Related papers: Universal Chern number statistics in random matrix…
In order to study continuous models of disordered topological phases, we construct an unbounded Kasparov module and a semifinite spectral triple for the crossed product of a separable $C^*$-algebra by a twisted $\mathbb{R}^d$-action. The…
The statistical properties of quantum transport through a chaotic cavity are encoded in the traces $\T={\rm Tr}(tt^\dag)^n$, where $t$ is the transmission matrix. Within the Random Matrix Theory approach, these traces are random variables…
We present a systematic construction of probes into the dynamics of isospectral ensembles of Hamiltonians by the notion of Isospectral twirling, expanding the scopes and methods of ref.[1]. The relevant ensembles of Hamiltonians are those…
A quantum anomalous Hall state with high Chern number has so far been realized in multiplayer structures consisting of alternating magnetic and undoped topological insulator layers. However, in previous proposals, the Chern number can be…
For a quantum system in a macroscopically large volume $V$, prepared in a pure state and subject to maximally noisy or ergodic unitary dynamics, the reduced density matrix of any sub-system $v\ll V$ is almost surely totally mixed. We show…
During the last years quantum graphs have become a paradigm of quantum chaos with applications from spectral statistics to chaotic scattering and wave function statistics. In the first part of this review we give a detailed introduction to…
The Chern character maps are one of the most important working tools in mathematics. Although they admit numerous different constructions, they are not yet fully understood at the conceptual level. In this note we eliminate this gap by…
Chern number is a crucial invariant for characterizing topological feature of two-dimensional quantum systems. Real-space Chern number allows us to extract topological properties of systems without involving translational symmetry, and…
The Harper-Hofstadter model provides a fractal spectrum containing topological bands of any integer Chern number, $C$. We study the many-body physics that is realized by interacting particles occupying Harper-Hofstadter bands with $|C|>1$.…
Quantum duality is a far reaching concept in contemporary theoretical physics. In the present paper, we reveal the quantum dualities in quantum anomalous Hall (QAH) phases through concrete two bands Hamiltonian models. Our models can…
Multi-parametric chiral random matrix ensembles are important tools to analyze the statistical behavior of generic complex systems with chiral symmetry. A recent study \cite{psmulti} of the former maps them to the chiral Brownian ensemble…
In this paper, we study random features manifested in components of energy eigenfunctions of quantum chaotic systems, given in the basis of unperturbed, integrable systems. Based on semiclassical analysis, particularly on Berry's…
In the framework of the random matrix approach, we apply the theory of Selberg's integral to problems of quantum transport in chaotic cavities. All the moments of transmission eigenvalues are calculated analytically up to the fourth order.…
We show that, for sudden quenches, the work distribution reduces to the statistics of traces of powers of Haar unitaries, which are random unitary matrices drawn uniformly from the unitary group. For translation-invariant quadratic…
In this work, we propose an exactly solvable two-dimensional lattice model of strongly correlated electrons that realizes a quantum anomalous Hall insulator with Chern number $\mathcal{C}=1$. First, we show that the interplay of ionic…
We present a theory of fractional Chern insulator stabilization against charge-ordered states. We argue that the phase competition is captured by an effective interaction range, which depends on both the bare interaction range and quantum…
The quantum anomalous Hall (QAH) state is a two-dimensional topological insulating state that has quantized Hall resistance of h/Ce2 and vanishing longitudinal resistance under zero magnetic field, where C is called the Chern number. The…
The main purpose of these lectures is to discuss briefly recent methods of calculation of statistical properties of quantum eigenvalues for chaotic systems based on semi-classical trace formulas. Under the assumption that periodic orbit…
Chaos and complexity entail an entropic and computational obstruction to describing a system, and thus are intrinsically difficult to characterize. In this paper, we consider time evolution by Gaussian Unitary Ensemble (GUE) Hamiltonians…
A Chern band is characterized by a Wannier obstruction indicating the absence of a basis of complete, orthogonal, and exponentially-localized states. Here, we study the properties of real space bases of a Chern band obtained by relaxing…