A Two-dimensional Infinte System Density Matrix Renormalization Group Algorithm

It has proved difficult to extend the density matrix renormalization group technique to large two-dimensional systems. In this Communication I present a novel approach where the calculation is done directly in two dimensions. This makes it possible to use an infinite system method, and for the first time the fixed point in two dimensions is studied. By analyzing several related blocking schemes I find that there exists an algorithm for which the local energy decreases monotonically as the system size increases, thereby showing the potential feasibility of this method.Comment: 5 pages, 6 figure

Accretion disk coronae

Recent observations of partial X-ray eclipses from 4U1822-37 have shown that the central X-ray source in this system is diffused by a large Compton-thick accretion disk corona (ADC). Another binary, 4U2129-47, also displays a partial eclipse and contains an ADC. The possible origin of an ADC is discussed and a simple hydrostatic evaporated ADC model is developed which, when applied to 4U1822-37, 4U2129+47 and Cyg X-3, can explain their temporal and spectral properties. The quasi-sinusoidal modulation of all three sources can be reconciled with the partial occultation of the ADC by a bulge at the edge of the accretion disk which is caused by the inflowing material. The height of this bulge is an order of magnitude larger than the hydrostatic disk height and is the result of turbulence in the outer region of the disk. The spectral properties of all three sources can be understood in terms of Compton scattering of the original source spectrum by the ADC. Spectral variations with epoch in Cyg X-3 are probably caused by changes in the optical depth of the corona. A consequence of our model is that any accreting neutron star X-ray source in a semi-detached binary system which is close to its Eddington limit most likely contains an optically thick ADC

Decomposable approximations of nuclear <i>C</i>^*-algebras

We show that nuclear &lt;i&gt;C&lt;/i&gt;&lt;sup&gt;*&lt;/sup&gt;-algebras have a refined version of the completely positive approximation property, in which the maps that approximately factorize through finite dimensional algebras are convex combinations of order zero maps. We use this to show that a separable nuclear &lt;i&gt;C&lt;/i&gt;&lt;sup&gt;*&lt;/sup&gt;-algebra A which is closely contained in a &lt;i&gt;C&lt;/i&gt;&lt;sup&gt;*&lt;/sup&gt;-algebra B embeds into B

Energetics of Domain Walls in the 2D t-J model

Using the density matrix renormalization group, we calculate the energy of a domain wall in the 2D t-J model as a function of the linear hole density \rho_\ell, as well as the interaction energy between walls, for J/t=0.35. Based on these results, we conclude that the ground state always has domain walls for dopings 0 < x < 0.3. For x < 0.125, the system has (1,0) domain walls with \rho_\ell ~ 0.5, while for 0.125 < x < 0.17, the system has a possibly phase-separated mixture of walls with \rho_\ell ~ 0.5 and \rho_\ell =1. For x > 0.17, there are only walls with \rho_\ell =1. For \rho_\ell = 1, diagonal (1,1) domain walls have very nearly the same energy as (1,0) domain walls.Comment: Several minor changes. Four pages, four encapsulated figure

Reconstruction with velocities

Reconstruction is becoming a crucial procedure of galaxy clustering analysis for future spectroscopic redshift surveys to obtain subper cent level measurement of the baryon acoustic oscillation scale. Most reconstruction algorithms rely on an estimation of the displacement field from the observed galaxy distribution. However, the displacement reconstruction degrades near the survey boundary due to incomplete data and the boundary effects extend to ∼100 Mpc/h within the interior of the survey volume. We study the possibility of using radial velocities measured from the cosmic microwave background observation through the kinematic Sunyaev-Zeldovich effect to improve performance near the boundary. We find that the boundary effect can be reduced to ∼30 − 40 Mpc/h with the velocity information from Simons Observatory. This is especially helpful for dense low redshift surveys where the volume is relatively small and a large fraction of total volume is affected by the boundary

Perturbations of C*-algebraic invariants

Kadison and Kastler introduced a metric on the set of all C*-algebras on a fixed Hilbert space. In this paper structural properties of C*-algebras which are close in this metric are examined. Our main result is that the property of having a positive answer to Kadison’s similarity problem transfers to close C*-algebras. In establishing this result we answer questions about closeness of commutants and tensor products when one algebra satisfies the similarity property. We also examine K-theory and traces of close C*-algebras, showing that sufficiently close algebras have isomorphic Elliott invariants when one algebra has the similarity property

Cooper-pair transport through a Hubbard chain sandwiched between two superconductors: Density matrix renormalization group calculations

We present a numerical approach to study the coherent transport of Cooper pairs through a Hubbard chain, and study the role of the contacts in achieving perfect Andreev reflection. We calculate the pair transport using the Density Matrix Renormalization Group by measuring the response of the system to quantum pair fields with complex phases on the two ends of an open system. This approach gives an effective superfluid weight which is in close agreement with the Bethe Ansatz results for the superfluid weight for closed Hubbard rings.Comment: 5 pages, 6 figure

Competition Between Stripes and Pairing in a t-t'-J Model

As the number of legs n of an n-leg, t-J ladder increases, density matrix renormalization group calculations have shown that the doped state tends to be characterized by a static array of domain walls and that pairing correlations are suppressed. Here we present results for a t-t'-J model in which a diagonal, single particle, next-near-neighbor hopping t' is introduced. We find that this can suppress the formation of stripes and, for t' positive, enhance the d_{x^2-y^2}-like pairing correlations. The effect of t' > 0 is to cause the stripes to evaporate into pairs and for t' < 0 to evaporate into quasi-particles. Results for n=4 and 6-leg ladders are discussed.Comment: Four pages, four encapsulated figure