Unfrustrated qudit chains and their ground states

Ramis Movassagh, Edward Farhi, Jeffrey Goldstone, Daniel Nagaj, Tobias J. Osborne, and Peter W. Shor
Phys. Rev. A 82, 012318 – Published 19 July 2010

Abstract

We investigate chains of d-dimensional quantum spins (qudits) on a line with generic nearest-neighbor interactions without translational invariance. We find the conditions under which these systems are not frustrated, that is, when the ground states are also the common ground states of all the local terms in the Hamiltonians. The states of a quantum spin chain are naturally represented in the matrix product states (MPS) framework. Using imaginary time evolution in the MPS ansatz, we numerically investigate the range of parameters in which we expect the ground states to be highly entangled and find them hard to approximate using our MPS method.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 25 March 2010

DOI:https://doi.org/10.1103/PhysRevA.82.012318

©2010 American Physical Society

Authors & Affiliations

Ramis Movassagh1,*, Edward Farhi2, Jeffrey Goldstone2, Daniel Nagaj3, Tobias J. Osborne4, and Peter W. Shor1

  • 1Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 2Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 3Research Center for Quantum Information, Institute of Physics, Slovak Academy of Sciences, Bratislava, Slovakia
  • 4Institute for Advanced Study, Wissenschaftskolleg zu Berlin, Berlin, Germany

  • *ramis@mit.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 82, Iss. 1 — July 2010

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review A

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×