Obtaining highly-excited eigenstates of many-body localized Hamiltonians by the density matrix renormalization group

The eigenstates of many-body localized (MBL) Hamiltonians exhibit low entanglement. We adapt the highly successful density-matrix renormalization group method, which is usually used to find modestly entangled ground states of local Hamiltonians, to find individual highly excited eigenstates of many body localized Hamiltonians. The adaptation builds on the distinctive spatial structure of such eigenstates. We benchmark our method against the well studied random field Heisenberg model in one dimension. At moderate to large disorder, we find that the method successfully obtains excited eigenstates with high accuracy, thereby enabling a study of MBL systems at much larger system sizes than those accessible to exact-diagonalization methods.Comment: Published version. Slightly expanded discussion; supplement adde

Strongly correlated fermions on a kagome lattice

We study a model of strongly correlated spinless fermions on a kagome lattice at 1/3 filling, with interactions described by an extended Hubbard Hamiltonian. An effective Hamiltonian in the desired strong correlation regime is derived, from which the spectral functions are calculated by means of exact diagonalization techniques. We present our numerical results with a view to discussion of possible signatures of confinement/deconfinement of fractional charges.Comment: 10 pages, 10 figure

Detection of Symmetry Protected Topological Phases in 1D

A topological phase is a phase of matter which cannot be characterized by a local order parameter. It has been shown that gapped phases in 1D systems can be completely characterized using tools related to projective representations of the symmetry groups. We show how to determine the matrices of these representations in a simple way in order to distinguish between different phases directly. From these matrices we also point out how to derive several different types of non-local order parameters for time reversal, inversion symmetry and $Z_2 \times Z_2$ symmetry, as well as some more general cases (some of which have been obtained before by other methods). Using these concepts, the ordinary string order for the Haldane phase can be related to a selection rule that changes at the critical point. We furthermore point out an example of a more complicated internal symmetry for which the ordinary string order cannot be applied.Comment: 12 pages, 9 Figure

Correlated Fermions on a Checkerboard Lattice

A model of strongly correlated spinless fermions hopping on a checkerboard lattice is mapped onto a quantum fully-packed loop model. We identify a large number of fluctuationless states specific to the fermionic case. We also show that for a class of fluctuating states, the fermionic sign problem can be gauged away. This claim is supported by numerically evaluating the energies of the low-lying states. Furthermore, we analyze in detail the excitations at the Rokhsar-Kivelson point of this model thereby using the relation to the height model and the single-mode approximation.Comment: 4 Pages, 3 Figures; v4: updated version published in Phys. Rev. Lett.; one reference adde

Dynamics after a sweep through a quantum critical point

The coherent quantum evolution of a one-dimensional many-particle system after sweeping the Hamiltonian through a critical point is studied using a generalized quantum Ising model containing both integrable and non-integrable regimes. It is known from previous work that universal power laws appear in such quantities as the mean number of excitations created by the sweep. Several other phenomena are found that are not reflected by such averages: there are two scaling regimes of the entanglement entropy and a relaxation that is power-law rather than exponential. The final state of evolution after the quench is not well characterized by any effective temperature, and the Loschmidt echo converges algebraically to a constant for long times, with cusplike singularities in the integrable case that are dynamically broadened by nonintegrable perturbations.Comment: 4 pages, 4 figure

On confined fractional charges: a simple model

We address the question whether features known from quantum chromodynamics (QCD) can possibly also show up in solid-state physics. It is shown that spinless fermions of charge $e$ on a checkerboard lattice with nearest-neighbor repulsion provide for a simple model of confined fractional charges. After defining a proper vacuum the system supports excitations with charges $\pm e/2$ attached to the ends of strings. There is a constant confining force acting between the fractional charges. It results from a reduction of vacuum fluctuations and a polarization of the vacuum in the vicinity of the connecting strings.Comment: 5 pages, 3 figure

Spectral bounds for the Hellmann potential

The method of potential envelopes is used to analyse the bound state spectrum of the Schroedinger Hamiltonian H=-\Delta+V(r), where the Hellmann potential is given by V(r) = -A/r + Be^{-Cr}/r, A and C are positive, and B can be positive or negative. We established simple formulas yielding upper and lower bounds for all the energy eigenvalues.Comment: 9 pages, 2 figures, typos correcte

The Misprediction of emotions in Track Athletics.: Is experience the teacher of all things?

People commonly overestimate the intensity of their emotions toward future events. In other words, they display an impact bias. This research addresses the question whether people learn from their experiences and correct for the impact bias. We hypothesize that athletes display an impact bias and, counterintuitively, that increased experience with an event increases this impact bias. A field study in the context of competitive track athletics supported our hypotheses by showing that athletes clearly overestimated their emotions toward the outcome of a track event and that this impact bias was more pronounced for negative events than for positive events. Moreover, with increased athletic experience this impact bias became larger. This effect could not be explained by athletes’ forecasted emotions, but it could be explained by the emotions they actually felt following the race. The more experience athletes had with athletics, the less they felt negative emotions after unsuccessful goal attainment. These findings are discussed in relation to possible underlying emotion regulation processes

Multi-epoch Near-Infrared Interferometry of the Spatially Resolved Disk Around the Be Star Zeta Tau

We present interferometric observations of the Be star Zeta Tau obtained using the MIRC beam combiner at the CHARA Array. We resolved the disk during four epochs in 2007-2009. We fit the data with a geometric model to characterize the circumstellar disk as a skewed elliptical Gaussian and the central Be star as a uniform disk. The visibilities reveal a nearly edge-on disk with a FWHM major axis of ~ 1.8 mas in the H-band. The non-zero closure phases indicate an asymmetry within the disk. Interestingly, when combining our results with previously published interferometric observations of Zeta Tau, we find a correlation between the position angle of the disk and the spectroscopic V/R ratio, suggesting that the tilt of the disk is precessing. This work is part of a multi-year monitoring campaign to investigate the development and outward motion of asymmetric structures in the disks of Be stars.Comment: Accepted for publication in the Astronomical Journal. 27 pages, 7 Figure

Exact and simple results for the XYZ and strongly interacting fermion chains

We conjecture exact and simple formulas for physical quantities in two quantum chains. A classic result of this type is Onsager, Kaufman and Yang's formula for the spontaneous magnetization in the Ising model, subsequently generalized to the chiral Potts models. We conjecture that analogous results occur in the XYZ chain when the couplings obey J_xJ_y + J_yJ_z + J_x J_z=0, and in a related fermion chain with strong interactions and supersymmetry. We find exact formulas for the magnetization and gap in the former, and the staggered density in the latter, by exploiting the fact that certain quantities are independent of finite-size effects