Systematic analysis of a spin-susceptibility representation of the pairing interaction in the 2D Hubbard model

A dynamic cluster quantum Monte Carlo algorithm is used to study a spin susceptibility representation of the pairing interaction for the two-dimensional Hubbard model with an on-site Coulomb interaction equal to the bandwidth for various doping levels. We find that the pairing interaction is well approximated by {3/2}\Ub(T)^2\chi(K-K') with an effective temperature and doping dependent coupling \Ub(T) and the numerically calculated spin susceptibility $\chi(K-K')$. We show that at low temperatures, \Ub may be accurately determined from a corresponding spin susceptibility based calculation of the single-particle self-energy. We conclude that the strength of the d-wave pairing interaction, characterized by the mean-field transition temperature, can be determined from a knowledge of the dressed spin susceptibility and the nodal quasiparticle spectral weight. This has important implications with respect to the questions of whether spin fluctuations are responsible for pairing in the high-T$_c$ cuprates.Comment: 5 pages, 5 figure

Cognition in Spatial Dispersion Games

In common-interest spatial-dispersion games the agents common goal is to choose distinct locations.We experimentally investigate the role of cognition in such games and compare it with the role of cognition in spatial matching games. In our setup cognition matters because agents may be differentially aware of the dispersion opportunities that are created by the history of the game.We ask whether cognitive constraints limit the agents ability to achieve dispersion and, if there is dispersion, whether these constraints affect the mode by which agents achieve dispersion.Our main finding is that strategic interaction magnifies the role of cognitive constraints.Specifically, with cognitive constraints, pairs of agents fail to solve a dispersion problem that poses little or no problem for individual agents playing against themselves.When we remove the cognitive constraints in our design, pairs of agents solve the same problem just as well as individuals do.In addition, we find that when playing against themselves agents do not change the mode by which they solve the dispersion problem when our design removes the cognitive constraints.noncooperative games;laboratory group behavior

Learning Strategic Sophistication

We experimentally investigate coordination games in which cognition plays an important role, i.e. where outcomes are affected by the agents level of understanding of the game and the beliefs they form about each others understanding.We ask whether and when repeated exposure permits agents to learn to improve cognition in a strategic setting.We find evidence for strategic sophistication being learned, generalized and promoted.Agents acquire strategic sophistication in simple settings.They may fail to do so in similar but more demanding settings.Given the opportunity, they transfer learning from the simple to the more demanding task.There is heterogeneity in sophistication.We find some evidence for sophisticated agents trying to spread sophistication early in the game, provided there is a long enough time horizon.noncooperative games;laboratory group behavior

Phase Diagram of the Hubbard Model: Beyond the Dynamical Mean Field

The Dynamical Cluster Approximation (DCA) is used to study non-local corrections to the dynamical mean field phase diagram of the two-dimensional Hubbard model. Regions of antiferromagnetic, d-wave superconducting, pseudo-gapped non-Fermi liquid, and Fermi liquid behaviors are found, in rough agreement with the generic phase diagram of the cuprates. The non-local fluctuations beyond the mean field both suppress the antiferromagnetism and mediate the superconductivity.Comment: 4 pages, 5 eps figures, submitted to PR

Effect of strain on hyperfine-induced hole-spin decoherence in quantum dots

We theoretically consider the effect of strain on the spin dynamics of a single heavy-hole (HH) confined to a self-assembled quantum dot and interacting with the surrounding nuclei via hyperfine interaction. Confinement and strain hybridize the HH states, which show an exponential decay for a narrowed nuclear spin bath. For different strain configurations within the dot, the dependence of the spin decoherence time $T_2$ on external parameters is shifted and the non-monotonic dependence of the peak is altered. Application of external strain yields considerable shifts in the dependence of $T_2$ on external parameters. We find that external strain affects mostly the effective hyperfine coupling strength of the conduction band (CB), indicating that the CB admixture of the hybridized HH states plays a crucial role in the sensitivity of $T_2$ on strain

Effective three-particle interactions in low-energy models for multiband systems

We discuss different approximations for effective low-energy interactions in multi-band models for weakly correlated electrons. In the study of Fermi surface instabilities of the conduction band(s), the standard approximation consists only keeping those terms in the bare interactions that couple only to the conduction band(s), while corrections due to virtual excitations into bands away from the Fermi surface are typically neglected. Here, using a functional renormalization group approach, we present an improved truncation for the treatment of the effective interactions in the conduction band that keeps track of the generated three-particle interactions (six-point term) and hence allows one to include important aspects of these virtual interband excitations. Within a simplified two-patch treatment of the conduction band, we demonstrate that these corrections can have a rather strong effect in parts of the phase diagram by changing the critical scales for various orderings and the phase boundaries.Comment: revised version, 16 pages, 13 figure