Criticality without Frustration for Quantum Spin-1 Chains

J 2012

Criticality without Frustration for Quantum Spin-1 Chains

BRAVYI, Sergey, Libor CAHA, Ramis MOVASSAGH, Daniel NAGAJ, Peter SHOR et. al.

Basic information

Original name

Criticality without Frustration for Quantum Spin-1 Chains

Authors

BRAVYI, Sergey (643 Russian Federation), Libor CAHA (203 Czech Republic, belonging to the institution), Ramis MOVASSAGH (840 United States of America), Daniel NAGAJ (703 Slovakia) and Peter SHOR (840 United States of America)

Edition

Physical Review Letters, COLLEGE PK, Americal Physical Society, 2012, 0031-9007

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10301 Atomic, molecular and chemical physics

Country of publisher

Netherlands

Confidentiality degree

není předmětem státního či obchodního tajemství

Impact factor

Impact factor: 7.943

RIV identification code

RIV/00216224:14330/12:00080251

Organization unit

Faculty of Informatics

DOI

http://dx.doi.org/10.1103/PhysRevLett.109.207202

UT WoS

000311137600010

Keywords in English

spin chains

Změněno: 22/5/2015 06:30, RNDr. Pavel Šmerk, Ph.D.

Abstract

V originále

Frustration-free (FF) spin chains have a property that their ground state minimizes all individual terms in the chain Hamiltonian. We ask how entangled the ground state of a FF quantum spin-s chain with nearest-neighbor interactions can be for small values of s. While FF spin-1/2 chains are known to have unentangled ground states, the case s 1 remains less explored. We propose the first example of a FF translation-invariant spin-1 chain that has a unique highly entangled ground state and exhibits some signatures of a critical behavior. The ground state can be viewed as the uniform superposition of balanced strings of left and right brackets separated by empty spaces. Entanglement entropy of one half of the chain scales as 1/2 logn + O(1), where n is the number of spins. We prove that the energy gap above the ground state is polynomial in 1/n. The proof relies on a new result concerning statistics of Dyck paths which might be of independent interest.

Citovat

BRAVYI, Sergey, Libor CAHA, Ramis MOVASSAGH, Daniel NAGAJ and Peter SHOR. Criticality without Frustration for Quantum Spin-1 Chains. Physical Review Letters. COLLEGE PK: Americal Physical Society, 2012, vol. 109, No 20, p. 1-5. ISSN 0031-9007. Available from: https://dx.doi.org/10.1103/PhysRevLett.109.207202.

@article{1299819,
   author = {Bravyi, Sergey and Caha, Libor and Movassagh, Ramis and Nagaj, Daniel and Shor, Peter},
   article_location = {COLLEGE PK},
   article_number = {20},
   doi = {http://dx.doi.org/10.1103/PhysRevLett.109.207202},
   keywords = {spin chains},
   language = {eng},
   issn = {0031-9007},
   journal = {Physical Review Letters},
   title = {Criticality without Frustration for Quantum Spin-1 Chains},
   volume = {109},
   year = {2012}
}

TY  - JOUR
ID  - 1299819
AU  - Bravyi, Sergey - Caha, Libor - Movassagh, Ramis - Nagaj, Daniel - Shor, Peter
PY  - 2012
TI  - Criticality without Frustration for Quantum Spin-1 Chains
JF  - Physical Review Letters
VL  - 109
IS  - 20
SP  - 1-5
EP  - 1-5
PB  - Americal Physical Society
SN  - 00319007
KW  - spin chains
N2  - Frustration-free (FF) spin chains have a property that their ground state minimizes all individual terms in the chain Hamiltonian. We ask how entangled the ground state of a FF quantum spin-s chain with nearest-neighbor interactions can be for small values of s. While FF spin-1/2 chains are known to have unentangled ground states, the case s 1 remains less explored. We propose the first example of a FF translation-invariant spin-1 chain that has a unique highly entangled ground state and exhibits some signatures of a critical behavior. The ground state can be viewed as the uniform superposition of balanced strings of left and right brackets separated by empty spaces. Entanglement entropy of one half of the chain scales as 1/2 logn + O(1), where n is the number of spins. We prove that the energy gap above the ground state is polynomial in 1/n. The proof relies on a new result concerning statistics of Dyck paths which might be of independent interest.
ER  -

BRAVYI, Sergey, Libor CAHA, Ramis MOVASSAGH, Daniel NAGAJ and Peter SHOR. Criticality without Frustration for Quantum Spin-1 Chains. \textit{Physical Review Letters}. COLLEGE PK: Americal Physical Society, 2012, vol.~109, No~20, p.~1-5. ISSN~0031-9007. Available from: https://dx.doi.org/10.1103/PhysRevLett.109.207202.

Detailed Information on Publication Record