The “sign problem” (SP) is a fundamental limitation to simulations of strongly correlated matter. It is often argued that the SP is not intrinsic to the physics of particular Hamiltonians because its behavior can be influenced by the choice of algorithm. By contrast, we show that the SP in determinant quantum Monte Carlo (QMC) is quantitatively linked to quantum critical behavior. We demonstrate this through simulations of several models with critical properties that are relatively well understood. We propose a reinterpretation of the low average sign for the Hubbard model on the square lattice away from half filling in terms of the onset of pseudogap behavior and exotic superconductivity. Our study charts a path for exploiting the average sign in QMC simulations to understand quantum critical behavior.
The BCS to BEC crossover in attractive Fermi systems is a prototype of weak to strong coupling evolution in many body physics. While extensive numerical results are available, and several approximate methods have been developed, most of these schemes are unsuccessful in the presence of spatial inhomogeneity. Such situations call for a real space approach that can handle large spatial scales and retain the crucial thermal fluctuations. With this in mind, we present comprehensive results of a real space auxiliary field approach to the BCS to BEC crossover in the attractive Hubbard model in two dimensions. The scheme reproduces the Hartree-Fock-Bogoliubov ground state, and leads to a Tc scale that agrees with quantum Monte Carlo estimates to within a few percent. We provide results on the Tc, amplitude and phase fluctuations, density of states, and the momentum resolved spectral function over the entire interaction and temperature window. We suggest how the method generalises successfully to the presence of disorder, trapping, and population imbalance. arXiv:1402.0817v1 [cond-mat.str-el]
While insensitive to weak non magnetic disorder, an s-wave superconductor can be driven insulating by strong disorder. Using a scheme that captures the correct ground state, and fully retains thermal amplitude and phase fluctuations, we describe the disorder driven superconductor-insulator transition at finite temperature. Our results on the resistivity suggest that beyond moderate disorder the low temperature superconducting state can arise out of an 'insulating' normal state. We also find that the low frequency weight in the density of states and optical conductivity are non monotonic in disorder, with a maximum near critical disorder, and their high temperature values correlate with the superconducting fraction in the disordered ground state.
We formulate an effective model for B-B' site ordering in double perovskite materials A2BB'O6. Even within the simple framework of lattice-gas type models, we are able to address several experimentally observed issues including nonmonotonic dependence of the degree of order on annealing temperature, and the rapid decrease of order upon overdoping with either B or B' species. We also study ordering in the 'ternary' compounds A2BB'1−yB"yO6. Although our emphasis is on the double perovskites, our results are easily generalizable to a wide variety of binary and ternary alloys.
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