Gapless Hamiltonians for the Toric Code Using the Projected Entangled Pair State Formalism

Fernández-González, Carlos and Schuch, Norbert and Wolf, Michael M. and Cirac, J. Ignacio and Pérez-García, David (2012) Gapless Hamiltonians for the Toric Code Using the Projected Entangled Pair State Formalism. Physical Review Letters, 109 (26). Art. No. 260401. ISSN 0031-9007. doi:10.1103/PhysRevLett.109.260401. https://resolver.caltech.edu/CaltechAUTHORS:20120713-104140016

PDF - Published Version
See Usage Policy.
309kB

Preview

PDF - Submitted Version
See Usage Policy.
691kB

PDF - Supplemental Material
See Usage Policy.
519kB

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20120713-104140016

Abstract

We study Hamiltonians which have Kitaev’s toric code as a ground state, and show how to construct a Hamiltonian which shares the ground space of the toric code, but which has gapless excitations with a continuous spectrum in the thermodynamic limit. Our construction is based on the framework of projected entangled pair states, and can be applied to a large class of two-dimensional systems to obtain gapless “uncle Hamiltonians.”

Item Type:

Article

Related URLs:

URL	URL Type	Description
http://arxiv.org/abs/1111.5817v2	arXiv	Discussion Paper
http://dx.doi.org/10.1103/PhysRevLett.109.260401	DOI	Article
http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.260401	Publisher	Article

ORCID:

Author	ORCID
Pérez-García, David	0000-0003-2990-791X

Alternate Title:

Gapless Hamiltonians for the toric code using the PEPS formalism

Additional Information:

© 2012 American Physical Society. Received 20 June 2012; published 26 December 2012. We especially thank Bruno Nachtergaele for useful comments and discussions. This work has been partially funded by the Spanish Grants No. I-MATH, No. MTM2008- 01366, No. S2009/ESP-1594 and QUITEMAD, the European project QUEVADIS, the Alexander von Humboldt Foundation, the Gordon and Betty Moore Foundation through Caltech’s Center for the Physics of Information, the NSF Grant No. PHY-0803371, and the ARO Grant No. W911NF-09-1-0442. We also acknowledge the hospitality of the Centro de Ciencias de Benasque Pedro Pascual and of the Perimeter Institute, where part of this work was carried out.

Group:

Institute for Quantum Information and Matter

Funders:

Funding Agency	Grant Number
Spanish Grants	I-MATH
Spanish Grants	MTM2008-01366
Spanish Grants	S2009/ESP-1594
QUITEMAD	UNSPECIFIED
European Project QUEVADIS	UNSPECIFIED
Alexander von Humboldt Foundation	UNSPECIFIED
Gordon and Betty Moore Foundation	UNSPECIFIED
NSF	PHY-0803371
Army Research Office (ARO)	W911NF-09-1-0442

Issue or Number:

Classification Code:

PACS numbers: 05.30.Rt, 03.65.Vf, 71.10.�w

DOI:

10.1103/PhysRevLett.109.260401

Record Number:

CaltechAUTHORS:20120713-104140016

Persistent URL:

https://resolver.caltech.edu/CaltechAUTHORS:20120713-104140016

Usage Policy:

No commercial reproduction, distribution, display or performance rights in this work are provided.

ID Code:

32422

Collection:

CaltechAUTHORS

Deposited By:

Tony Diaz

Deposited On:

19 Jul 2012 22:53

Last Modified:

09 Nov 2021 21:27

Repository Staff Only: item control page