Numerical Contractor Renormalization Method for Quantum Spin Models

We demonstrate the utility of the numerical Contractor Renormalization (CORE) method for quantum spin systems by studying one and two dimensional model cases. Our approach consists of two steps: (i) building an effective Hamiltonian with longer ranged interactions using the CORE algorithm and (ii) solving this new model numerically on finite clusters by exact diagonalization. This approach, giving complementary information to analytical treatments of the CORE Hamiltonian, can be used as a semi-quantitative numerical method. For ladder type geometries, we explicitely check the accuracy of the effective models by increasing the range of the effective interactions. In two dimensions we consider the plaquette lattice and the kagome lattice as non-trivial test cases for the numerical CORE method. On the plaquette lattice we have an excellent description of the system in both the disordered and the ordered phases, thereby showing that the CORE method is able to resolve quantum phase transitions. On the kagome lattice we find that the previously proposed twofold degenerate S=1/2 basis can account for a large number of phenomena of the spin 1/2 kagome system. For spin 3/2 however this basis does not seem to be sufficient anymore. In general we are able to simulate system sizes which correspond to an 8x8 lattice for the plaquette lattice or a 48-site kagome lattice, which are beyond the possibilities of a standard exact diagonalization approach.Comment: 15 page

Cavity QED with hybrid nanocircuits: from atomic-like physics to condensed matter phenomena

Circuit QED techniques have been instrumental to manipulate and probe with exquisite sensitivity the quantum state of superconducting quantum bits coupled to microwave cavities. Recently, it has become possible to fabricate new devices where the superconducting quantum bits are replaced by hybrid mesoscopic circuits combining nanoconductors and metallic reservoirs. This mesoscopic QED provides a new experimental playground to study the light-matter interaction in electronic circuits. Here, we present the experimental state of the art of Mesoscopic QED and its theoretical description. A first class of experiments focuses on the artificial atom limit, where some quasiparticles are trapped in nanocircuit bound states. In this limit, the Circuit QED techniques can be used to manipulate and probe electronic degrees of freedom such as confined charges, spins, or Andreev pairs. A second class of experiments consists in using cavity photons to reveal the dynamics of electron tunneling between a nanoconductor and fermionic reservoirs. For instance, the Kondo effect, the charge relaxation caused by grounded metallic contacts, and the photo-emission caused by voltage-biased reservoirs have been studied. The tunnel coupling between nanoconductors and fermionic reservoirs also enable one to obtain split Cooper pairs, or Majorana bound states. Cavity photons represent a qualitatively new tool to study these exotic condensed matter states.Comment: 34 pages, 18 figures, 1 table, minor differences with the published version to appear in Journal of Physics: Condensed Matter as a topical revie

Valence Bond Entanglement Entropy

We introduce for SU(2) quantum spin systems the Valence Bond Entanglement Entropy as a counting of valence bond spin singlets shared by two subsystems. For a large class of antiferromagnetic systems, it can be calculated in all dimensions with Quantum Monte Carlo simulations in the valence bond basis. We show numerically that this quantity displays all features of the von Neumann entanglement entropy for several one-dimensional systems. For two-dimensional Heisenberg models, we find a strict area law for a Valence Bond Solid state and multiplicative logarithmic corrections for the Neel phase.Comment: 4 pages, 3 figures, v2: small corrections, published versio

Rigidity and intermediate phases in glasses driven by speciation

The rigid to floppy transitions and the associated intermediate phase in glasses are studied in the case where the local structure is not fully determined from the macroscopic concentration. The approach uses size increasing cluster approximations and constraint counting algorithms. It is shown that the location and the width of the intermediate phase and the corresponding structural, mechanical and energetical properties of the network depend crucially on the way local structures are selected at a given concentration. The broadening of the intermediate phase is obtained for networks combining a large amount of flexible local structural units and a high rate of medium range order.Comment: 4 pages, 4 figure

The origin of short-lived radionuclides and the astrophysical environment of solar system formation

