## HTSC: High-Temperture Superconductivity and Scalability of Software Architecture for HPC

### Project summary

The general idea of this project consists in providing a new
local

concept for treating solid-state physics and material
properties on the basis of high-performance computing (HPC). This idea
may be viewed as proliferating the information contained in a
microscopic cluster and its interacting electrons and ions to the
infinite system size of the macroscopic solid. If this is possible
then, for example, local binding concepts of chemistry can be used to
systematically make contact with material science. This concept has
indeed been worked out already to some extent in our Theory Group in
connection with earlier KONWIHR Projects (OOPCV

and
CUHE

) in the last few years aiming at the microscopic theory,
i. e. the fundamental understanding of High-Temperature
Superconductivity (HTSC).

The numerical implementation of these so called embedded cluster
schemes

requires first the solution of the isolated cluster
problem. For this we are routinely using Exact Diagonalization for
extracting the ground-state and Quantum-Monte-Carlo (QMC) for
obtaining the finite-temperature properties. Within a typical QMC
algorithm, the calculation is carried out, with each core performing
its own QMC procedure, including the so-called warm-up phase

,
which is required to place the simulated system in thermal
equilibrium. This creates a rather substantial waste of computer
resources, which we want to avoid in this project. The idea is to
combine many cores, which perform the QMC updating process, in one QMC
step. The overall communication between the combined

cores will
be managed by tools like the Message-Passing-Interface (MPI).

The applications, which then can use substantially larger individual clusters, will center around two topics:

- We have recently obtained in KONWIHR-supported embedded cluster calculations the phase diagram of the high-Tc Superconductors (HTSC) on the basis of a model (Hubbard model) which reproduced salient features of the experiments (competition of Anti-ferromagnetism (AF) and superconductivity (SC)). Here, we aim at a deeper understanding of what drives superconductivity and what is the underlying pairing mechanism in this proto-type model of a so-called doped Mott Insulator. Is it spin-fluctuations being related to the AF phase or charge-fluctuations? What is the dynamics of the pairing interaction in the high-Tc cuprate superconductors? Is it retarded or non-retarded, i.e. instantaneous?
- The ongoing search for new high-temperature SC has recently resulted in yet another surprise: The discovery of SC in the iron-based compound LaOI-x Fx Fe P sparked a new direction to explore SC in a completely new class of materials. Very recently, the substitution of P by As and of La by Nd and Pr raised Tc to over 50 K with the corresponding material becoming the superconductor with the highest Tc among non-cuprate based solids. In this part (b), we aim at exploring and understanding the mechanism of SC in these and similar iron-based compounds, an understanding of which holds a lot of promise for systematically increasing Tc, maybe even beyond the records (approx. 130K) in the cuprate superconductors.

### KONWIHR funding

- KONWIHR funding of HTSC: 9/2008 - 8/2011

### Contact:

- Prof. Dr. Werner Hanke, Lehrstuhl für Theoretische Physik I, Uni-Würzburg

### Project staff:

- N.N.

### Publications and presentations

- G. Li, M. Laubach, A. Fleszar, W. Hanke:
*Geometrical frustration and the competing phases of the Sn/Si(111) sqrt{3}.sqrt{3}R30° surface systems*, Phys. Rev. B, 83 (2011) 041104. 10.1103/PhysRevB.83.041104 - R. Thomale, C. Platt, W. Hanke, B.A. Bernevig:
*Mechanism for Explaining Differences in the Order Parameters of FeAs-Based and FeP-Based Pnictide Superconductors*, Phys. Rev. Lett., 106 (2011) 187003. 10.1103/PhysRevLett.106.187003 - S. Brehm, E. Arrigoni, M. Aichhorn, W. Hanke:
*Theory of two-particle excitations and the magnetic susceptibility in high-Tc cuprate superconductors*, Europhysics Letters, 89 (2010) 27005. DOI: 10.1209/0295-5075/89/27005 - W. Hanke, M.L. Kiesel, M. Aichhorn, S. Brehm, E. Arrigoni:
*The 3-Band Hubbard-Model versus the 1-Band Model for the high-Tc Cuprates: Pairing Dynamics, Superconductivity and the Ground-State Phase Diagram*, Eur. Phys. J. Special Topics, 188 (2010) 15-32. 10.1140/epjst/e2010-01294-y - E. Arrigoni, M. Aichhorn, M. Daghofer, W. Hanke:
*Phase diagram and single-particle spectrum of CuO2 high-Tc layers: variational cluster approach to the three-band Hubbard model*, New J. Phys., 11 (2009) 055066. DOI: 10.1088/1367-2630/11/5/055066 - G. Li, W. Hanke, A.N. Rubtsov, S. Bäse, M. Potthoff:
*Accessing thermodynamics from dynamical cluster-embedding approaches*, Phys. Rev. B, 80 (2009) 195118. DOI: 10.1103/PhysRevB.80.195118 - G. Li, W. Hanke, A.N. Rubtsov, S. Bäse, M. Potthoff:
*Accessing thermodynamics from dynamical cluster-embedding approaches*, Phys. Rev. B, 80 (2009) 195118. DOI: 10.1103/PhysRevB.80.195118 - C. Platt, C. Honerkamp, W. Hanke:
*Pairing in the iron arsenides: a functional RG treatment*, New J. Phys., 11 (2009) 055058. DOI: 10.1088/1367-2630/11/5/055058