The occurrence of high-T_c superconductivity in systems including the cuprates and the iron-based superconductors, is known to coincide with the existence of anomalous normal-state properties which have been associated with quantum criticality. We ar
gue here that this observation results from the fact that quantum criticality can allow the occurrence of very-strong-coupling superconductivity by preventing its suppression due to competing symmetry-breaking instabilities. Treating the electrons through a large-U ansatz yields their separation into boson quasiparticles which are directly involved in the formation of these instabilities, represented as their Bose condensates, and charge-carrying fermion quasiparticles which are affected by them indirectly. Within the critical regime, condensates corresponding to the different broken-symmetry states are combined; consequently their negative effect on the pairing of the fermions is strongly diminished, enabling high-T_c superconductivity to occur. The observed phase diagram of the hole-doped cuprates then derives from a hidden T=0 quantum phase transition between a Fermi-liquid and a non-Fermi-liquid broken-symmetry striped state. The pseudogap range within this diagram is found to include two distinct regimes, with partial pairing occurring in one of them.
A grand challenge in many-body quantum physics is to explain the apparent connection between quantum criticality and high-temperature superconductivity in the cuprates and similar systems, such as the iron pnictides and chalcogenides. Here we argue t
hat the quantum-critical regime plays an essential role in activating a strong-pairing mechanism: although pairing bosons create a symmetry-breaking instability which suppresses pairing, the combination of these broken-symmetry states within the critical regime can restore this symmetry for the paired quasiparticles. This condition is shown to be met within a large-U ansatz. A hidden quantum phase transition then arises between a Fermi-liquid and a non-Fermi-liquid broken-symmetry striped state, and a critical regime in which the broken-symmetry states are combined.
Proponents of Complexity Science believe that the huge variety of emergent phenomena observed throughout nature, are generated by relatively few microscopic mechanisms. Skeptics however point to the lack of concrete examples in which a single mechani
stic model manages to capture relevant macroscopic and microscopic properties for two or more distinct systems operating across radically different length and time scales. Here we show how a single complexity model built around cluster coalescence and fragmentation, can cross the fundamental divide between many-body quantum physics and social science. It simultaneously (i) explains a mysterious recent finding of Fratini et al. concerning quantum many-body effects in cuprate superconductors (i.e. scale of 10^{-9} - 10^{-4} meters and 10^{-12} - 10^{-6} seconds), (ii) explains the apparent universality of the casualty distributions in distinct human insurgencies and terrorism (i.e. scale of 10^3 - 10^6 meters and 10^4 - 10^8 seconds), (iii) shows consistency with various established empirical facts for financial markets, neurons and human gangs and (iv) makes microscopic sense for each application. Our findings also suggest that a potentially productive shift can be made in Complexity research toward the identification of equivalent many-body dynamics in both classical and quantum regimes.
