Many-body localization in a disordered quantum Ising chain

Many-body localization occurs in isolated quantum systems when Anderson localization persists in the presence of finite interactions. Despite strong evidence for the existence of a many-body localization transition a reliable extraction of the critical disorder strength is difficult due to a large drift with system size in the studied quantities. In this work we explore two entanglement properties that are promising for the study of the manybody localization transition: the variance of the half-chain entanglement entropy of exact eigenstates and the long time change in entanglement after a local quench from an exact eigenstate. We investigate these quantities in a disordered quantum Ising chain and use them to estimate the critical disorder strength and its energy dependence. In addition, we analyze a spin-glass transition at large disorder strength and provide evidence for it being a separate transition. We thereby give numerical support for a recently proposed phase diagram of many-body localization with localization protected quantum order [Huse et al. Phys. Rev. B 88, 014206 (2013)].Comment: 4+ pages + 1.5 pages appendix, 5 figure

Unbounded growth of entanglement in models of many-body localization

An important and incompletely answered question is whether a closed quantum system of many interacting particles can be localized by disorder. The time evolution of simple (unentangled) initial states is studied numerically for a system of interacting spinless fermions in one dimension described by the random-field XXZ Hamiltonian. Interactions induce a dramatic change in the propagation of entanglement and a smaller change in the propagation of particles. For even weak interactions, when the system is thought to be in a many-body localized phase, entanglement shows neither localized nor diffusive behavior but grows without limit in an infinite system: interactions act as a singular perturbation on the localized state with no interactions. The significance for proposed atomic experiments is that local measurements will show a large but nonthermal entropy in the many-body localized state. This entropy develops slowly (approximately logarithmically) over a diverging time scale as in glassy systems.Comment: 4 pages, 2 figures, v2. added more dat

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

Quantum Mutual Information as a Probe for Many-Body Localization

We demonstrate that the quantum mutual information (QMI) is a useful probe to study many-body localization (MBL). First, we focus on the detection of a metal--insulator transition for two different models, the noninteracting Aubry-Andr\'e-Harper model and the spinless fermionic disordered Hubbard chain. We find that the QMI in the localized phase decays exponentially with the distance between the regions traced out, allowing us to define a correlation length, which converges to the localization length in the case of one particle. Second, we show how the QMI can be used as a dynamical indicator to distinguish an Anderson insulator phase from an MBL phase. By studying the spread of the QMI after a global quench from a random product state, we show that the QMI does not spread in the Anderson insulator phase but grows logarithmically in time in the MBL phase.Comment: 4+2 pages, 5+5 figure

Let’s Talk About Money: The Role of Attachment Styles in Couples’ Financial Communication, Financial Management, and Financial Conflict

There are many households with financial problems, but most research on financial management is restricted to individual effects, not taking into account the relationship these individuals are in. The current investigation tests whether a person’s attachment style predicts how comfortable they are talking about financial issues with their partner and how that relates to different financial outcome variables. Two cross-sectional survey studies in the Netherlands and the US, each with more than 100 participants show that a higher score on anxious attachment is related to less communication about money with one’s partner. Less financial communication is related to worse financial management within the couple, which in turn predicts conflicts about money. A third survey with 770 participants shows that less financial communication is related to more financial problems. These findings highlight the need to take relationship variables into account to understand financial processes in couples

Real-time dynamics in the one-dimensional Hubbard model

We consider single-particle properties in the one-dimensional repulsive Hubbard model at commensurate fillings in the metallic phase. We determine the real-time evolution of the retarded Green's function by matrix-product state methods. We find that at sufficiently late times the numerical results are in good agreement with predictions of nonlinear Luttinger liquid theory. We argue that combining the two methods provides a way of determining the single-particle spectral function with very high frequency resolution.Comment: 10 pages, 6 figures. Minor edits from v1. Version as publishe

Infinite density matrix renormalization group for multicomponent quantum Hall systems

While the simplest quantum Hall plateaus, such as the $\nu = 1/3$ state in GaAs, can be conveniently analyzed by assuming only a single active Landau level participates, for many phases the spin, valley, bilayer, subband, or higher Landau level indices play an important role. These `multi-component' problems are difficult to study using exact diagonalization because each component increases the difficulty exponentially. An important example is the plateau at $\nu = 5/2$, where scattering into higher Landau levels chooses between the competing non-Abelian Pfaffian and anti-Pfaffian states. We address the methodological issues required to apply the infinite density matrix renormalization group to quantum Hall systems with multiple components and long-range Coulomb interactions, greatly extending accessible system sizes. As an initial application we study the problem of Landau level mixing in the $\nu = 5/2$ state. Within the approach to Landau level mixing used here, we find that at the Coulomb point the anti-Pfaffian is preferred over the Pfaffian state over a range of Landau level mixing up to the experimentally relevant values.Comment: 12 pages, 9 figures. v2 added more data for different amounts of Landau level mixing at 5/2 fillin