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Phys. Rev. Lett. 102, 057202 (2009) [4 pages]

Density Matrix Renormalization Group in the Heisenberg Picture

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Michael J. Hartmann1,2,3,*, Javier Prior2,3,4, Stephen R. Clark4,5, and Martin B. Plenio2,3
1Physik Department I, Technische Universität München, James Franck Strasse, 85748 Garching, Germany
2Institute for Mathematical Sciences, Imperial College London, London SW7 2PG, United Kingdom
3QOLS, The Blackett Laboratory, Imperial College London, London SW7 2BW, United Kingdom
4Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
5Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore

Received 5 August 2008; revised 19 December 2008; published 2 February 2009

In some cases the state of a quantum system with a large number of subsystems can be approximated efficiently by the density-matrix renormalization group, which makes use of redundancies in the description of the state. Here we show that the achievable efficiency can be much better when performing density-matrix renormalization group calculations in the Heisenberg picture, as only the observable of interest but not the entire state is considered. In some nontrivial cases, this approach can even be exact for finite bond dimensions.

© 2009 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.102.057202
DOI:
10.1103/PhysRevLett.102.057202
PACS:
75.10.Pq, 02.70.−c, 03.67.Mn

*michael.hartmann@ph.tum.de

 
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