Topological insulators and superconductors support extended surface states protected against the otherwise localizing effects of static disorder. Specifically, in the Wigner-Dyson insulators belonging to the symmetry classes A, AI, and AII, a band of extended surface states is continuously connected to a likewise extended set of bulk states forming a “bridge” between different surfaces via the mechanism of spectral flow. In this work we show that this mechanism is absent in the majority of non-Wigner-Dyson topological superconductors and chiral topological insulators. In these systems, there is precisely one point with granted extended states, the center of the band, <math display="inline"><mi>E</mi><mo>=</mo><mn>0</mn></math>. Away from it, states are spatially localized, or can be made so by the addition of spatially local potentials. Considering the three-dimensional insulator in class AIII and winding number <math display="inline"><mi>ν</mi><mo>=</mo><mn>1</mn></math> as a paradigmatic case study, we discuss the physical principles behind this phenomenon, and its methodological and applied consequences. In particular, we show that low-energy Dirac approximations in the description of surface states can be treacherous in that they tend to conceal the localizability phenomenon. We also identify markers defined in terms of Berry curvature as measures for the degree of state localization in lattice models, and back our analytical predictions by extensive numerical simulations. A main conclusion of this work is that the surface phenomenology of non-Wigner-Dyson topological insulators is a lot richer than that of their Wigner-Dyson siblings, extreme limits being spectrumwide quantum critical delocalization of all states versus full localization except at the <math display="inline"><mi>E</mi><mo>=</mo><mn>0</mn></math> critical point. As part of our study we identify possible experimental signatures distinguishing between these different alternatives in transport or tunnel spectroscopy.

Continuer la lecture Share

Chiral Spin Liquids (CSL) based on spin-1/2 fermionic Projected Entangled Pair States (fPEPS) are considered on the square lattice. First, fPEPS approximants of Gutzwiller-projected Chern insulators (GPCI) are investigated by Variational Monte Carlo (VMC) techniques on finite size tori. We show that such fPEPS of finite bond dimension can correctly capture the topological properties of the chiral spin liquid, as the exact GPCI, with the correct topological ground state degeneracy on the torus. Further, more general fPEPS are considered and optimized (on the infinite plane) to describe the CSL phase of a chiral frustrated Heisenberg antiferromagnet. The chiral modes are computed on the edge of a semi-infinite cylinder (of finite circumference) and shown to follow the predictions from Conformal Field Theory. In contrast to their bosonic analogs the (optimized) fPEPS do not suffer from the replication of the chiral edge mode in the odd topological sector.

Continuer la lecture Share

Non-abelian symmetries are thought to be incompatible with many-body localization, but have been argued to produce in certain disordered systems a broad non-ergodic regime distinct from many-body localization. In this context, we present a numerical study of properties of highly-excited eigenstates of disordered chains with SU(3) symmetry. We find that while weakly disordered systems rapidly thermalize, strongly-disordered systems indeed exhibit non-thermal signatures over a large range of system sizes, similar to the one found in previously studied SU(2) systems. Our analysis is based on the spectral, entanglement, and thermalization properties of eigenstates obtained through large-scale exact diagonalization exploiting the full SU(3) symmetry.

Continuer la lecture Share

Despite enormous efforts devoted to the study of the many-body localization (MBL) phenomenon, the nature of the high-energy behavior of the Heisenberg spin chain in a strong random magnetic field is lacking consensus. Here, we take a step back by exploring the weak interaction limit starting from the Anderson localized (AL) insulator. Through shift-invert diagonalization, we find that below a certain disorder threshold $h^*$, weak interactions necessarily lead to ergodic instability, whereas at strong disorder the AL insulator directly turns into MBL. This agrees with a simple interpretation of the avalanche theory for restoration of ergodicity. We further map the phase diagram for the generic XXZ model in the disorder $h$-- interaction $\Delta$ plane. Taking advantage of the total magnetization conservation, our results unveil the remarkable behavior of the spin-spin correlation functions: in the regime indicated as MBL by standard observables, their exponential decay undergoes a unique inversion of orientation $\xi_z>\xi_x$. We find that the longitudinal length $\xi_z$ is a key quantity for capturing ergodic instabilities, as it increases with system size near the thermal phase, in sharp contrast to its transverse counterpart $\xi_x$.

Continuer la lecture Share