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Recent Progress in Many-Body Theories

Point Defect Disorder in Models of High Temperature Superconductivity

J. W. Halleý, C. Das Gupta, S. Davis, X.-F. Wang

Published Jan 1, 1992• 3 citations
Publisher
DOI
10.1007/978-1-4615-3466-2_12

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The momentum-shell renormalization group (RG) is used to study the condensation of interacting Bose gases without and with disorder. First of all, for the homogeneous disorder-free Bose gas the interaction-induced shifts in the critical temperature and chemical potential are determined up to second order in the scattering length. The approach does not make use of dimensional reduction and is thus independent of previous derivations. Secondly, the RG is used together with the replica method to study the interacting Bose gas with delta-correlated disorder. The flow equations are derived and found to reduce, in the high-temperature limit, to the RG equations of the classical Landau-Ginzburg model with random-exchange defects. The random fixed point is used to calculate the condensation temperature under the combined influence of particle interactions and disorder.
In transverse-field Ising models, disorder in the couplings gives rise to a drastic reduction of the critical energy gap and, accordingly, to an unfavorable, slower-than-algebraic scaling of the density of defects produced when the system is driven through its quantum critical point. By applying Kibble-Zurek theory and numerical calculations, we demonstrate in the one-dimensional model that the scaling of defect density with annealing time can be made algebraic by balancing the coupling disorder with suitably chosen inhomogeneous driving fields. Depending on the tail of the coupling distribution at zero, balancing can be either perfect, leading to the well-known inverse-square law of the homogeneous system, or partial, still resulting in an algebraic decrease but with a smaller, nonuniversal exponent. We also study defect production during an environment-temperature quench of the open variant of the model in which the system is slowly cooled down to its quantum critical point. According to our scaling and numerical results, uncorrelated disorder induces a logarithmic temporal decrease of the defect density, while balanced disorder leads again to an algebraic decay.