Disorder, Interactions and Coherence: Warps and Delights

Anomalous Hall effect is crucially affected by skew scattering on pairs of closely located impurities. We demonstrate that proper description of this mechanism requires a calculation beyond the commonly employed non-crossing approximation. Inclusion of X and $\mathrm{\Psi}$ diagrams with a single pair of intersecting disorder lines essentially modifies previously obtained results. These diagrams constitute an inherent part of the full skew scattering amplitude. Our argumentation applies to all models of anomalous Hall effect and related phenomena, e.g spin-orbit torque and spin Hall effect. For illustration, we revise the results for 2D massive Dirac fermions [1] and for the Bychkov-Rashba ferromagnet [2]. [1] I. A. Ado, I. A. Dmitriev, P. M. Ostrovsky, and M. Titov, EPL 111, 37004 (2015). [2] I. A. Ado, I. A. Dmitriev, P. M. Ostrovsky, and M. Titov, arXiv:1511.07413 (2015).

We predict a universal echo phenomenon present in the time evolution of many-body states of interacting quantum systems described by Fermi-Hubbard models. It consists of the coherent revival of transition probabilities echoing a sudden flip of the spins that, contrary to its single-particle (Hahn) version, is {\it not} dephased by interactions or spin-orbit coupling. The many-body spin echo signal has a universal shape independent of the interaction strength, and an amplitude and sign depending only on combinatorial relations between the number of particles and the number of applied spin flips. Our analytical predictions, based on semiclassical interfering amplitudes in Fock space associated with chaotic mean-field solutions, are tested against extensive numerical simulations confirming that the coherent origin of the echo lies in the existence of anti-unitary symmetries.

In most experimental systems on qubits, the qubit is weakly coupled to an environment, such as an electronic gate or a collection of nuclear spins. Often this environment is disordered. Our goal is to quantify the effect of the disorder on the dynamics of the qubit. Conversely, we can also use the dynamics of the qubit to probe the disordered system directly. For this, we solved the dynamics of a qubit (two level system) attached to an infinite random chain. We obtained expressions for the decoherence rate of the qubit as a function of the disorder of the random chain, which can be expressed in terms of the transmission through the chain evaluated at the eigenenergy of the qubit. Hence, we found a direct correspondence between the dynamics of the qubit and the transmission properties of the disordered environment. This work was done in collaboration with H. Eleuch and R. Mackenzie.

We are interested in the effects of dephasing on the fermionic systems. We study the effects of dephasing noise on a prototypical many-body localized system -- the XXZ spin 1/2 chain with a disordered magnetic field. At times longer than the inverse dephasing strength the dynamics of the system is described by a probabilistic Markov process on the space of diagonal density matrices, while all off-diagonal elements of the density matrix decay to zero. The generator of the Markovian process is a bond-disordered spin chain. The scaling variable is identified, and independence of relaxation on the interaction strength is demonstrated. We show that purity and von Neumann entropy are extensive, showing no signatures of localization, while the operator space entanglement entropy exhibits a logarithmic growth with time until the final saturation corresponding to localization breakdown, suggesting a many-body localized dynamics of the effective Markov process. We also present that a spectrum of dissipative fermionic system can be found exactly from the Bethe ansatz equations. We analyze the type of Bethe-ansatz excitations which are the most relevant for the relaxation of the system towards non-equilibrium steady state. Then investigating the Bethe-ansatz wave-function we obtain that the system behaves in a diffusive way. We conclude by presenting future directions where known Bethe-ansatz solvable models can be used to analyze dynamics of dissipative systems.

