Topological R\'enyi entropy after a quantum quench

We present an analytical study on the resilience of topological order after a quantum quench. The system is initially prepared in the ground state of the toric-code model, and then quenched by switching on an external magnetic field. During the subsequent time evolution, the variation in topological order is detected via the topological Renyi entropy of order 2. We consider two different quenches: the first one has an exact solution, while the second one requires perturbation theory. In both cases, we find that the long-term time average of the topological Renyi entropy in the thermodynamic limit is the same as its initial value. Based on our results, we argue that topological order is resilient against a wide range of quenches.Comment: 5 pages, 4 figures, published version with structural changes, see supplemental material at http://link.aps.org/supplemental/10.1103/PhysRevLett.110.17060

Universality and robustness of revivals in the transverse field XY model

We study the structure of the revivals in an integrable quantum many-body system, the transverse field XY spin chain, after a quantum quench. The time evolutions of the Loschmidt echo, the magnetization, and the single spin entanglement entropy are calculated. We find that the revival times for all of these observables are given by integer multiples of T_rev \sim L / v_max where L is the linear size of the system and v_max is the maximal group velocity of quasiparticles. This revival structure is universal in the sense that it does not depend on the initial state and the size of the quench. Applying non-integrable perturbations to the XY model, we observe that the revivals are robust against such perturbations: they are still visible at time scales much larger than the quasiparticle lifetime. We therefore propose a generic connection between the revival structure and the locality of the dynamics, where the quasiparticle speed v_max generalizes into the Lieb$-$Robinson speed v_LR.Comment: completely overhauled version including results on non integrable model

Observing spin fractionalization in the Kitaev spin liquid via temperature evolution of indirect resonant inelastic x-ray scattering

Motivated by the ongoing effort to search for high-resolution signatures of quantum spin liquids, we investigate the temperature dependence of the indirect resonant inelastic x-ray scattering (RIXS) response for the Kitaev honeycomb model. We find that, as a result of spin fractionalization, the RIXS response changes qualitatively at two well-separated temperature scales, $T_L$ and $T_H$, which correspond to the characteristic energies of the two kinds of fractionalized excitations, $\mathbb{Z}_2$ gauge fluxes and Majorana fermions, respectively. While thermally excited $\mathbb{Z}_2$ gauge fluxes at temperature $T_L$ lead to a general broadening and softening of the response, the thermal proliferation of Majorana fermions at temperature $T_H \sim 10 \, T_L$ results in a significant shift of the spectral weight, both in terms of energy and momentum. Due to its exclusively indirect nature, the RIXS process we consider gives rise to a universal magnetic response and, from an experimental perspective, it directly corresponds to the $K$-edge of Ru$^{3+}$ in the Kitaev candidate material $\alpha$-RuCl$_3$.Comment: 8 pages, 5 figures, published version with infinitesimal change

Doping a topological quantum spin liquid: slow holes in the Kitaev honeycomb model

We present a controlled microscopic study of mobile holes in the spatially anisotropic (Abelian) gapped phase of the Kitaev honeycomb model. We address the properties of (i) a single hole [its internal degrees of freedom as well as its hopping properties]; (ii) a pair of holes [their (relative) particle statistics and interactions]; (iii) the collective state for a finite density of holes. We find that each hole in the doped model has an eight-dimensional internal space, characterized by three internal quantum numbers: the first two "fractional" quantum numbers describe the binding to the hole of the fractional excitations (fluxes and fermions) of the undoped model, while the third "spin" quantum number determines the local magnetization around the hole. The fractional quantum numbers also encode fundamentally distinct particle properties, topologically robust against small local perturbations: some holes are free to hop in two dimensions, while others are confined to hop in one dimension only; distinct hole types have different particle statistics, and in particular, some of them exhibit non-trivial (anyonic) relative statistics. These particle properties in turn determine the physical properties of the multi-hole ground state at finite doping, and we identify two distinct ground states with different hole types that are stable for different model parameters. The respective hopping dimensionalities manifest themselves in an electrical conductivity approximately isotropic in one ground state and extremely anisotropic in the other one. We also compare our microscopic study with related mean-field treatments, and discuss the main discrepancies between the two approaches, which in particular involve the possibility of binding fractional excitations as well as the particle statistics of the holes.Comment: 29 pages, 14 figures, published version with infinitesimal change

A körösi várjobbágyok útja a nemességbe

In the medieval Slavonia, the castle warriors had a special type of liberty which was not equal to the liberty of nobles. They had to pay some taxes and offer military service. The higher 'class' of castle warriors held the positions of the 'várispánság' (Lat. comitatus, Eng. castle district) and they had the opportunity before 1430 to become members of the true nobility and some of them were successful. The elevated families henceforward had functions in the comitatus as well. In 1430, the castle warriors of Krizevci were collectively ennobled by king Sigismund. The paper analyses the common elements of the 'successful stories', in other words of the known ennoblements. The father or the grandfather who had held the office of the comes terrestris, the highest position of the castle-district was a good starting point for his descendants. Those who had been ennobled were surely forced in the army and were the familiaris of a magnate or the king