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In order to study the behaviour of discrete dynamical systems under adiabatic cyclic variations of their parameters, we consider discrete versions of adiabatically-rotated rotators. Paralleling the studies in continuous systems, we…
Transport properties of disordered electron system can be characterized by the conductance, Lyapunov exponent, or level spacing. Two additional parameters, $K_{11}$ and $\gamma $ were introduced recently which measure the non-homogeneity of…
We calculate the phase diagram of a model for topological superconducting wires with local s-wave pairing, spin-orbit coupling $\vec{\lambda}$ and magnetic field $\vec{B}$ with arbitrary orientations. This model is a generalized lattice…
We consider a classically chaotic system that is described by an Hamiltonian $H(Q,P;x)$ where x is a constant parameter. Our main interest is in the case of a gas-particle inside a cavity, where $x$ controls a deformation of the boundary or…
One of the problems concerning topological phases in solid-state systems which still remains urgent is an issue of many-body effects. In this study we address it within perturbative theory framework by considering topological phase…
We show that the pair of Majorana modes at each end of a 1D spin triplet superconductor with total Cooper pair spin S_x=0 (i.e., Delta_{up,up} = -Delta_{down,down} = p*Delta_0; two uncoupled time reversed copies of the Kitaev p-wave chain)…
For a wide class of noninteracting tight-binding models in one dimension we present an analytical solution for all scattering and edge states on a half-infinite system. Without assuming any symmetry constraints we consider models with…
We study the superconducting state of Sr$_2$RuO$_4$ on the bases of a phenomenological but orbital specific description of the electron-electron attraction and a realistic quantitative account of the electronic structure in the normal…
The Kitaev chain model with a spatially modulated phase in the superconducting order parameter exhibits two types of topological transitions, namely a band topology transition between trivial and topological gapped phases, and a Fermi…
Within the real space renormalization group we obtain the phase portrait of the anisotropic quantum XY model on square lattice in presence of Dzyaloshinskii-Moriya (DM) interaction. The model is characterized by two parameters, $\lambda$…
The thermodynamic formalism expresses chaotic properties of dynamical systems in terms of the Ruelle pressure $\psi(\beta)$. The inverse-temperature like variable $\beta$ allows one to scan the structure of the probability distribution in…
Fracton topological order (FTO) is a new classification of correlated phases in three spatial dimensions with topological ground state degeneracy (GSD) scaling up with system size, and fractional excitations which are immobile or have…
A discrete time crystal (DTC) is a remarkable non-equilibrium phase of matter characterized by the persistent sub-harmonic oscillations of physical observables in periodically driven many-body systems. Motivated by the question of whether…
I review the principal theories that have been proposed for the superconducting phases of UPt$_3$. The detailed H-T phase diagram places constraints on any theory for the multiple superconducting phases. I comment on the limitations of the…
We explore the salient features of the `Kitaev ladder', a two-legged ladder version of the spin-1/2 Kitaev model on a honeycomb lattice, by mapping it to a one-dimensional fermionic p-wave superconducting system. We examine the connections…
We determine the quantum phase diagram of the Hubbard chain with electron-hole symmetric correlated hopping at 1/2- and 1/4-filling using geometric concepts and continuum limit field theory. The long distance behavior of various correlation…
When two periodic potentials compete in materials, one may adopt the other, which straightforwardly generates topological defects. Of particular interest are domain walls in charge-, dipole-, and spin-ordered systems, which govern…
In this paper, we present a detailed study on the phase diagrams of superconducting topological surface states, especially, focusing on the interplay between crystalline symmetry and topology of the effective BdG Hamiltonian. We show that…
Magnetism and superconductivity of new heavy fermion compounds CeTIn$_5$ (T=Co, Rh and Ir) are investigated by applying fluctuation exchange approximation to an orbital degenerate Hubbard model. The superconducting phase with…
Topological characteristics of quantum systems are typically determined by the closing of a gap, while the dynamical quantum phase transition (DQPT) during quantum real-time evolution has emerged as a nonequilibrium analog to the quantum…