Persistence of phase boundaries between a topological and trivial Z2 insulator

When time reversal symmetry is present there is a sharp distinction between topological and trivial band insulators which ensures that, as parameters are varied, these phases are separated by a phase transition at which the bulk gap closes. Surprisingly we find that even in the absence of time reversal symmetry, gapless regions originating from the phase boundaries persist. Moreover the critical line generically opens up to enclose Chern insulating phases that are thin but of finite extent in the phase diagram. We explain the topological origin of this effect in terms of quantized charge pumping, showing in particular that it is robust to the effect of disorder and interactions

Delayed currents and interaction effects in mesoscopic capacitors

We propose an alternative derivation for the dynamic admittance of a gated quantum dot connected by a single-channel lead to an electron reservoir. Our derivation, which reproduces the result of Pr\^{e}tre, Thomas, and B\"{u}ttiker for the universal charge-relaxation resistance, shows that at low frequencies, the current leaving the dot lags after the entering one by the Wigner-Smith delay time. We compute the capacitance when interactions are taken into account only on the dot within the Hartree-Fock approximation and study the Coulomb-blockade oscillations as a function of the Fermi energy in the reservoir. In particular we find that those oscillations disappear when the dot is fully `open', thus we reconcile apparently conflicting previous results.Comment: 9 pages, 8 figure

Determining topological order from a local ground state correlation function

Topological insulators are physically distinguishable from normal insulators only near edges and defects, while in the bulk there is no clear signature to their topological order. In this work we show that the Z index of topological insulators and the Z index of the integer quantum Hall effect manifest themselves locally. We do so by providing an algorithm for determining these indices from a local equal time ground-state correlation function at any convenient boundary conditions. Our procedure is unaffected by the presence of disorder and can be naturally generalized to include weak interactions. The locality of these topological indices implies bulk-edge correspondence theorem.Comment: 7 pages, 3 figures. Major changes: the paper was divided into sections, the locality of the order in 3D topological insulators is also discusse

Optimal Renormalization Group Transformation from Information Theory

Recently a novel real-space RG algorithm was introduced, identifying the relevant degrees of freedom of a system by maximizing an information-theoretic quantity, the real-space mutual information (RSMI), with machine learning methods. Motivated by this, we investigate the information theoretic properties of coarse-graining procedures, for both translationally invariant and disordered systems. We prove that a perfect RSMI coarse-graining does not increase the range of interactions in the renormalized Hamiltonian, and, for disordered systems, suppresses generation of correlations in the renormalized disorder distribution, being in this sense optimal. We empirically verify decay of those measures of complexity, as a function of information retained by the RG, on the examples of arbitrary coarse-grainings of the clean and random Ising chain. The results establish a direct and quantifiable connection between properties of RG viewed as a compression scheme, and those of physical objects i.e. Hamiltonians and disorder distributions. We also study the effect of constraints on the number and type of coarse-grained degrees of freedom on a generic RG procedure.Comment: Updated manuscript with new results on disordered system