bands
- Ground state overlap and quantum phase transitions
- Geometrodynamics of Spinning Light
- Quantum critical scaling of the geometric tensors
- Geometry and non-adiabatic response in quantum and classical systems
- Fluctuations of the inverse participation ratio at the Anderson transition
- Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model
- Classifying and measuring the geometry of the quantum ground state manifold
- The Anderson transition: time reversal symmetry and universality
- Critical exponent for the Anderson transition in the three dimensional orthogonal universality class
- Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model
- Universal nonequilibrium quantum dynamics in imaginary time
- Scaling of the gap, fidelity susceptibility, and Bloch oscillations across the superfluid to Mott insulator transition in the one-dimensional Bose-Hubbard model
- Multifractal analysis of the metal-insulator transition in the 3D Anderson model I: Symmetry relation under typical averaging
- Observation of Majorana Quantum Critical Behavior in a Resonant Level Coupled to a Dissipative Environment
- Fidelity approach to the disordered quantum XY model
- Geometrical spin dephasing in quantum dots
- Anderson transition in three-dimensional disordered systems with symplectic symmetry
- Crossover from critical orthogonal to critical unitary statistics at the Anderson transition
- Level Curvatures and Conductances: A Numerical Study of the Thouless Relation
- Fidelity in topological quantum phases of matter
- Finite-size scaling and multifractality at the Anderson transition for the three Wigner-Dyson symmetry classes in three dimensions
- Scaling theory of magneto-resistance in disordered local moment ferromagnets
- Drude weight fluctuations in many-body localized systems
- Distribution of level curvatures for the Anderson model at the localization-delocalization transition
- Anderson Localization and Quantum Hall Effect: Numerical Observation of Two Parameter Scaling
- Two parameter flow of σ_{xx}(ω) - σ_{xy}(ω) for the graphene quantum Hall system in ac regime