期刊
JOURNAL OF MATHEMATICAL PHYSICS
卷 51, 期 9, 页码 -出版社
AMER INST PHYSICS
DOI: 10.1063/1.3490188
关键词
boson systems; fermion systems; polynomials; quantum theory; renormalisation
资金
- EU
- Alexander von Humboldt
By using the properties of orthogonal polynomials, we present an exact unitary transformation that maps the Hamiltonian of a quantum system coupled linearly to a continuum of bosonic or fermionic modes to a Hamiltonian that describes a one-dimensional chain with only nearest-neighbor interactions. This analytical transformation predicts a simple set of relations between the parameters of the chain and the recurrence coefficients of the orthogonal polynomials used in the transformation and allows the chain parameters to be computed using numerically stable algorithms that have been developed to compute recurrence coefficients. We then prove some general properties of this chain system for a wide range of spectral functions and give examples drawn from physical systems where exact analytic expressions for the chain properties can be obtained. Crucially, the short-range interactions of the effective chain system permit these open-quantum systems to be efficiently simulated by the density matrix renormalization group methods. (C) 2010 American Institute of Physics. [doi:10.1063/1.3490188]
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