Coulomb potentials and Taylor expansions in time-dependent density-functional theory
Fournais, Søren, Lampert, Jonas, Lewin, Mathieu and Østergaard Sørensen, Thomas
Phys. Rev. A , Volume 92(062510)
June 2016

Abstract: We investigate when Taylor expansions can be used to prove the Runge-Gross theorem, which is at the foundation of time-dependent density-functional theory (TDDFT). We start with a general analysis of the conditions for the Runge-Gross argument, especially the time differentiability of the density. The latter should be questioned in the presence of singular (e.g., Coulomb) potentials. Then we show that a singular potential in a one-body operator considerably decreases the class of time-dependent external potentials to which the original argument can be applied. A two-body singularity has an even stronger impact and an external potential is essentially incompatible with it. For the Coulomb interaction and all reasonable initial many-body states, the Taylor expansion only exists to a finite order, except for constant external potentials. Therefore, high-order Taylor expansions are not the right tool to study atoms and molecules in TDDFT.

Ubiquity of Exciton Localization in Cryogenic Carbon Nanotubes
Hofmann, Matthias, Noe, Jonathan, Kneer, Alexander, Crochet, Jared and Högele, Alexander
Nano Lett. , Volume 16(5), page: 2958–2962
April 2016

Abstract: We present photoluminescence studies of individual semiconducting single-wall carbon nanotubes at room and cryogenic temperatures. From the analysis of spatial and spectral features of nanotube photoluminescence, we identify characteristic signatures of unintentional exciton localization. Moreover, we quantify the energy scale of exciton localization potentials as ranging from a few to a few tens of millielectronvolts and stemming from both environmental disorder and shallow covalent side-wall defects. Our results establish disorder-induced crossover from the diffusive to the localized regime of nanotube excitons at cryogenic temperatures as a ubiquitous phenomenon in micelle-encapsulated and as-grown carbon nanotubes.

Griffiths effects and slow dynamics in nearly many-body localized systems
Gopalakrishnan, Sarang, Agarwal, Kartiek, Demler, Eugene A., Huse, David A. and Knap, Michael
Phys. Rev. B , Volume 93(134206)
April 2016

Abstract: The low-frequency response of systems near a many-body localization transition can be dominated by rare regions that are locally critical or “in the other phase.” It is known that in one dimension, these rare regions can cause the dc conductivity and diffusion constant to vanish even inside the delocalized thermal phase. Here, we present a general analysis of such Griffiths effects in the thermal phase near the many-body localization transition: we consider both one-dimensional and higher-dimensional systems, subject to quenched randomness, and discuss both linear response (including the frequency- and wave-vector-dependent conductivity) and more general dynamics. In all the regimes we consider, we identify observables that are dominated by rare-region effects. In some cases (one-dimensional systems and Floquet systems with no extensive conserved quantities), essentially all long-time local observables are dominated by rare-region effects; in others, generic observables are instead dominated by hydrodynamic long-time tails throughout the thermal phase, and one must look at specific probes, such as spin echo, to see Griffiths behavior.

Protected gates for topological quantum field theories
Beverland, Michael E., Buerschaper, Oliver and König, Robert

Abstract: We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators — for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons, in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group.

Quantum Phase Transition and Protected Ideal Transport in a Kondo Chain
Tsvelik, A. M. and Yevtushenko, O. M.
PRL , Volume 115(216402)
November 2015

Abstract: We study the low energy physics of a Kondo chain where electrons from a one-dimensional band interact with magnetic moments via an anisotropic exchange interaction. It is demonstrated that the anisotropy gives rise to two different phases which are separated by a quantum phase transition. In the phase with easy plane anisotropy, Z2 symmetry between sectors with different helicity of the electrons is broken. As a result, localization effects are suppressed and the dc transport acquires (partial) symmetry protection. This effect is similar to the protection of the edge transport in time-reversal invariant topological insulators. The phase with easy axis anisotropy corresponds to the Tomonaga-Luttinger liquid with a pronounced spin-charge separation. The slow charge density wave modes have no protection against localization.

