Related papers: Quantization of Topological Invariants under Symme…
There has been recent interest in conformal twisted boundary conditions and their realisations in solvable lattice models. For the Ising and Potts quantum chains, these amount to boundary terms that are related to duality, which is a proper…
Axion insulators are generally understood as magnetic topological insulators whose Chern-Simons axion coupling term is quantized and equal to $\pi$. Inversion and time reversal, or the composition of either one with a rotation or a…
We discuss the relation between bulk topological invariants and the spectrum of surface states in three dimensional non-interacting topological insulators. By studying particular models, and considering general boundary conditions for the…
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…
We analyse the topological transition and localization evolution of disordered two dimensional systems with non trivial topology based on bipartite lattices. Chern insulators with broken time reversal symmetry show non standard behavior for…
Disorder, ubiquitously present in solids, is normally detrimental to the stability of ordered states of matter. In this letter we demonstrate that not only is the physics of a strong topological insulator robust to disorder but, remarkably,…
We describe recent progress in our understanding of the interplay between interactions, symmetry, and topology in states of quantum matter. We focus on a minimal generalization of the celebrated topological band insulators to interacting…
We argue that symmetry-broken phases proximate in phase space to symmetry-protected topological phases can exhibit dynamical signatures of topological physics. This dynamical, symmetry-protected "topological" regime is characterized by…
Entanglement is known to serve as an order parameter for true topological order in two-dimensional systems. We show how entanglement of disconnected partitions defines topological invariants for one-dimensional topological superconductors.…
Topological invariants are a significant ingredient in the study of topological phases of matter that intertwines the supposedly contradicting concepts of bulk and boundary. The nature of the invariants differ depending on the dimension of…
We discuss some bulk-surfaces gapped Hamiltonians on a lattice with corners and propose a periodic table for topological invariants related to corner states aimed at studies of higher-order topological insulators. Our table is based on four…
We study the homotopy classification of symmetry representations to describe the bulk topological invariants protected by the combined operation of a two-fold rotation $C_{2z}$ and time-reversal $T$ symmetries. We define topological…
We study non-interacting electrons in disordered materials which exhibit a spectral gap, in each of the ten Altland--Zirnbauer symmetry classes, in all space dimensions. We define an appropriate space of Hamiltonians and a topology on it so…
We demonstrate that the presence of a localized state at the corner of an insulating domain is not always a predictor of a certain non-trivial higher-order topological invariant, even though they appear to co-exist in the same Hamiltonian…
We develop a unified view of topological phase transitions (TPTs) in solids by revising the classical band theory with the inclusion of topology. Re-evaluating the band evolution from an "atomic crystal" [a normal insulator (NI)] to a solid…
Topological invariants, rigorously defined only in the thermodynamic limit, have been generalized to topological indicators applicable to finite-size disordered systems. However, in many experimentally relevant situations, such as…
Time-reparametrization invariance in general relativistic space-time does not allow us to single out a time in quantum mechanics in a mechanical way of measurement. Motivated by this problem, we examine this gauge invariance in the ground…
Recent attempts at topological materials have revealed a large class of materials that show gapless surface states protected by time-reversal symmetry and crystal symmetries. Among them, topological insulating states protected by crystal…
We show that higher order inter-group covariances involving even number of qubits are necessarily positive semidefinite for N qubit separable states, which are completely symmetric under permutations of the qubits. This identification leads…
We revisit the classification of polarization observables of the cosmic microwave background. There exists a unified approach to the $3 \times 3$ density matrix by which intensity, linear and circular polarization are treated on an equal…