相关论文: Topology vs localization in synthetic dimensions
In chaotic deterministic systems, seemingly stochastic behavior is generated by relatively simple, though hidden, organizing rules and structures. Prominent among the tools used to characterize this complexity in 1D and 2D systems are…
It is shown that the mean-field description of a boson-fermion mixture with a dominating fermionic component, loaded in a one-dimensional optical lattice, is reduced to the nonlinear Schr\"{o}dinger equation with a periodic potential and…
We investigate how imposing kinetic restrictions on quantum particles that would otherwise hop freely on a two-dimensional lattice can lead to topologically ordered states. The kinetically constrained models introduced here are derived as a…
We discuss a method for determining the optimally-localized set of generalized Wannier functions associated with a set of Bloch bands in a crystalline solid. By ``generalized Wannier functions'' we mean a set of localized orthonormal…
Topological quantum states are characterized by nonlocal invariants, and their detection is intrinsically challenging. Various strategies have been developed to study topological Hamiltonians through their equilibrium states. We present a…
Topological properties lie at the heart of many fascinating phenomena in solid state systems such as quantum Hall systems or Chern insulators. The topology can be captured by the distribution of Berry curvature, which describes the geometry…
We describe the strong dual space $({\mathcal O} (D))^*$ for the space ${\mathcal O} (D)$ of holomorphic functions of several complex variables over a bounded Lipschitz domain $D$ with connected boundary $\partial D$ (as usual, ${\mathcal…
We investigate the self-organization of strongly interacting particles confined in 1D and 2D. We consider hardcore bosons in spinless Hubbard lattice models with short-range interactions. We show that many-body states with topological…
Topology ultimately unveils the roots of the perfect quantization observed in complex systems. The 2D quantum Hall effect is the celebrated archetype. Remarkably, topology can manifest itself even in higher-dimensional spaces in which…
Symmetry-protected topological phases host gapless modes at their boundary with a featureless environment of the same dimension or a trivial vacuum. In this study, we explore their behavior in a higher-dimensional environment, which itself…
Chaotic linear dynamics deals primarily with various topological ergodic properties of semigroups of continuous linear operators acting on a topological vector space. We treat questions of characterizing which of the spaces from a given…
Two-dimensional lattice models subjected to an external effective magnetic field can form nontrivial band topologies characterized by nonzero integer band Chern numbers. In this Letter, we investigate such a lattice model originating from…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…
In this paper we explore the effects of quasiperiodicity in paradigmatic models of Chern insulators. We identify a plethora of topological phase transitions and characterize them based on spectral and localization properties. Contrary to…
We present new results on the localization of gauge fields in thick brane models. The four-dimensional observable universe is considered to be a topological defect which is generated by two scalar fields coupled with gravity embedded in a…
The extended Bloch representation of quantum mechanics was recently derived to offer a (hidden-measurement) solution to the measurement problem. In this article we use it to investigate the geometry of superposition and entangled states,…
The discovery of topological states of matter has profoundly augmented our understanding of phase transitions in physical systems. Instead of local order parameters, topological phases are described by global topological invariants and are…
A sudden quantum quench of a Bloch band from one topological phase toward another has been shown to exhibit an intimate connection with the notion of a dynamical quantum phase transition (DQPT), where the returning probability of the…
We consider the two-dimensional topological Chern insulator in the presence of static disorder. Generic quantum states in this system are Anderson localized. However, topology requires the presence of a subset of critical states, with…
The global topology of the Universe could, in principle, affect quantum systems through boundary condition constraints. We investigate this connection by analyzing how compact, flat, cosmologically inspired topologies, specifically the…