Massive Goldstone (Higgs) mode in two-dimensional ultracold atomic lattice systems
Liu, Longxiang, Chen, Kun, Deng, Youjin, Endress, Manuel, Pollet, Lode and Prokof'ev, Nikolay
Phys. Rev. B , Volume 92(174521)
November 2015

Abstract: We discuss how to reveal the massive Goldstone mode, often referred to as the Higgs amplitude mode, near the superfluid-to-insulator quantum critical point (QCP) in a system of two-dimensional ultracold bosonic atoms in optical lattices. The spectral function of the amplitude response is obtained by analytic continuation of the kinetic energy correlation function calculated by Monte Carlo methods. Our results enable a direct comparison with the recent experiment [M. Endres, T. Fukuhara, D. Pekker, M. Cheneau, P. Schauß, C. Gross, E. Demler, S. Kuhr, and I. Bloch, Nature (London) 487, 454 (2012)] and demonstrate a good agreement for temperature shifts induced by lattice modulation. Based on our numerical analysis, we formulate the necessary conditions in terms of homogeneity, detuning from the QCP and temperature in order to reveal the massive Goldstone resonance peak in spectral functions experimentally. We also propose to apply a local modulation at the trap center to overcome the inhomogeneous broadening caused by the parabolic trap confinement.

Prethermal Floquet Steady States and Instabilities in the Periodically Driven, Weakly Interacting Bose-Hubbard Model
Bukov, Marin, Gopalakrishnan, Sarang, Knap, Michael and Demler, Eugene
Phys. Rev. Lett. , Volume 115(205301)
November 2015

Abstract: We explore prethermal Floquet steady states and instabilities of the weakly interacting two-dimensional Bose-Hubbard model subject to periodic driving. We develop a description of the nonequilibrium dynamics, at arbitrary drive strength and frequency, using a weak-coupling conserving approximation. We establish the regimes in which conventional (zero-momentum) and unconventional [(π,π)-momentum] condensates are stable on intermediate time scales. We find that condensate stability is enhanced by increasing the drive strength, because this decreases the bandwidth of quasiparticle excitations and thus impedes resonant absorption and heating. Our results are directly relevant to a number of current experiments with ultracold bosons.

Far-from-Equilibrium Field Theory of Many-Body Quantum Spin Systems: Prethermalization and Relaxation of Spin Spiral States in Three Dimensions
Babadi, Mehrtash, Demler, Eugene and Knap, Michael
Phys. Rev. X , Volume 5(041005)
October 2015

Abstract: We study theoretically the far-from-equilibrium relaxation dynamics of spin spiral states in the three-dimensional isotropic Heisenberg model. The investigated problem serves as an archetype for understanding quantum dynamics of isolated many-body systems in the vicinity of a spontaneously broken continuous symmetry. We present a field-theoretical formalism that systematically improves on the mean field for describing the real-time quantum dynamics of generic spin-1/2 systems. This is achieved by mapping spins to Majorana fermions followed by a 1/N expansion of the resulting two-particle-irreducible effective action. Our analysis reveals rich fluctuation-induced relaxation dynamics in the unitary evolution of spin spiral states. In particular, we find the sudden appearance of long-lived prethermalized plateaus with diverging lifetimes as the spiral winding is tuned toward the thermodynamically stable ferro- or antiferromagnetic phases. The emerging prethermalized states are characterized by different bosonic modes being thermally populated at different effective temperatures and by a hierarchical relaxation process reminiscent of glassy systems. Spin-spin correlators found by solving the nonequilibrium Bethe-Salpeter equation provide further insight into the dynamic formation of correlations, the fate of unstable collective modes, and the emergence of fluctuation-dissipation relations. Our predictions can be verified experimentally using recent realizations of spin spiral states with ultracold atoms in a quantum gas microscope [S. Hild et al., Phys. Rev. Lett. 113, 147205 (2014)].