We will discuss the many-body physics that is realised by interacting particles occupying topological flat bands of the Harper-Hofstadter model with Chern number $|C|>1$ [1,2]. We formulate the predictions of Chern-Simons or composite fermion theory in terms of the filling factor, $\nu$, defined as the ratio of particle density to the number of single-particle states per unit area. We show that this theory predicts a series of fractional quantum Hall states with filling factors $\nu = r/(r|C| +1)$ for bosons, or $\nu = r/(2r|C| +1)$ for fermions. This series includes a bosonic integer quantum Hall state (bIQHE) in $|C|=2$ bands. We construct specific cases where a single band of the Harper-Hofstadter model is occupied. For these cases, we provide numerical evidence that several states in this series are realized as incompressible quantum liquids for bosons with contact interactions, with characteristics matching the predictions of composite fermion theory. Finally, we discuss how band-geometric measures influence the stability of generic fractional Chern insulator phases, providing evidence that the many-body gap correlates not only with the flatness of the Berry-curvature, but additionally we demonstrate the influence of the Fubini-Study metric tensor [3]. [1] G. Möller, N.R. Cooper, Phys. Rev. Lett. 103, 105303 (2009). [2] G. Möller, N.R. Cooper, Phys. Rev. Lett. 115, 126401 (2015). [3] T. Jackson, G. Möller, R. Roy, Nature Communications 6, 8629 (2015).

We investigate non-equilibrium magnon distribution induced by a short laser pulse in a half-metal ferromagnet described by the s-d model. Using non-equilibrium Green's function formalism we derive and analyse quantum kinetic equation for magnons. We demonstrate that non-quasiparticle states in the ferromagnet play the key role in the energy transfer from conduction electrons to magnons.

We present the first ever experimental demonstration of length-dependent conductivity $\sigma$ consistent with the scaling hypothesis of localisation [1,2]. By measuring the length ($L$)-dependent transport characteristics of several (> 18) two-dimensional electron gases (2DEGs) of mesoscopic dimensions, we observe a clear and systematic decrease $\sigma$ as $L$ increases. We then use a single parameter fit to extract the electronic mean free path $\ell$ of the 2DEGs and find that the relation $k_F \ell \neq \sigma/\sigma_0$ where $\sigma_0 = e^2/h$, the conductance quantum. We discuss the implications of this result within the framework of the putative two-dimensional metal-insulator transition. An important conclusion of our experimental results is that the 2DEG maintains phase coherence over the 2DEG dimensions which can be as high as 10~$\mu$m at 0.3~K. This remarkable and unexpected result gains support from thermopower measurements which show anomalous fluctuations and sign changes as a function of carrier concentration [3,4], as well as asymmetric characteristics upon magnetic field reversal [5], both of which are anticipated in phase coherent systems. We argue that this behaviour arises due to a decoupling of the 2DEG from the lattice bath due to the specific geometry of the devices, and discuss the relevance of our results to recent ideas [6] pertaining to many-body localization [7]. [1] D. Backes, R. Hall, M. Pepper, H. E. Beere, D. Ritchie and V. Narayan, Phys. Rev. B 92, 174426 (2015). [2] D. Backes, R. Hall, M. Pepper, H. E. Beere, D. Ritchie and V. Narayan, J. Phys. Condens. Matter 28, 01LT01 (2016). [3] V. Narayan et al., Phys. Rev. B 86, 125406 (2012). [4] V. Narayan et al., New J. Phys. 16, 085009 (2014). [5] V. Narayan et al., in preparation (2016). [6] S. Banerjee and E. Altman, Phys. Rev. Lett. 116, 116601 (2016). [7] D. M. Basko, I.L. Aleiner, B.L. Altshuler, Ann. Phys. 321, 1126 (2006).

