Improved numerical methods for infinite spin chains with long-range interactions

We present several improvements of the infinite matrix product state (iMPS) algorithm for finding ground states of one-dimensional quantum systems with long-range interactions. As a main new ingredient we introduce the superposed multi-optimization (SMO) method, which allows an efficient optimization of exponentially many MPS of different length at different sites all in one step. Hereby the algorithm becomes protected against position dependent effects as caused by spontaneously broken translational invariance. So far, these have been a major obstacle to convergence for the iMPS algorithm if no prior knowledge of the systems translational symmetry was accessible. Further, we investigate some more general methods to speed up calculations and improve convergence, which might be partially interesting in a much broader context, too. As a more special problem, we also look into translational invariant states close to an invariance braking phase transition and show how to avoid convergence into wrong local minima for such systems. Finally, we apply the new methods to polar bosons with long-range interactions. We calculate several detailed Devil's Staircases with the corresponding phase diagrams and investigate some supersolid properties.Comment: Main text: 17 pages plus references, 8 figures. Supplementary info: 6 pages. v2: improved presentation and more results adde

Geometric phase gate on an optical transition for ion trap quantum computation

We propose a geometric phase gate of two ion qubits that are encoded in two levels linked by an optical dipole-forbidden transition. Compared to hyperfine geometric phase gates mediated by electric dipole transitions, the gate has many interesting properties, such as very low spontaneous emission rates, applicability to magnetic field insensitive states, and use of a co-propagating laser beam geometry. We estimate that current technology allows for infidelities of around 10$^{-4}$.Comment: 4 pages, 2 figure

A matrix product solution for a nonequilibrium steady state of an XX chain

A one dimensional XX spin chain of finite length coupled to reservoirs at both ends is solved exactly in terms of a matrix product state ansatz. An explicit representation of matrices of fixed dimension 4 independent of the chain length is found. Expectations of all observables are evaluated, showing that all connected correlations, apart from nearest neighbor z-z, are zero.Comment: 11 page

A Transport and Microwave Study of Superconducting and Magnetic RuSr2EuCu2O8

We have performed susceptibility, thermopower, dc resistance and microwave measurements on RuSr2EuCu2O8. This compound has recently been shown to display the coexistence of both superconducting and magnetic order. We find clear evidence of changes in the dc and microwave resistance near the magnetic ordering temperature (132 K). The intergranular effects were separated from the intragranular effects by performing microwave measurements on a sintered ceramic sample as well as on a powder sample dispersed in an epoxy resin. We show that the data can be interpreted in terms of the normal-state resistivity being dominated by the CuO2 layers with exchange coupling to the Ru moments in the RuO2 layers. Furthermore, most of the normal-state semiconductor-like upturn in the microwave resistance is found to arise from intergranular transport. The data in the superconducting state can be consistently interpreted in terms of intergranular weak-links and an intragranular spontaneous vortex phase due to the ferromagnetic component of the magnetization arising from the RuO2 planes.Comment: 20 pages including 6 figures in pdf format. To be published in Phys. Rev.

Decoupled CuO_2 and RuO_2 layers in superconducting and magnetically ordered RuSr_2GdCu_2O_8

Comprehensive measurements of dc and ac susceptibility, dc resistance, magnetoresistance, Hall resistivity, and microwave absorption and dispersion in fields up to 8 T have been carried out on RuSr_2GdCu_2O_8 with the aim to establish the properties of RuO_2 and CuO_2 planes. At ~130 K, where the magnetic order develops in the RuO_2 planes, one observes a change in the slope of dc resistance, change in the sign of magnetoresistance, and the appearance of an extraordinary Hall effect. These features indicate that the RuO_2 planes are conducting. A detailed analysis of the ac susceptibility and microwave data on both, ceramic and powder samples show that the penetration depth remains frequency dependent and larger than the London penetration depth even at low temperatures. We conclude that the conductivity in the RuO_2 planes remains normal even when superconducting order is developed in the CuO_2 planes below \~45 K. Thus, experimental evidence is provided in support of theoretical models which base the coexistence of superconductivity and magnetic order on decoupled CuO_2 and RuO_2 planes.Comment: 11 pages, 11 figures, submitted to PR

Concatenated tensor network states

We introduce the concept of concatenated tensor networks to efficiently describe quantum states. We show that the corresponding concatenated tensor network states can efficiently describe time evolution and possess arbitrary block-wise entanglement and long-ranged correlations. We illustrate the approach for the enhancement of matrix product states, i.e. 1D tensor networks, where we replace each of the matrices of the original matrix product state with another 1D tensor network. This procedure yields a 2D tensor network, which includes -- already for tensor dimension two -- all states that can be prepared by circuits of polynomially many (possibly non-unitary) two-qubit quantum operations, as well as states resulting from time evolution with respect to Hamiltonians with short-ranged interactions. We investigate the possibility to efficiently extract information from these states, which serves as the basic step in a variational optimization procedure. To this aim we utilize known exact and approximate methods for 2D tensor networks and demonstrate some improvements thereof, which are also applicable e.g. in the context of 2D projected entangled pair states. We generalize the approach to higher dimensional- and tree tensor networks.Comment: 16 pages, 4 figure

Deformation analysis of a metropolis from C- to X-band PSI: proof-of-concept with Cosmo-Skymed over Rome, Italy

Stability of monuments and subsidence of residential quarters in Rome (Italy) are depicted based on geospatial analysis of more than 310,000 Persistent Scatterers (PS) obtained from Stanford Method for Persistent Scatterers (StaMPS) processing of 32 COSMO-SkyMed 3m-resolution HH StripMap ascending mode scenes acquired between 21 March 2011 and 10 June 2013. COSMO-SkyMed PS densities and associated displacement velocities are compared with almost 20 years of historical C-band ERS- 1/2, ENVISAT and RADARSAT-1/2 imagery. Accounting for differences in image processing algorithms and satellite acquisition geometries, we assess the feasibility of ground motion monitoring in big cities and metropolitan areas by coupling newly acquired and legacy SAR in full time series. Limitations and operational benefits of the transition from medium resolution C-band to high resolution X-band PS data are discussed, alongside the potential impact on the management of expanding urban environments