Solving Frustration-Free Spin Systems

N. de Beaudrap, M. Ohliger, T. J. Osborne, and J. Eisert
Phys. Rev. Lett. 105, 060504 – Published 6 August 2010

Abstract

We identify a large class of quantum many-body systems that can be solved exactly: natural frustration-free spin-1/2 nearest-neighbor Hamiltonians on arbitrary lattices. We show that the entire ground-state manifold of such models can be found exactly by a tensor network of isometries acting on a space locally isomorphic to the symmetric subspace. Thus, for this wide class of models, real-space renormalization can be made exact. Our findings also imply that every such frustration-free spin model satisfies an area law for the entanglement entropy of the ground state, establishing a novel large class of models for which an area law is known. Finally, we show that our approach gives rise to an ansatz class useful for the simulation of almost frustration-free models in a simple fashion, outperforming mean-field theory.

  • Figure
  • Received 22 May 2010

DOI:https://doi.org/10.1103/PhysRevLett.105.060504

© 2010 The American Physical Society

Authors & Affiliations

N. de Beaudrap1, M. Ohliger1, T. J. Osborne2, and J. Eisert1,2

  • 1Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
  • 2Institute for Advanced Study Berlin, 14193 Berlin, Germany

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Issue

Vol. 105, Iss. 6 — 6 August 2010

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