We present a new continuous-time solver for quantum impurity models such as those relevant to dynamical mean field theory. It is based on a stochastic sampling of a perturbation expansion in the impurity-bath hybridization parameter. Comparisons with Monte Carlo and exact diagonalization calculations confirm the accuracy of the new approach, which allows very efficient simulations even at low temperatures and for strong interactions. As examples of the power of the method we present results for the temperature dependence of the kinetic energy and the free energy, enabling an accurate location of the temperature-driven metal-insulator transition.

Since their discovery in 1986, the high-temperature copper-oxide superconductors have been a central object of study in condensed-matter physics. Their highly unusual properties are widely (although not universally) believed to be a consequence of electron-electron interactions that are so strong that the traditional paradigms of condensed-matter physics do not apply: instead, entirely new concepts and techniques are required to describe the physics. In particular, the superconductivity is obtained by adding carriers to insulating 'parent compounds'. These parent compounds have been identified 1 as 'Mott' insulators, in which the lack of conduction arises from anomalously strong electron-electron repulsion. The unusual properties of Mott insulators are widely 2 believed to be responsible for the high-temperature superconductivity. Here, we present a comparison of new theoretical calculations and published 3-8 optical conductivity measurements, which challenges this belief. The analysis indicates that the correlation strength in the cuprates is not as strong as previously believed, in particular that the materials are not properly regarded as Mott insulators. Rather, antiferromagnetism seems to be necessary to obtain the insulating state. By implication, antiferromagnetism is essential to the properties of the doped metallic and superconducting state as well.The prototypical 'parent compound' is La 2 CuO 4 , in which the lattice structure and electron counting is such that there is an odd number of electrons per formula unit. Thus, in the absence of further symmetry breaking, conventional band theory would predict that the material is a good metal. La 2 CuO 4 is however not metallic; it is an insulator with a gap determined by optical spectroscopy to be approximately 1.8 eV (refs 3,4). From one perspective, the insulating behaviour is not surprising. At temperature T = 0, La 2 CuO 4 has two-sublattice Néel order, so that the magnetic unit cell contains two formula units and thus an even number of electrons, compatible with the observed insulating behaviour. However, the consensus has been that the antiferromagnetic order is irrelevant. Instead, the materials have been identified 1,2 as 'Mott insulators' . (Although the cuprates are properly regarded as 'charge-transfer' and not 'Mott' insulators in the sense of ref. 9, we believe this issue is not relevant here: the high-energy-scale physics and chemistry of transition metal (Cu) and ligand (O) ions produces one band of electrons, with an effective interaction strength U which we aim to determine. In particular, optical data show that the nearest bands (arising mainly from the non-bonding oxygen orbitals) are 5-6 eV removed in energy, with only a weak absorption tail extending down to the energies of relevance here. The issue is discussed in more detail in the Supplementary Information.) In a Mott or charge-transfer insulator, the electron-electron interactions are so strong that a density of one electron per unit cell implies a 'jammed' situation: no electron ca...

An investigation is presented of the utility of semiclassical approximations for solving the quantum-impurity problems arising in the dynamical-mean-field approach to the correlated-electron models. The method is based on performing a exact numerical integral over the zero-Matsubarafrequency component of the spin part of a continuous Hubbard-Stratonovich field, along with a spin-field-dependent steepest descents treatment of the charge part. We test this method by applying it to one or two site approximations to the single band Hubbard model with different band structures, and comparing the results to quantum Monte-Carlo and simplified exact diagonalization calculations. The resulting electron self-energies, densities of states and magnetic transition temperatures show reasonable agreement with the quantum Monte-Carlo simulation over wide parameter ranges, suggesting that the semiclassical method is useful for obtaining a reasonable picture of the physics in situations where other techniques are too expensive.