Time-reversal symmetry breaking Abelian chiral spin liquid in Mott phases of three-component fermions on the triangular lattice

We provide numerical evidence in favor of spontaneous chiral symmetry breaking and the concomitant appearance of an Abelian chiral spin liquid for three-component fermions on the triangular lattice described by an SU(3) symmetric Hubbard model with hopping amplitude $-t$ ($t>0$) and on-site interaction $U$. This chiral phase is stabilized in the Mott phase with one particle per site in the presence of a uniform $\pi$-flux per plaquette, and in the Mott phase with two particles per site without any flux. Our approach relies on effective spin models derived in the strong-coupling limit in powers of $t/U$ for general SU$(N)$ and arbitrary uniform charge flux per plaquette, which are subsequently studied using exact diagonalizations and variational Monte Carlo simulations for $N=3$, as well as exact diagonalizations of the SU($3$) Hubbard model on small clusters. Up to third order in $t/U$, and for the time-reversal symmetric cases (flux $0$ or $\pi$), the low-energy description is given by the $J$-$K$ model with Heisenberg coupling $J$ and real ring exchange $K$. The phase diagram in the full $J$-$K$ parameter range contains, apart from three already known, magnetically long-range ordered phases, two previously unreported phases: i) a lattice nematic phase breaking the lattice rotation symmetry and ii) a spontaneous time-reversal and parity symmetry breaking Abelian chiral spin liquid. For the Hubbard model, an investigation that includes higher-order itinerancy effects supports the presence of a phase transition inside the insulating region, occurring at $(t/U)_{\rm c}\approx 0.07$ [$(U/t)_{\rm c} \approx 13$] between the three-sublattice magnetically ordered phase at small $t/U$ and this Abelian chiral spin liquid.Comment: 21 pages, 23 figure

Quantum Flutter: Signatures and Robustness

We investigate the motion of an impurity particle injected with finite velocity into an interacting one-dimensional quantum gas. Using large-scale numerical simulations based on matrix product states, we observe and quantitatively analyze long-lived oscillations of the impurity momentum around a nonzero saturation value, called quantum flutter. We show that the quantum flutter frequency is equal to the energy difference between two branches of collective excitations of the model. We propose an explanation of the finite saturation momentum of the impurity based on the properties of the edge of the excitation spectrum. Our results indicate that quantum flutter exists away from integrability and provide parameter regions in which it could be observed in experiments with ultracold atoms using currently available technology.Physic

Time Evolution within a Comoving Window: Scaling of signal fronts and magnetization plateaus after a local quench in quantum spin chains

We present a modification of Matrix Product State time evolution to simulate the propagation of signal fronts on infinite one-dimensional systems. We restrict the calculation to a window moving along with a signal, which by the Lieb-Robinson bound is contained within a light cone. Signal fronts can be studied unperturbed and with high precision for much longer times than on finite systems. Entanglement inside the window is naturally small, greatly lowering computational effort. We investigate the time evolution of the transverse field Ising (TFI) model and of the S=1/2 XXZ antiferromagnet in their symmetry broken phases after several different local quantum quenches. In both models, we observe distinct magnetization plateaus at the signal front for very large times, resembling those previously observed for the particle density of tight binding (TB) fermions. We show that the normalized difference to the magnetization of the ground state exhibits similar scaling behaviour as the density of TB fermions. In the XXZ model there is an additional internal structure of the signal front due to pairing, and wider plateaus with tight binding scaling exponents for the normalized excess magnetization. We also observe parameter dependent interaction effects between individual plateaus, resulting in a slight spatial compression of the plateau widths. In the TFI model, we additionally find that for an initial Jordan-Wigner domain wall state, the complete time evolution of the normalized excess longitudinal magnetization agrees exactly with the particle density of TB fermions.Comment: 10 pages with 5 figures. Appendix with 23 pages, 13 figures and 4 tables. Largely extended and improved versio

Health literacy in Europe. comparative results of the European health literacy survey (HLS-EU)

Sørensen K, Pelikan JM, Röthlin F, et al. Health literacy in Europe. comparative results of the European health literacy survey (HLS-EU). The European Journal of Public Health. 2015;25(6):1053-1058

