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The fate of the current carrying states of a quantum Hall system is considered in the situation when the disorder strength is increased and the transition from the quantum Hall liquid to the Hall insulator takes place. We investigate a…
As a model for the transitions between plateaus in the fractional Quantum Hall effect we study the critical behavior of non-interacting charged particles in a static random magnetic field with finite mean value. We argue that this model…
Metallic quantum criticality is a central theme in a variety of strongly correlated systems. Recent experiments have raised the fundamental question of how the charge response can be singular in cases where the Landau framework of quantum…
We explore critical properties of two-dimensional lattices of spins interacting via an anisotropic Heisenberg Hamiltonian and subject to incoherent spin flips. We determine the steady-state solution of the master equation for the density…
A mapping is developed between the quantum Hall plateau transition and two-dimensional self-interacting lattice polymers. This mapping is exact in the classical percolation limit of the plateau transition, and diffusive behavior at the…
We consider network models for localisation problems belonging to symmetry class C. This symmetry class arises in a description of the dynamics of quasiparticles for disordered spin-singlet superconductors which have a Bogoliubov - de…
We derive the condition for the occurrence of the integer quantum Hall effect in two-dimensional lattice systems with interactions, expressed as $\phi\nu-\rho\in\mathbb{Z}$, where $\phi$, $\nu$, and $\rho$ denote the magnetic flux, the…
We revisit the problem of the plateau transition in the integer quantum Hall effect. Here we develop an analytical approach for this transition, based on the theory of conformal restriction. This is a mathematical theory that was recently…
We investigate the boundary critical phenomena of the one-dimensional quantum Ashkin-Teller model using boundary conformal field theory and density matrix renormalization group (DMRG) simulations. Based on the $\mathbb{Z}_2$-orbifold of the…
Quantum criticality that goes beyond the Landau framework of order-parameter fluctuations is playing a central role in elucidating the behavior of strange metals. A prominent case appears in Kondo lattice systems, which have been…
It is an outstanding goal to unveil the key features of quantum dynamics at eigenstate transitions. Focusing on quadratic fermionic Hamiltonians that exhibit localization transitions, we identify physical observables that exhibit…
We consider the anisotropic effect in the quantum Hall systems by applying a confining potential that is not of parabolic type. This can be done by extending Susskind--Polychronakos's approach to involve the matrices of two coupled harmonic…
Statistics of level spacing and magnetization are studied for the phase diagram of the integer quantum Hall effect in a 2D finite lattice model with Anderson disorder.
We propose an experimental scheme to realize and detect the quantum anomalous Hall effect in an anisotropic square optical lattice which can be generated from available experimental set-ups of double-well lattices with minor modifications.…
Recent experiments on He3 bilayers adsorbed on Graphite have shown striking quantum critical properties at the point where the first layer localizes. We model this system with the Anderson lattice plus inter-layer Coulomb repulsion in two…
In this chapter we discuss aspects of the quantum critical behavior that occurs at a quantum phase transition separating a topological phase from a conventionally ordered one. We concentrate on a family of quantum lattice models, namely…
We investigate numerically whether the chiral symmetry is the sole factor dominating the criticality of the quantum Hall transitions in disordered graphene. When the disorder respects the chiral symmetry, the plateau-to-plateau transition…
We propose a new viewpoint on the study of localization transitions in disordered quantum systems, showing how critical properties can be seen also as a geometric transition in the data space generated by the classically encoded…
In contrast to the first-order correlation-driven Mott metal-insulator transition (MIT), contin- uous disorder-driven transitions are intrinsically quantum critical. Here, we investigate transport quantum criticality in the Falicov-Kimball…
Critical points of classical and quantum lattice models are often described by scale-invariant Lifshitz theories which are anisotropic in the continuum limit, as characterized by a dynamical critical exponent $z\neq1$. This type of critical…