Matrix Product Approximations to Multipoint Functions in TwoDimensional Conformal Field Theory
Physical Review Letters
, Volume 117, page: 121601
September
2016
Abstract: Matrix product states (MPSs) illustrate the suitability of tensor networks for the description of interacting manybody systems: ground states of gapped 1D systems are approximable by MPSs, as shown by Hastings [M. B. Hastings, J. Stat. Mech. (2007) P08024]. By contrast, whether MPSs and more general tensor networks can accurately reproduce correlations in critical quantum systems or quantum field theories has not been established rigorously. Ample evidence exists: entropic considerations provide restrictions on the form of suitable ansatz states, and numerical studies show that certain tensor networks can indeed approximate the associated correlation functions. Here, we provide a complete positive answer to this question in the case of MPSs and 2D conformal field theory: we give quantitative estimates for the approximation error when approximating correlation functions by MPSs. Our work is constructive and yields an explicit MPS, thus providing both suitable initial values and a rigorous justification of variational methods. 
Regimes of heating and dynamical response in driven manybody localized systems
Phys. Rev. B
, Volume 94(094201)
September
2016
Abstract: We explore the response of manybody localized (MBL) systems to periodic driving of arbitrary amplitude, focusing on the rate at which they exchange energy with the drive. To this end, we introduce an infinitetemperature generalization of the effective “heating rate” in terms of the spread of a random walk in energy space. We compute this heating rate numerically and estimate it analytically in various regimes. When the drive amplitude is much smaller than the frequency, this effective heating rate is given by linear response theory with a coefficient that is proportional to the optical conductivity; in the opposite limit, the response is nonlinear and the heating rate is a nontrivial power law of time. We discuss the mechanisms underlying this crossover in the MBL phase. We comment on implications for the subdiffusive thermal phase near the MBL transition, and for response in imperfectly isolated MBL systems. 
Spin structure factors of chiral quantum spin liquids on the kagome lattice
Phys. Rev. B
, Volume 94(104413)
September
2016
Abstract: We calculate dynamical spin structure factors for gapped chiral spin liquid states in the spin1/2 Heisenberg antiferromagnet on the kagome lattice using Schwingerboson meanfield theory. In contrast to static (equaltime) structure factors, the dynamical structure factor shows clear signatures of timereversal symmetry breaking for chiral spin liquid states. In particular, momentum inversion k→−k symmetry as well as the sixfold rotation symmetry around the Γ point are lost. We highlight other interesting features, such as a relatively flat onset of the twospinon continuum for the cuboc1 state. Our work is based on the projective symmetry group classification of timereversal symmetry breaking Schwingerboson meanfield states by Messio, Lhuillier, and Misguich. 
Coulomb potentials and Taylor expansions in timedependent densityfunctional theory
Phys. Rev. A
, Volume 92(062510)
June
2016
Abstract: We investigate when Taylor expansions can be used to prove the RungeGross theorem, which is at the foundation of timedependent densityfunctional theory (TDDFT). We start with a general analysis of the conditions for the RungeGross 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 onebody operator considerably decreases the class of timedependent external potentials to which the original argument can be applied. A twobody singularity has an even stronger impact and an external potential is essentially incompatible with it. For the Coulomb interaction and all reasonable initial manybody states, the Taylor expansion only exists to a finite order, except for constant external potentials. Therefore, highorder Taylor expansions are not the right tool to study atoms and molecules in TDDFT. 
Ubiquity of Exciton Localization in Cryogenic Carbon Nanotubes
Nano Lett.
, Volume 16(5), page: 2958–2962
April
2016
Abstract: We present photoluminescence studies of individual semiconducting singlewall 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 sidewall defects. Our results establish disorderinduced crossover from the diffusive to the localized regime of nanotube excitons at cryogenic temperatures as a ubiquitous phenomenon in micelleencapsulated and asgrown carbon nanotubes. 
Griffiths effects and slow dynamics in nearly manybody localized systems
Phys. Rev. B
, Volume 93(134206)
April
2016
Abstract: The lowfrequency response of systems near a manybody 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 manybody localization transition: we consider both onedimensional and higherdimensional systems, subject to quenched randomness, and discuss both linear response (including the frequency and wavevectordependent conductivity) and more general dynamics. In all the regimes we consider, we identify observables that are dominated by rareregion effects. In some cases (onedimensional systems and Floquet systems with no extensive conserved quantities), essentially all longtime local observables are dominated by rareregion effects; in others, generic observables are instead dominated by hydrodynamic longtime 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
Abstract: We study restrictions on localitypreserving unitary logical gates for topological quantum codes in two spatial dimensions. A localitypreserving operation is one which maps local operators to local operators — for example, a constantdepth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically local boundedstrength Hamiltonian. Localitypreserving 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 twodimensional topological field theories, we find that the localitypreserving logical gates are severely limited for codes which admit nonabelian anyons, in particular, there are no localitypreserving 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 Mpunctured sphere, localitypreserving 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 Fmoves and the mapping class group. DOI: 10.1063/1.4939783

Quantum Phase Transition and Protected Ideal Transport in a Kondo Chain
PRL
, Volume 115(216402)
November
2015
Abstract: We study the low energy physics of a Kondo chain where electrons from a onedimensional 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 timereversal invariant topological insulators. The phase with easy axis anisotropy corresponds to the TomonagaLuttinger liquid with a pronounced spincharge separation. The slow charge density wave modes have no protection against localization. 
Massive Goldstone (Higgs) mode in twodimensional ultracold atomic lattice systems
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 superfluidtoinsulator quantum critical point (QCP) in a system of twodimensional 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 BoseHubbard Model
Phys. Rev. Lett.
, Volume 115(205301)
November
2015
Abstract: We explore prethermal Floquet steady states and instabilities of the weakly interacting twodimensional BoseHubbard model subject to periodic driving. We develop a description of the nonequilibrium dynamics, at arbitrary drive strength and frequency, using a weakcoupling conserving approximation. We establish the regimes in which conventional (zeromomentum) 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. 
FarfromEquilibrium Field Theory of ManyBody Quantum Spin Systems: Prethermalization and Relaxation of Spin Spiral States in Three Dimensions
Phys. Rev. X
, Volume 5(041005)
October
2015
Abstract: We study theoretically the farfromequilibrium relaxation dynamics of spin spiral states in the threedimensional isotropic Heisenberg model. The investigated problem serves as an archetype for understanding quantum dynamics of isolated manybody systems in the vicinity of a spontaneously broken continuous symmetry. We present a fieldtheoretical formalism that systematically improves on the mean field for describing the realtime quantum dynamics of generic spin1/2 systems. This is achieved by mapping spins to Majorana fermions followed by a 1/N expansion of the resulting twoparticleirreducible effective action. Our analysis reveals rich fluctuationinduced relaxation dynamics in the unitary evolution of spin spiral states. In particular, we find the sudden appearance of longlived 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. Spinspin correlators found by solving the nonequilibrium BetheSalpeter equation provide further insight into the dynamic formation of correlations, the fate of unstable collective modes, and the emergence of fluctuationdissipation 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
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 singleparticle 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 lasercoupled atomic ensembles. As a result, multiple excitation of a micrometersized cloud can be blocked while the lightmatter coupling becomes collectively enhanced. The resulting twolevel 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 subshotnoise precision by local manipulation of a twodimensional Mott insulator. We microscopically confirm the superatom picture by in situ detection of the Rydberg excitations and observe the characteristic squareroot 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 manybody 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. 
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