Numerical Method for Disordered Quantum Phase Transitions in the Large-N Limit
We develop an efficient numerical method to study the quantum critical behavior of disordered systems with O(N) order-parameter symmetry in the large-N limit. It is based on the iterative solution of the large-N saddle-point equations combined with a fast algorithm for inverting the arising large sparse random matrices. As an example, we consider the superconductor-metal quantum phase transition in disordered nanowires. We study the behavior of various observables near the quantum phase transition. Our results agree with recent renormalization group predictions, i.e., the transition is governed by an infinite-randomness critical point, accompanied by quantum Griffiths singularities. In contrast to the existing numerical approach to this problem, our method gives direct access to the temperature dependencies of observables. Moreover, our algorithm is highly efficient because the numerical effort for each iteration scales linearly with the system size. This allows us to study larger systems, with up to 1024 sites, than previous methods. We also discuss generalizations to higher dimensions and other systems including the itinerant antiferromagnetic transitions in disordered metals.
D. Nozadze and T. Vojta, "Numerical Method for Disordered Quantum Phase Transitions in the Large-N Limit," physica status solidi (b), vol. 251, no. 3, pp. 675 - 682, Wiley-VCH Verlag GmbH & Co., Mar 2014.
The definitive version is available at https://doi.org/10.1002/pssb.201350152
Center for High Performance Computing Research
Keywords and Phrases
Infinite Randomness; Large-N Limit; Quantum Griffiths Phase; Quantum Phase Transition
International Standard Serial Number (ISSN)
Article - Journal
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01 Mar 2014