Document Type


Publication Date

March 2011

Publication Title

Philosophical Transactions of the Royal Society A



Issue Number





Quantum, Hubbard, Dynamical, Cluster, Thermodynamic


Physical Sciences and Mathematics | Physics


Transport measurements on the cuprates suggest the presence of a quantum critical point (QCP) hiding underneath the superconducting dome near optimal hole doping. We provide numerical evidence in support of this scenario via a dynamical cluster quantum Monte Carlo study of the extended two-dimensional Hubbard model. Single-particle quantities, such as the spectral function, the quasi-particle weight and the entropy, display a crossover between two distinct ground states: a Fermi liquid at low filling and a non-Fermi liquid with a pseudo-gap at high filling. Both states are found to cross over to a marginal Fermi-liquid state at higher temperatures. For finite next-nearest-neighbour hopping t′, we find a classical critical point at temperature Tc. This classical critical point is found to be associated with a phase-separation transition between a compressible Mott gas and an incompressible Mott liquid corresponding to the Fermi liquid and the pseudo-gap state, respectively. Since the critical temperature Tc extrapolates to zero as t′ vanishes, we conclude that a QCP connects the Fermi liquid to the pseudo-gap region, and that the marginal Fermi-liquid behaviour in its vicinity is the analogue of the supercritical region in the liquid–gas transition.


This is the Postprint of an article that was published in Philosophical Transactions of the Royal Society A: Mathematical, Physical, and Engineering Sciences, volume 369, issue 1941, 2011. The Version of Record can be found online at this link.
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