Related papers: Detecting Bulk Topology of Quadrupolar Phase from …
Topological quantum phases cannot be characterized by local order parameters in the bulk. In this work however, we show that signatures of a topological quantum critical point do remain in local observables in the bulk, and manifest…
Recent discoveries have spurred the theoretical prediction and experimental realization of novel materials that have topological properties arising from band inversion. Such topological insulators are insulating in the bulk but have…
The topology of a single-particle band structure plays a fundamental role in understanding a multitude of physical phenomena. Motivated by the connection between quantum walks and such topological band structures, we demonstrate that a…
We study the quench dynamics of a topologically trivial one-dimensional gapless wire following its sudden coupling to topological bound states. We find that as the bound states leak into and propagate through the wire, signatures of their…
The modern theory of electric polarization in crystals associates the dipole moment of an insulator with a Berry phase of its electronic ground state [1, 2]. This concept constituted a breakthrough that not only solved the long-standing…
Equilibrium topological phases are robust against weak static disorder but may break down in the strong disorder regime. Here we explore the stability of the quench-induced emergent dynamical topology in the presence of dynamical noise. We…
A hallmark feature of topological physics is the presence of one-way propagating chiral modes at the system boundary. The chirality of edge modes is a consequence of the topological character of the bulk. For example, in a non-interacting…
This paper reviews recent results on the classification of partial differential operators modeling bulk and interface topological insulators in Euclidean spaces. Our main objective is the mathematical analysis of the unusual,…
In recent years, there is considerable experimental effort using cold atoms to study strongly correlated many-body systems. One class of phenomena of particularly interests is quantum critical (QC) phenomena. While prevalent in many…
Crystalline symmetry can be used to predict bulk and surface properties of topological phases. For non-interacting cases, symmetry-eigenvalue analysis of Bloch states at high symmetry points in the Brillouin zone simplifies the calculation…
A formula for the corner charge in terms of the bulk quadrupole moment is derived for two-dimensional periodic systems. This is an analog of the formula for the surface charge density in terms of the bulk polarization. In the presence of an…
We present a general scheme for measuring the bulk properties of non-interacting tight-binding models realized in arrays of coupled photonic cavities. Specifically, we propose to implement a single unit cell of the targeted model with…
Competition among repetitive measurements of noncommuting observables and unitary dynamics can give rise to a wide variety of entanglement phases. Here, we propose a general framework based on Lyapunov analysis to characterize topological…
We introduce and study dynamical probes of band structure topology in the post-quench time-evolution from mixed initial states of quantum many-body systems. Our construction generalizes the notion of dynamical quantum phase transitions…
In this article we extend the celebrated Berry-phase formulation of electric polarization in crystals to higher electric multipole moments. We determine the necessary conditions under which, and minimal models in which, the quadrupole and…
The Berry phase associated with energy bands in crystals can lead to quantized quantities, such as the quantization of electric dipole polarization in an insulator, known as a one-dimensional (1D) topological insulator (TI) phase. Recent…
We study quench dynamics of the Bose-Hubbard model by exact diagonalization. Initially the system is at thermal equilibrium and of a finite temperature. The system is then quenched by changing the on-site interaction strength $U$ suddenly.…
We study the topological properties of one dimensional systems undergoing unitary time evolution. We show that symmetries possessed both by the initial wavefunction and by the Hamiltonian at all times may not be present in the…
The modern theory of charge polarization in solids is based on a generalization of Berry's phase. Its possible quantization lies at the heart of our understanding of all systems with topological band structures that were discovered over the…
Topological magnon insulators exhibit robust edge modes with chiral properties similar to quantum Hall edge states. However, due to their strong localization at the edges, interactions between these chiral edge magnons can be significant,…