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

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