Time-Dependent Variational Principle for Quantum Lattices

Jutho Haegeman, J. Ignacio Cirac, Tobias J. Osborne, Iztok Pižorn, Henri Verschelde, and Frank Verstraete
Phys. Rev. Lett. 107, 070601 – Published 10 August 2011

Abstract

We develop a new algorithm based on the time-dependent variational principle applied to matrix product states to efficiently simulate the real- and imaginary-time dynamics for infinite one-dimensional quantum lattices. This procedure (i) is argued to be optimal, (ii) does not rely on the Trotter decomposition and thus has no Trotter error, (iii) preserves all symmetries and conservation laws, and (iv) has low computational complexity. The algorithm is illustrated by using both an imaginary-time and a real-time example.

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  • Received 30 May 2011

DOI:https://doi.org/10.1103/PhysRevLett.107.070601

© 2011 American Physical Society

Authors & Affiliations

Jutho Haegeman1, J. Ignacio Cirac2, Tobias J. Osborne3, Iztok Pižorn4, Henri Verschelde1, and Frank Verstraete4,5

  • 1Department of Physics and Astronomy, Ghent University, Krijgslaan 281-S9, B-9000 Ghent, Belgium
  • 2Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, Garching, D-85748, Germany
  • 3Institute of Theoretical Physics, Leibniz Universität Hannover, Appelstrasse 2, D-30167 Hannover, Germany
  • 4Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Wien, Austria
  • 5C. N. Yang Institute for Theoretical Physics, SUNY, Stony Brook, New York 11794-3840, USA

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Vol. 107, Iss. 7 — 12 August 2011

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