Based on early solar system abundances of short-lived radionuclides (SRs), such as $^{26}$Al (T$_{1/2} = 0.74$ Myr) and $^{60}$Fe (T$_{1/2} = 1.5$ Myr), it is often asserted that the Sun was born in a large stellar cluster, where a massive star contaminated the protoplanetary disk with freshly nucleosynthesized isotopes from its supernova (SN) explosion. To account for the inferred initial solar system abundances of short-lived radionuclides, this supernova had to be close ($\sim$ 0.3 pc) to the young ($\leqslant$ 1 Myr) protoplanetary disk. Here we show that massive star evolution timescales are too long, compared to typical timescales of star formation in embedded clusters, for them to explode as supernovae within the lifetimes of nearby disks. This is especially true in an Orion Nebular Cluster (ONC)-type of setting, where the most massive star will explode as a supernova $\sim$ 5 Myr after the onset of star formation, when nearby disks will have already suffered substantial photoevaporation and/or formed large planetesimals. We quantify the probability for {\it any} protoplanetary disk to receive SRs from a nearby supernova at the level observed in the early solar system. Key constraints on our estimate are: (1) SRs have to be injected into a newly formed ($\leqslant$ 1 Myr) disk, (2) the disk has to survive UV photoevaporation, and (3) the protoplanetary disk must be situated in an enrichment zone permitting SR injection at the solar system level without disk disruption. The probability of protoplanetary disk contamination by a supernova ejecta is, in the most favorable case, 3 $\times$ 10$^{-3}$

Spin States Protected from Intrinsic Electron-Phonon-Coupling Reaching 100 ns Lifetime at Room Temperature in MoSe2_2

We present time-resolved Kerr rotation measurements, showing spin lifetimes of over 100 ns at room temperature in monolayer MoSe$_2$. These long lifetimes are accompanied by an intriguing temperature dependence of the Kerr amplitude, which increases with temperature up to 50 K and then abruptly switches sign. Using ab initio simulations we explain the latter behavior in terms of the intrinsic electron-phonon coupling and the activation of transitions to secondary valleys. The phonon-assisted scattering of the photo-excited electron-hole pairs prepares a valley spin polarization within the first few ps after laser excitation. The sign of the total valley magnetization, and thus the Kerr amplitude, switches as a function of temperature, as conduction and valence band states exhibit different phonon-mediated inter-valley scattering rates. However, the electron-phonon scattering on the ps time scale does not provide an explanation for the long spin lifetimes. Hence, we deduce that the initial spin polarization must be transferred into spin states which are protected from the intrinsic electron-phonon coupling, and are most likely resident charge carriers which are not part of the itinerant valence or conduction band states.Comment: 18 pages, 17 figure

Field induced stationary state for an accelerated tracer in a bath

Our interest goes to the behavior of a tracer particle, accelerated by a constant and uniform external field, when the energy injected by the field is redistributed through collision to a bath of unaccelerated particles. A non equilibrium steady state is thereby reached. Solutions of a generalized Boltzmann-Lorentz equation are analyzed analytically, in a versatile framework that embeds the majority of tracer-bath interactions discussed in the literature. These results --mostly derived for a one dimensional system-- are successfully confronted to those of three independent numerical simulation methods: a direct iterative solution, Gillespie algorithm, and the Direct Simulation Monte Carlo technique. We work out the diffusion properties as well as the velocity tails: large v, and either large -v, or v in the vicinity of its lower cutoff whenever the velocity distribution is bounded from below. Particular emphasis is put on the cold bath limit, with scatterers at rest, which plays a special role in our model.Comment: 20 pages, 6 figures v3:minor corrections in sec.III and added reference

Existence of global strong solutions to a beam-fluid interaction system

We study an unsteady non linear fluid-structure interaction problem which is a simplified model to describe blood flow through viscoleastic arteries. We consider a Newtonian incompressible two-dimensional flow described by the Navier-Stokes equations set in an unknown domain depending on the displacement of a structure, which itself satisfies a linear viscoelastic beam equation. The fluid and the structure are fully coupled via interface conditions prescribing the continuity of the velocities at the fluid-structure interface and the action-reaction principle. We prove that strong solutions to this problem are global-in-time. We obtain in particular that contact between the viscoleastic wall and the bottom of the fluid cavity does not occur in finite time. To our knowledge, this is the first occurrence of a no-contact result, but also of existence of strong solutions globally in time, in the frame of interactions between a viscous fluid and a deformable structure