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Role of rotational invariance in the properties of Hamiltonians

Source: Phys. Rev. A 80, 040301(R) (2009); doi:10.1103/PhysRevA.80.040301

Published 2 October 2009

KEYWORDS and PACS
Keywords
PACS
  • 03.67.Ac
    Quantum algorithms, protocols and simulations
  • 89.70.Eg
    Computational complexity
  • YEAR: 2009
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PUBLICATION DATA
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Alastair Kay
Centre for Quantum Computation, DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom and Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany
Is it possible to prove that the properties of Hamiltonians, such as the ground-state energy, results of dynamical evolution, or thermal state expectation values, can be efficiently calculated when the Hamiltonians have physically motivated constraints such as translational or rotational invariance? We report that rotational invariance does not reduce the difficulty of finding the ground-state energy of the system. Crucially, the construction preserves the translational invariance of a Hamiltonian. The failure of the construction for the properties of thermal states at finite temperatures is discussed. ©2009 The American Physical Society
History: Received 28 July 2009; published 2 October 2009
Permalink: http://link.aps.org/abstract/PRA/v80/e040301

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