Microscopic observation of magnon bound states and their dynamics

More than eighty years ago, H. Bethe pointed out the existence of bound states of elementary spin waves in one-dimensional quantum magnets. To date, identifying signatures of such magnon bound states has remained a subject of intense theoretical research while their detection has proved challenging for experiments. Ultracold atoms offer an ideal setting to reveal such bound states by tracking the spin dynamics after a local quantum quench with single-spin and single-site resolution. Here we report on the direct observation of two-magnon bound states using in-situ correlation measurements in a one-dimensional Heisenberg spin chain realized with ultracold bosonic atoms in an optical lattice. We observe the quantum walk of free and bound magnon states through time-resolved measurements of the two spin impurities. The increased effective mass of the compound magnon state results in slower spin dynamics as compared to single magnon excitations. In our measurements, we also determine the decay time of bound magnons, which is most likely limited by scattering on thermal fluctuations in the system. Our results open a new pathway for studying fundamental properties of quantum magnets and, more generally, properties of interacting impurities in quantum many-body systems.Comment: 8 pages, 7 figure

Steady-state spectra, current and stability diagram of a quantum dot: a non-equilibrium Variational Cluster Approach

We calculate steady-state properties of a strongly correlated quantum dot under voltage bias by means of non-equilibrium Cluster Perturbation Theory and the non-equilibrium Variational Cluster Approach, respectively. Results for the steady-state current are benchmarked against data from accurate Matrix Product State based time evolution. We show that for low to medium interaction strength, non-equilibrium Cluster Perturbation Theory already yields good results, while for higher interaction strength the self-consistent feedback of the non-equilibrium Variational Cluster Approach significantly enhances the accuracy. We report the current-voltage characteristics for different interaction strengths. Furthermore we investigate the non-equilibrium local density of states of the quantum dot and illustrate that within the variational approach a linear splitting and broadening of the Kondo resonance is predicted which depends on interaction strength. Calculations with applied gate voltage, away from particle hole symmetry, reveal that the maximum current is reached at the crossover from the Kondo regime to the doubly-occupied or empty quantum dot. Obtained stability diagrams compare very well to recent experimental data [Phys. Rev. B, 84, 245316 (2011)].Comment: 13 pages, 7 figure

Experimental observation of Bethe strings

Almost a century ago, string states-complex bound states of magnetic excitations-were predicted to exist in one-dimensional quantum magnets(1). However, despite many theoretical studies(2-11), the experimental realization and identification of string states in a condensed-matter system have yet to be achieved. Here we use high-resolution terahertz spectroscopy to resolve string states in the antiferromagnetic Heisenberg-Ising chain SrCo2V2O8 in strong longitudinal magnetic fields. In the field-induced quantum-critical regime, we identify strings and fractional magnetic excitations that are accurately described by the Bethe ansatz(1,3,4). Close to quantum criticality, the string excitations govern the quantum spin dynamics, whereas the fractional excitations, which are dominant at low energies, reflect the antiferromagnetic quantum fluctuations. Today, Bethe's result(1) is important not only in the field of quantum magnetism but also more broadly, including in the study of cold atoms and in string theory; hence, we anticipate that our work will shed light on the study of complex many-body systems in general

Quantum dynamics of a single, mobile spin impurity

Quantum magnetism describes the properties of many materials such as transition metal oxides and cuprate superconductors. One of its elementary processes is the propagation of spin excitations. Here we study the quantum dynamics of a deterministically created spin-impurity atom, as it propagates in a one-dimensional lattice system. We probe the full spatial probability distribution of the impurity at different times using single-site-resolved imaging of bosonic atoms in an optical lattice. In the Mott-insulating regime, a post-selection of the data allows to reduce the effect of temperature, giving access to a space- and time-resolved measurement of the quantum-coherent propagation of a magnetic excitation in the Heisenberg model. Extending the study to the bath's superfluid regime, we determine quantitatively how the bath strongly affects the motion of the impurity. The experimental data shows a remarkable agreement with theoretical predictions allowing us to determine the effect of temperature on the coherence and velocity of impurity motion. Our results pave the way for a new approach to study quantum magnetism, mobile impurities in quantum fluids, and polarons in lattice systems