Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Entanglement in Valence-Bond-Solid States and Quantum Search

Ying Dong Xu

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

Stony Brook University Libraries. \nDepartment of Physics and Astronomy. Lawrence Martin (Dean of Graduate School), Vladimir E. Korepin { Dissertation Advisor \nProfessor, C.N. Yang Institute for Theoretical Physics, Warren D. Siegel { Chairperson of Defense \nProfessor, C.N. Yang Institute for Theoretical Physics, Dominik A. Schneble \nAssistant Professor, Department of Physics and Astronomy, Barry McCoy \nDistinguished Professor, C.N. Yang Institute for Theoretical Physics, Peter van Nieuwenhuizen \nDistinguished Professor, C.N. Yang Institute for Theoretical Physics, Alexander Kirillov, Jr. \nAssociate professor \nDepartment of Mathematics.

Related papers

ENTANGLEMENT IN VALENCE-BOND-SOLID STATES

V. E. Korepin, YING XU

This article reviews the quantum entanglement in Valence-Bond-Solid (VBS) states defined on a lattice or a graph. The subject is presented in a self-contained and pedagogical way. The VBS state was first introduced in the celebrated paper by I. Affleck, T. Kennedy, E. H. Lieb and H. Tasaki (abbreviation AKLT is widely used). It became essential in condensed matter physics and quantum information (measurement-based quantum computation). Many publications have been devoted to the subject. Recently entanglement was studied in the VBS state. In this review, we start with the definition of a general AKLT spin chain and the construction of VBS ground state. In order to study entanglement, a block subsystem is introduced and described by the density matrix. Density matrices of 1-dimensional models are diagonalized and the entanglement entropies (the von Neumann entropy and Rényi entropy) are calculated. In the large block limit, the entropies also approach finite limits. Study of the spectrum of the density matrix led to the discovery that the density matrix is proportional to a projector.

arXiv:0908.2345•International Journal of Modern Physics B•Apr 30, 2010•30 citations

Correlation functions of one-dimensional impenetrable anyons

Ionel Ovidiu Patu

Stony Brook University Libraries.\nSBU Graduate School in Physics and Astronomy.\nLawrence Martin (Dean of Graduate School), Barry McCoy Dissertation Advisor\nDistinguished Professor, C.N. Yang Institute for Theoretical Physics, Vladimir Korepin Chairperson of Defense\nProfessor, C.N. Yang Institute for Theoretical Physics, Dmitri Averin\nProfessor, Department of Physics and Astronomy, Abhay Deshpande\nProfessor, Department of Physics and Astronomy, Leon Takhtajan\nProfessor\nDepartment of Mathematics, Stony Brook University.

•May 1, 2009•0 citations

PROF. C. N. YANG AND QUANTUM ENTANGLEMENT IN PARTICLE PHYSICS

Yu Shi

Conference in Honor of C N Yang's 85th Birthday•Dec 1, 2008•1 citation

Quantum Gases in State-Dependent Optical Potentials

René Reimann

Stony Brook University Libraries. SBU Graduate School in Physics and Astronomy. Lawrence Martin (Dean of Graduate School), Dominik Schneble Thesis Advisor \nAssistant Professor, Department of Physics and Astronomy \nStony Brook University, Harold Metcalf Chairperson of Defense \nDistinguished Teaching Professor, Department of Physics and Astronomy \nStony Brook University, Thomas Bergeman \nAdjunct Professor, Department of Physics and Astronomy \nStony Brook University.

•Aug 1, 2009•0 citations

The Influence of Disorder on Bloch Oscillations in a System of Ultracold Atoms in an Optical Lattice

Stefan Walter

Stony Brook University Libraries. SBU Graduate School in Physics and Astronomy. Lawrence Martin (Dean of Graduate School), Adam C. Durst – Thesis Advisor \nAssistant Professor, Department of Physics and Astronomy, Thomas Tzu Szu Kuo – Chairperson of Defense \nProfessor, Department of Physics and Astronomy, Dominik Schneble \nAssistant Professor, Department of Physics and Astronomy.

•Jan 1, 2009•0 citations

Supersymmetry of Pauli Hamiltonian and entanglement

V. M. Tkachuk, S. I. Vakarchuk

СУПЕРСИМЕТРIЯ ГАМIЛЬТОНIАНА ПАУЛI ТА СПЛУТАНIСТЬ КВАНТОВИХ СТАНIВВ. М. Ткачук, С.I

Journal of Physical Studies•Jan 1, 2008•2 citations
Stony Brook University Libraries. \nDepartment of Physics and Astronomy. Lawrence Martin (Dean of Graduate School), Vladimir E. Korepin { Dissertation Advisor \nProfessor, C.N. Yang Institute for Theoretical Physics, Warren D. Siegel { Chairperson of Defense \nProfessor, C.N. Yang Institute for Theoretical Physics, Dominik A. Schneble \nAssistant Professor, Department of Physics and Astronomy, Barry McCoy \nDistinguished Professor, C.N. Yang Institute for Theoretical Physics, Peter van Nieuwenhuizen \nDistinguished Professor, C.N. Yang Institute for Theoretical Physics, Alexander Kirillov, Jr. \nAssociate professor \nDepartment of Mathematics.
This article reviews the quantum entanglement in Valence-Bond-Solid (VBS) states defined on a lattice or a graph. The subject is presented in a self-contained and pedagogical way. The VBS state was first introduced in the celebrated paper by I. Affleck, T. Kennedy, E. H. Lieb and H. Tasaki (abbreviation AKLT is widely used). It became essential in condensed matter physics and quantum information (measurement-based quantum computation). Many publications have been devoted to the subject. Recently entanglement was studied in the VBS state. In this review, we start with the definition of a general AKLT spin chain and the construction of VBS ground state. In order to study entanglement, a block subsystem is introduced and described by the density matrix. Density matrices of 1-dimensional models are diagonalized and the entanglement entropies (the von Neumann entropy and Rényi entropy) are calculated. In the large block limit, the entropies also approach finite limits. Study of the spectrum of the density matrix led to the discovery that the density matrix is proportional to a projector.
Stony Brook University Libraries.\nSBU Graduate School in Physics and Astronomy.\nLawrence Martin (Dean of Graduate School), Barry McCoy Dissertation Advisor\nDistinguished Professor, C.N. Yang Institute for Theoretical Physics, Vladimir Korepin Chairperson of Defense\nProfessor, C.N. Yang Institute for Theoretical Physics, Dmitri Averin\nProfessor, Department of Physics and Astronomy, Abhay Deshpande\nProfessor, Department of Physics and Astronomy, Leon Takhtajan\nProfessor\nDepartment of Mathematics, Stony Brook University.