Three `species' of Schr\"odinger cat states in an infinite-range spin model

We explore a transverse-field Ising model that exhibits both spontaneous symmetry-breaking and eigenstate thermalization. Within its ferromagnetic phase, the exact eigenstates of the Hamiltonian of any large but finite-sized system are all Schr\"odinger cat states: superpositions of states with `up' and `down' spontaneous magnetization. This model exhibits two dynamical phase transitions {\it within} its ferromagnetic phase: In the lowest-temperature phase the magnetization can macroscopically oscillate between up and down. The relaxation of the magnetization is always overdamped in the remainder of the ferromagnetic phase, which is divided in to phases where the system thermally activates itself {\it over} the barrier between the up and down states, and where it quantum tunnels.Comment: 7 pages, added numerical result

Thermal inclusions: how one spin can destroy a many-body localized phase

Many-body localized (MBL) systems lie outside the framework of statistical mechanics, as they fail to equilibrate under their own quantum dynamics. Even basic features of MBL systems such as their stability to thermal inclusions and the nature of the dynamical transition to thermalizing behavior remain poorly understood. We study a simple model to address these questions: a two level system interacting with strength $J$ with $N\gg 1$ localized bits subject to random fields. On increasing $J$, the system transitions from a MBL to a delocalized phase on the \emph{vanishing} scale $J_c(N) \sim 1/N$, up to logarithmic corrections. In the transition region, the single-site eigenstate entanglement entropies exhibit bi-modal distributions, so that localized bits are either "on" (strongly entangled) or "off" (weakly entangled) in eigenstates. The clusters of "on" bits vary significantly between eigenstates of the \emph{same} sample, which provides evidence for a heterogenous discontinuous transition out of the localized phase in single-site observables. We obtain these results by perturbative mapping to bond percolation on the hypercube at small $J$ and by numerical exact diagonalization of the full many-body system. Our results imply the MBL phase is unstable in systems with short-range interactions and quenched randomness in dimensions $d$ that are high but finite.Comment: 17 pages, 12 figure

Permutation-Symmetric Multicritical Points in Random Antiferromagnetic Spin Chains

The low-energy properties of a system at a critical point may have additional symmetries not present in the microscopic Hamiltonian. This letter presents the theory of a class of multicritical points that provide an interesting example of this in the phase diagrams of random antiferromagnetic spin chains. One case provides an analytic theory of the quantum critical point in the random spin-3/2 chain, studied in recent work by Refael, Kehrein and Fisher (cond-mat/0111295).Comment: Revtex, 4 pages (2 column format), 2 eps figure

Letter from Helen C. Huse to John Muir, 1889 Nov 1.

2606 Pacific Ave.,Nov. 1st. 1889.My dear Mr. Muir:Mr. Keith has spoken to you of our club and of our great desire to have you give us a talk upon Alaska, or any subject that you may prefer. We all know and remember your Wind Storm in the High Sierras, The little Douglas Squirrel. etc., etc. aside from your scientific articles of the wonderful stories of the glaciers of this coast.I remember our delight at listening to you at Mr. McChesney\u27s, again at Sisson\u27s. My heart is just set upon having the ladies of our Club have the same pleasure and profit. I have to secure someone for the first Wed. P.M. of every month. I want you to do me and our Club the great favor of addressing us the 1st Wed. of Dec., if that time is convenient to you. Mr. Keith, I am sure, will be equally kind and talk to us upon Art the 1st Wed. in Jan. He says you must speak first. Please excuse informality and answer me as I feel sure your kindness and interest in the subject will prompt you to do.Most sincerely yours,Helen C. Hus

Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations

We present an adaptive algorithm which optimizes the statistical-mechanical ensemble in a generalized broad-histogram Monte Carlo simulation to maximize the system's rate of round trips in total energy. The scaling of the mean round-trip time from the ground state to the maximum entropy state for this local-update method is found to be O([N log N]^2) for both the ferromagnetic and the fully frustrated 2D Ising model with N spins. Our new algorithm thereby substantially outperforms flat-histogram methods such as the Wang-Landau algorithm.Comment: 6 pages, 5 figure

