Related papers: Bott-Kitaev Periodic Table and the Diagonal Map
We consider the Sachdev-Ye-Kitaev (SYK) model as an effective theory arising at the zero-dimensional boundary of a many-body localized, Fermionic symmetry protected topological (SPT) phase in one spatial dimension. The Fermions at the…
The symmetry-based indicator [H. C. Po, A. Vishwanath, H. Watanabe, Nat. Commun. 8, 50 (2017)] is a practical tool to diagnose topological materials in the band theory. In this note, we present two directions to generalize the…
Compass models are theories of matter in which the couplings between the internal spin (or other relevant field) components are inherently spatially (typically, direction) dependent. Compass-type interactions appear in diverse physical…
Systems of free fermions are classified by symmetry, space dimensionality, and topological properties described by K-homology. Those systems belonging to different classes are inequivalent. In contrast, we show that by taking a…
In this paper, we introduce a variation of the notion of topological phase reflecting metric structure of the position space. This framework contains not only periodic and non-periodic systems with symmetries in Kitaev's periodic table but…
We prove that if a certain entry in the map of the Hadamard-Perron theorem is $T$-periodic in one of the variables, then the stable manifold guaranteed by the Hadamard-Perron theorem is a graph of a $T$-periodic function. As an application,…
We study the gapped phase of the Kitaev model on the honeycomb lattice using perturbative continuous unitary transformations. The effective low-energy Hamiltonian is found to be an extended toric code with interacting anyons. High-energy…
Non-Hermitian matrices are ubiquitous in the description of nature ranging from classical dissipative systems, including optical, electrical, and mechanical metamaterials, to scattering of waves and open quantum many-body systems. Seminal…
As a model to provide a hands-on, elementary understanding of "vortex dynamics", we introduce a piecewise linear non-invertible map called a twisted baker map. We show that the set of hyperbolic repelling periodic points with complex…
We present generic conditions for phase band crossings for a class of periodically driven integrable systems represented by free fermionic models subjected to arbitrary periodic drive protocols characterized by a frequency $\omega_D$. These…
This paper is an interval dynamics counterpart of three theories founded earlier by the authors, S. Smirnov and others in the setting of the iteration of rational maps on the Riemann sphere: the equivalence of several notions of non-uniform…
Classifications of symmetry-protected topological (SPT) phases provide a framework to systematically understand the physical properties and potential applications of topological systems. While such classifications have been widely explored…
The quantum adiabatic theorem ensures that a slowly changing system, initially prepared in its ground state, will evolve to its final ground state with arbitrary precision. As a first result this thesis extends the original theorem to…
We develop a systematic and unified random matrix theory to classify Sachdev-Ye-Kitaev (SYK) and supersymmetric (SUSY) SYK models and also work out the structure of the energy levels in one periodic table. The SYK with even $q$- and SUSY…
We present a dichotomy for surface homeomorphisms in the isotopy class of the identity. We show that, in the absence of a degenerate fixed point set, either there exists a uniform bound on the diameter of orbits of non-wandering points for…
We study topological insulators, regarded as physical systems giving rise to topological invariants determined by symmetries both linear and anti-linear. Our perspective is that of noncommutative index theory of operator algebras. In…
Dynamical phases with novel topological properties are known to arise in driven systems of free fermions. In this paper, we obtain a `periodic table' to describe the phases of such time-dependent systems, generalizing the periodic table for…
We study a family of non-Abelian topological models in a lattice that arise by modifying the Kitaev model through the introduction of single-qudit terms. The effect of these terms amounts to a reduction of the discrete gauge symmetry with…
In general case, a Hamiltonian system with three degrees of freedom describing the motion of a rigid body in two constant fields does not admit any symmetry groups. H.Yehia has found conditions under which the equations of motion of the…
The construction of the topologically protected code space of Kitaev's model for fault-tolerant quantum computation is extended from complex semisimple to arbitrary finite-dimensional Hopf algebras admitting pairs in involution. One input…