In recent years the effects of spin degree of freedom of electrons on the transport properties of nanoelectromechanical (NEM) systems have been studied intensively. The reason for this is additional possibility to control electric current by using external magnetic field or/and spin-orbit interaction. We have suggested a spin-mediated coupling between high-frequency electromagnetic microwave field and low-frequency (\omega) mechanical vibrations in magnetic NEM device. The system comprises a single-wall carbon nanotube (CNT) suspended between two ferromagnetic electrodes with opposite magnetizations. A magnetic tip placed near the CNT produces non-homogeneous magnetic field B_{\par}, which induces magnetic force that acts on suspended part of nanowire and depends on its deflection and electron spin-projection. Therefore, magnetic field provides coupling between electronic spin and mechanical degree of freedom. The system is subjected into external microwave field. The specific orientation of a magnetic component of the microwave field B_{\perp} and additional condition of coincidence of the field frequency (\Omega) and Zeeman energy splitting (\Delta) result in spin-flip processes and facilitate the electron transport through NEM device. To analyse the effective coupling between microwave field and soft mechanical vibrations we investigate the time evolution of CNT flexural oscillations with respect to electron degree of freedom. The vibrational "ground state" becomes unstable in the case of parallel magnetization between magnetic tip and source electrode when \Delta<\hbar \Omega. It means, that system transfer to the regime of shuttling, when mechanical instability develops into pronounced self-sustained vibrations of CNT resonator. The criterion of shuttle instability is investigated in the case of Coulomb blockade and in the limit of adiabatic motion \omega<\Gamma, where \Gamma is electron energy level width. Different regimes of nano-mechanical oscillations are analysed.

Coherent backscattering generally refers to a significant and robust enhancement of the average backscattering probability of a wave within a disordered medium, which from a semiclassical point of view arises due to the constructive interference between backscattered trajectories and their time-reversed counterparts. We recently investigated the manifestation of this wave interference phenomenon in the Fock space of a disordered Bose-Hubbard system of finite extent [1], which can potentially be realized using ultracold bosonic atoms within optical lattices. Preparing the atoms in a well-defined Fock state of the lattice and letting the system evolve for a finite time will, for suitable parameters of the system and upon some disorder average over random on-site energies of the lattice, generally give rise to an equidistribution of the occupation probability within the energy shell of the Fock space that corresponds to the initial energy of the system, in accordance with the quantum microcanonical ensemble. We find, however, that the initial state is twice as often encountered as other Fock states with comparable total energy, which is a consequence of coherent backscattering [1]. Most recently, we showed that this phenomenon also arises in spin 1/2 Fermi-Hubbard rings that involve Rashba hopping terms (which combine inter-site hoppings with spin flips and arise from spin-orbit coupling), for which a newly developed semiclassical theory [2] correctly predicts a coherent enhancement of the occupation probabilities of the initial state and its spin-flipped counterpart. Moreover, performing a global spin flip within this Fermi-Hubbard system will give rise to significant spin echo peaks on those two Fock states, which is again a consequence of quantum many-body interference [3]. The semiclassical predictions of these enhancements and peaks are found to be in very good agreement with numerical findings obtained from the exact quantum time evolution within this Fermi-Hubbard system. [1] T. Engl, J. Dujardin, A. Argüelles, P. Schlagheck, K. Richter, and J. D. Urbina, Phys. Rev. Lett. 112, 140403 (2014). [2] T. Engl, P. Plößl, J. D. Urbina, and K. Richter, Theoretical Chemistry Accounts 133, 1563 (2014). [3] T. Engl, J. D. Urbina, and K. Richter, arXiv:1409.5684.

We study thermal conductivity in the disordered two-dimensional electron liquid in the presence of long-range Coulomb interactions. We present a Renormalization Group (RG) analysis and include scattering processes induced by the Coulomb interaction in the sub-temperature energy range. For the thermal conductivity, unlike for the electric conductivity, these scattering processes yield a logarithmic correction which may compete with the RG-corrections. We use the theory to describe thermal transport on the metallic side of the metal-insulator transition in Si MOSFETs. G. Schwiete and A. M. Finkel’stein, PRB 90, 060201(R) (2014), PRB 90, 155441 (2014), arXiv:1509:02519, arXiv:1510.06529

Several condensed matter systems obey conformal Schroedinger symmetry. These include anyons, non-viscous fluids or cold atoms. Unlike the relativistic case the symmetry group itself is not powerful enough to determine the three-point correlation functions completely. However, for a certain class of operators symmetry group together with the Schroedinger equation fixes the three-point correlation functions up to a constant. I will show that this observation is a necessary first step towards the non-relativistic bootstrap approach. I will also show how to determine the conformal blocks of non-relativistic CFTs. Finally I will discuss the example of anyons, which is a solvable toy model, which is useful to test the above ideas.