Dimensional crossover and cold-atom realization of topological Mott insulators

We propose a cold-atom setup which allows for a dimensional crossover from a two-dimensional quantum spin Hall insulating phase to a three-dimensional strong topological insulator by tuning the hopping between the layers. We further show that additional Hubbard onsite interactions can give rise to spin liquid-like phases: weak and strong topological Mott insulators. They represent the celebrated paradigm of a quantum state of matter which merely exists because of the interplay of the non-trivial topology of the band structure and strong interactions. While the theoretical understanding of this phase has remained elusive, our proposal shall help to shed some light on this exotic state of matter by paving the way for a controlled experimental investigation in optical lattices.Comment: 4+ pages, 3 figures; includes Supplemental Material (3 pages, 1 figure

Hierarchy of Information Scrambling, Thermalization, and Hydrodynamic Flow in Graphene

We determine the information scrambling rate $\lambda_{L}$ due to electron-electron Coulomb interaction in graphene. $\lambda_{L}$ characterizes the growth of chaos and has been argued to give information about the thermalization and hydrodynamic transport coefficients of a many-body system. We demonstrate that $\lambda_{L}$ behaves for strong coupling similar to transport and energy relaxation rates. A weak coupling analysis, however, reveals that scrambling is related to dephasing or single particle relaxation. Furthermore, $\lambda_{L}$ is found to be parametrically larger than the collision rate relevant for hydrodynamic processes, such as electrical conduction or viscous flow, and the rate of energy relaxation, relevant for thermalization. Thus, while scrambling is obviously necessary for thermalization and quantum transport, it does generically not set the time scale for these processes. In addition we derive a quantum kinetic theory for information scrambling that resembles the celebrated Boltzmann equation and offers a physically transparent insight into quantum chaos in many-body systems

Non-adiabatic processes in Majorana qubit systems

We investigate the non-adiabatic processes occurring during the manipulations of Majorana qubits in 1-D semiconducting wires with proximity induced superconductivity. Majorana qubits are usually protected by the excitation gap. Yet, manipulations performed at a finite pace can introduce both decoherence and renormalization effects. Though exponentially small for slow manipulations, these effects are important as they may constitute the ultimate decoherence mechanism. Moreover, as adiabatic topological manipulations fail to produce a universal set of quantum gates, non-adiabatic manipulations might be necessary to perform quantum computation.Comment: 14 pages, 5 figure

Protection of parity-time symmetry in topological many-body systems: non-Hermitian toric code and fracton models

In the study of $\mathcal{P}\mathcal{T}$-symmetric quantum systems with non-Hermitian perturbations, one of the most important questions is whether eigenvalues stay real or whether $\mathcal{P}\mathcal{T}$-symmetry is spontaneously broken when eigenvalues meet. A particularly interesting set of eigenstates is provided by the degenerate ground-state subspace of systems with topological order. In this paper, we present simple criteria that guarantee the protection of $\mathcal{P}\mathcal{T}$-symmetry and, thus, the reality of the eigenvalues in topological many-body systems. We formulate these criteria in both geometric and algebraic form, and demonstrate them using the toric code and several different fracton models as examples. Our analysis reveals that $\mathcal{P}\mathcal{T}$-symmetry is robust against a remarkably large class of non-Hermitian perturbations in these models; this is particularly striking in the case of fracton models due to the exponentially large number of degenerate states.Comment: 20 pages, 6 figure

Pair breaking due to orbital magnetism in iron-based superconductors

We consider superconductivity in the presence of impurities in a two-band model suited for the description of iron-based superconductors. We analyze the effect of interband scattering processes on superconductivity, allowing for orbital, i.e., nonspin-magnetic but time-reversal symmetry-breaking impurities. Pair breaking in such systems is described by a nontrivial phase in an interband-scattering matrix element. We find that the transition temperature of conventional superconductors can be suppressed due to interband scattering, whereas unconventional superconductors may be unaffected. We also discuss the stability of density wave phases in the presence of impurities. As an example, we consider impurities associated with imaginary charge density waves that are of interest for iron-based superconductors.Comment: 12 pages, 4 figure