Microscopic Characterization of Scalable Coherent Rydberg Superatoms
Zeiher, J., Schauss, P., Hild, S., Macri, T., Bloch, I. and Gross, C.
Physical Review X , Volume 5(031015)
August 2015

Abstract: Strong interactions can amplify quantum effects such that they become important on macroscopic scales. Controlling these coherently on a single-particle level is essential for the tailored preparation of strongly correlated quantum systems and opens up new prospects for quantum technologies. Rydberg atoms offer such strong interactions, which lead to extreme nonlinearities in laser-coupled atomic ensembles. As a result, multiple excitation of a micrometer-sized cloud can be blocked while the light-matter coupling becomes collectively enhanced. The resulting two-level system, often called a “superatom,” is a valuable resource for quantum information, providing a collective qubit. Here, we report on the preparation of 2 orders of magnitude scalable superatoms utilizing the large interaction strength provided by Rydberg atoms combined with precise control of an ensemble of ultracold atoms in an optical lattice. The latter is achieved with sub-shot-noise precision by local manipulation of a two-dimensional Mott insulator. We microscopically confirm the superatom picture by in situ detection of the Rydberg excitations and observe the characteristic square-root scaling of the optical coupling with the number of atoms. Enabled by the full control over the atomic sample, including the motional degrees of freedom, we infer the overlap of the produced many-body state with a W state from the observed Rabi oscillations and deduce the presence of entanglement. Finally, we investigate the breakdown of the superatom picture when two Rydberg excitations are present in the system, which leads to dephasing and a loss of coherence.

Spatially Resolved Detection of a Spin-Entanglement Wave in a Bose-Hubbard Chain
Fukuhara, T., Hild, S., Zeiher, J., Schauss, P., Bloch, I., Endres, M. and Gross, C.
Physical Review Letters , Volume 115(035302)
July 2015

Abstract: Entanglement is an essential property of quantum many-body systems. However, its local detection is challenging and was so far limited to spin degrees of freedom in ion chains. Here we measure entanglement between the spins of atoms located on two lattice sites in a one-dimensional BoseHubbard chain which features both local spin- and particle-number fluctuations. Starting with an initially localized spin impurity, we observe an outwards propagating entanglement wave and show quantitatively how entanglement in the spin sector rapidly decreases with increasing particle-number fluctuations in the chain.

Symmetric minimally entangled typical thermal states
Bruognolo, Benedikt, von Delft, Jan and Weichselbaum, Andreas
Phys. Rev. B , Volume 92(115105)
June 2015

Abstract: We extend White's minimally entangled typically thermal states approach (METTS) to allow Abelian and non-Ablian symmetries to be exploited when computing finite-temperature response functions in one-dimensional (1D) quantum systems. Our approach, called SYMETTS, starts from a METTS sample of states that are not symmetry eigenstates, and generates from each a symmetry eigenstate. These symmetry states are then used to calculate dynamic response functions. SYMETTS is ideally suited to determine the low-temperature spectra of 1D quantum systems with high resolution. We employ this method to study a generalized diamond chain model for the natural mineral azurite Cu3(CO3)2(OH)2, which features a plateau at 13 in the magnetization curve at low temperatures. Our calculations provide new insight into the effects of temperature on magnetization and excitation spectra in the plateau phase, which can be fully understood in terms of the microscopic model.

Crystallization in Ising quantum magnets
Schauss, P., Zeiher, J., Fukuhara, T., Hild, S., Cheneau, M., Macri, T., Pohl, T., Bloch, I. and Gross, C.
Science , Volume 347(6229), page: 1455-1458
March 2015

Abstract: Dominating finite-range interactions in many-body systems can lead to intriguing self-ordered phases of matter. For quantum magnets, Ising models with power-law interactions are among the most elementary systems that support such phases. These models can be implemented by laser coupling ensembles of ultracold atoms to Rydberg states. Here, we report on the experimental preparation of crystalline ground states of such spin systems. We observe a magnetization staircase as a function of the system size and show directly the emergence of crystalline states with vanishing susceptibility. Our results demonstrate the precise control of Rydberg many-body systems and may enable future studies of phase transitions and quantum correlations in interacting quantum magnets.

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