Physics – Quantum Physics
Scientific paper
2010-06-23
J. Math. Phys. 51, 092109 (2010)
Physics
Quantum Physics
24 pages, 1 figure, final version
Scientific paper
10.1063/1.3490188
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-neighbour 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 permits these open quantum systems to be efficiently simulated by the density matrix renormalization group methods.
Chin Alex. W.
Huelga Susana F.
Plenio Martin . B.
Rivas Ángel
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