NERSC Initiative for Scientific Exploration (NISE) 2011 Awards

Numerical Investigations of Symmetry Breaking, Magnetism and the Pseudogap in the Three-Orbital Hubbard Model

Thomas Devereaux, Stanford Linear Accelerator Center

Associated NERSC Project: Simulation of Photon Spectroscopies for Correlated Electron Systems (m772)

Our proposed research addresses two central issues regarding the pseudogap regime and the magnetic phase of copper-based high-temperature superconductors. The proposed simulations would provide clear experimental predictions and help unravel the nature of these phases in the cuprates, which is now considered the key to understand their high-temperature superconducting mechanism.

We propose simulations using a massively paralleled exact diagonalization (ED) algorithm to address two central issues in the field of high temperature superconductivity. These problems concern the nature of the pseudogap regime in the phase diagram of cuprate superconductors and the two-magnon Raman spectra performed on these materials. The proposed simulations with our state-of-the-art ED code are well suited for high-performance parallel computing architectures and benefit directly from the large-memory nodes at NERSC.

While it is widely believed that an understanding of the way in which antiferromagnetism disappears with oxygen doping in the cuprates holds the secret to understanding high temperature superconductivity, the region that lies between the two - the so-called pseudogap is poorly understood. One theory compatible with recent experiments involves a circulating current looping around the Cu and O atoms. However, this model is highly disputed as no experiment to date can directly probe such an order parameter. Alternatively, experimental observations could be instead interpreted as a particular ordering of spin moments on oxygen atoms. Results from numerically-unbiased techniques such as ED and DMRG remain controversial because prior work either neglected the effects of multi-orbital characters or worked in restricted dimensions. To address this issue, here we propose performing large-scale ED calculations on a multi-orbital Cu8O16 cluster. With the ground state wavefunction obtained from numerical diagonalization, we can directly test the existence and stability of the circulating current phase by studying its correlation function. Results from these state-of-the-art simulations would serve as clear experimental predictions to benchmark the existence of a circulating current, and to place an upper bound on its strength if such a phase exists. These simulations would thus substantially advance our current understanding of high temperature superconductivity.

Magnetic Raman scattering detects local two-magnon excitations and is instrumental in the first accurate determination of the exchange interactions in cuprate superconductors. A correct description of magnetic scattering as a function of doping will tell us how antiferromagnetism becomes short ranged and what are the characteristics of short range magnetism. After over 20 years of investigations, the Raman lineshape is still poorly understood. In this NISE application, we further propose calculating two-magnon Raman spectra with the ED technique on a 40-site square Heisenberg cluster. Our proposed calculations of two-magnon Raman cross-sections would be the first ever computation of dynamical quantities performed on such a cluster. Besides simulating the two-magnon spectra to compare directly to experiments, we will also calculate the first few spectral moments. Magnetic Raman scattering is a robust measure of the underlying spin interactions, and it can also provides crucial information on the amount of magnetic frustration. Therefore, our proposed simulations would concern not only the cuprates, but also have a broader applicability to other antiferromagnetic systems.