Authors: Gang Li and Werner Hanke
Geometric frustration and its interplay with strong electronic correlations has long been a subject of very active research, since Anderson suggested that a spin-1/2 Heisenberg antiferromagnet (AF) on the triangular lattice would have a gapless quantum spin-liquid (QSL) ground state, i.e. a resonant valence bond (RVB) state. Quite generally, this interplay is believed to be the source of a variety of exotic phases in triangular systems: examples span from the possible QSL state in -(ET)2Cu2(CN) 3 over to a magnetically ordered Mott insulator, which provides the parent phase for the superconductivity (SC) found in -(BEDT-TTF) 2X organics and NaxCoO2.yH2O, with the latter having possibly a topological SC phase, i.e. a gap structure breaking time-reversal symmetry.
To verify the validity of a microscopic, i.e. triangular Hubbard model in this context, we explore its phase diagram using a combination of advanced many-body approaches, such as the dynamical cluster approach (DCA), the dual-fermion (DF) approach, as well as the variational cluster approach and the functional renormalization-group method. It is shown that this model contains the essential phases resolved experimentally in the organic salts, such as a paramagnetic metal for smaller interactions, a paramagnetic insulator for larger interactions and higher temperatures, as well as a Mott insulator with spiral AF correlations for large interactions and lower temperatures. In addition, we found evidence for the existence of a non-magnetic insulator (which can be a candidate of a SL) at intermediate interaction and low temperature. We also examined two thermodynamic relations with respect to entropy and found the constant-entropy curve to monotonically decrease in the metallic state with increasing of interactions. Thus, "adiabatic cooling" should be possible in a triangular lattice and be used to reach a magnetic ordered phase in a corresponding cold-atom system, which is a topic much under study presently. Doping the triangular system, we found the entropy to be maximized at the electron doped side with a concentration which coincides with the maximum Tc for SC found in NaxCoO2.yH2O. The large entropy near optimal doping emerges from the interplay (crossover) of localized spins (remnants of the Mott insulator) and charge degress of freedom via doping. The existence of a topological SC phase (with a d+id symmetry) in this doped regime is also verified by our calculations.
One topical issue, which has recently been intensively studied, is the possibility of a magnetically ordered state appearing despite the frustration and, in particular, how to pin down its appearance in a convincing theoretical and experimental manner. In our work, we show that the one-electron spectral function is the key quantity to extract detailed information on the complex spin pattern in a frustrated magnetic system. This is demonstrated here by a detailed comparison of theory, which combines a priori density-functional (LDA) with cluster many-body (LDA + DCA) calculations, with high-precision angle-resolved photoelectron spectroscopy (ARPES). The role model in this work is the isotropic triangular antiferromagnetic adatom system Sn/Si(111). Its geometric frustration and strong electronic correlations are shown at low temperatures to combine to an unexpected magnetic, i.e. collinear order, and not the possible spiral (120oantiferromagnetic order or a disordered spin-liquid phase.
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