Maximizing the Neel temperature of fermions in a simple-cubic optical lattice

For a simple-cubic optical lattice with lattice spacing d, occupied by two species of fermionic atoms of mass m that interact repulsively, we ask what conditions maximize the Neel temperature in the Mott insulating phase at density one atom per site, with equal numbers of the two species. This maximum occurs near the edge of the regime where the system is well-approximated by the usual Hubbard model. The correction to the Hubbard-model approximation that produces a "direct" ferromagnetic interaction between atoms in nearest-neighbor Wannier orbitals is the leading term that limits how high the Neel temperature can be made.Comment: 4 pages, 3 figures, minor changes. A new paper, arXiv:0903.0108, expands on this paper and contains most of its result

Relative selectivity in trawls, longline and gillnets on Greenland halibut

Gear selection and sampling gears. Proceedings of the seventh IMR-PINRO Symposium. Murmansk, 23-24 June 1997.Selectivity parameters for Greenland halibut (Reinhardtius hippoglossoides, Walbaum) are compared to catches reported fiom trawl, gillnets and longline in the Norwegian scientific fisheries for Greenland halibut. A trouser trawl selectivity experiment reported here gives an L50 at 43 cm in 135 mm codend. A selectivity analysis of the gillnets using loglinear models is done, and show maximum retention probability for lengths at 40.6 - 63.8 cm for the five mesh-sizes used. The effect of the fishiig strategy is analysed in respect to the selectivity of the gear used and the diskibution of length and age in the catches. To avoid possible bias from strong dominating yearclasses and selection in these comparisons, length-at-age data are used. The sex-ratio in gillnet catches is shown to be a linear fiinction of meshsize. Our data show no trend in length distribution with depth. We show that calculated growth of female Greenland halibut is affected by the selectivity of the gears. It is shown that growth parameters calculated fiom gillnet catches may be biased due to the selection properties in the gillnets. These analyses will provide a better understanding of possible sarnpling bias when sampling a stock with only one gear

Strong-disorder renormalization for interacting non-Abelian anyon systems in two dimensions

We consider the effect of quenched spatial disorder on systems of interacting, pinned non-Abelian anyons as might arise in disordered Hall samples at filling fractions \nu=5/2 or \nu=12/5. In one spatial dimension, such disordered anyon models have previously been shown to exhibit a hierarchy of infinite randomness phases. Here, we address systems in two spatial dimensions and report on the behavior of Ising and Fibonacci anyons under the numerical strong-disorder renormalization group (SDRG). In order to manage the topology-dependent interactions generated during the flow, we introduce a planar approximation to the SDRG treatment. We characterize this planar approximation by studying the flow of disordered hard-core bosons and the transverse field Ising model, where it successfully reproduces the known infinite randomness critical point with exponent \psi ~ 0.43. Our main conclusion for disordered anyon models in two spatial dimensions is that systems of Ising anyons as well as systems of Fibonacci anyons do not realize infinite randomness phases, but flow back to weaker disorder under the numerical SDRG treatment.Comment: 12 pages, 12 figures, 1 tabl

Finite Size Effects in Vortex Localization

The equilibrium properties of flux lines pinned by columnar disorder are studied, using the analogy with the time evolution of a diffusing scalar density in a randomly amplifying medium. Near H_{c1}, the physical features of the vortices in the localized phase are shown to be determined by the density of states near the band edge. As a result, H_{c1} is inversely proportional to the logarithm of the sample size, and the screening length of the perpendicular magnetic field decreases with temperature. For large tilt the extended ground state turns out to wander in the plane perpendicular to the defects with exponents corresponding to a directed polymer in a random medium, and the energy difference between two competing metastable states in this case is extensive. The divergence of the effective potential associated with strong pinning centers as the tilt approaches its critical value is discussed as well.Comment: 10 pages, 2 figure

Nonlocal Conductivity in the Vortex-Liquid Regime of a Two-Dimensional Superconductor

We have simulated the time-dependent Ginzburg-Landau equation with thermal fluctuations, to study the nonlocal dc conductivity of a superconducting film. Having examined points in the phase diagram at a wide range of temperatures and fields below the mean-field upper critical field, we find a portion of the vortex-liquid regime in which the nonlocal ohmic conductivity in real space is negative over a distance several times the spacing between vortices. The effect is suppressed when driven beyond linear response. Earlier work had predicted the existence of such a regime, due to the high viscosity of a strongly-correlated vortex liquid. This behavior is clearly distinguishable from the monotonic spatial fall-off of the conductivity in the higher temperature or field regimes approaching the normal state. The possibilities for experimental study of the nonlocal transport properties are discussed.Comment: 18 pages, revtex, 6 postscript figure