Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials

By Alex W. Chin, 'Angel Rivas, Susana F. Huelga, Martin Bodo Plenio. 2010

297 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/abf19a3710ade39426d3b9acb5e8cd3c975050e0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

  1. Daniel Alonso
  2. I. D. Vega
  3. Susana F. Huelga
  4. Martin Bodo Plenio
  5. Fernando G. S. L. Brandão

In Atomic and Molecular Physics, and Optics

  1. Susana F. Huelga
  2. Daniel Alonso
  3. I. D. Vega
  4. Martin Bodo Plenio
  5. Fernando G. S. L. Brandão
  6. Seogjoo J. Jang
  7. Benedetta Mennucci
  8. Michael J. Hartmann

Citations in the corpus