Details
| Original language | English |
|---|---|
| Pages (from-to) | 281-296 |
| Number of pages | 16 |
| Journal | Journal of Statistical Physics |
| Volume | 178 |
| Issue number | 1 |
| Early online date | 2 Dec 2019 |
| Publication status | Published - Jan 2020 |
Abstract
A rigorous proof is presented of the boundedness of the entanglement entropy of a block of spins for the ground state of the one-dimensional quantum Ising model with sufficiently strong transverse field. This is proved by a refinement of the stochastic geometric arguments in the earlier work by Grimmett et al. (J Stat Phys 131:305–339, 2008). The proof utilises a transformation to a model of classical probability called the continuum random-cluster model. Our method of proof is fairly robust, and applies also to certain disordered systems.
Keywords
- Area law, Entanglement, Entropy, Quantum Ising model, Random-cluster model
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Mathematical Physics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Journal of Statistical Physics, Vol. 178, No. 1, 01.2020, p. 281-296.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Bounded Entanglement Entropy in the Quantum Ising Model
AU - Grimmett, Geoffrey R.
AU - Osborne, Tobias J.
AU - Scudo, Petra F.
PY - 2020/1
Y1 - 2020/1
N2 - A rigorous proof is presented of the boundedness of the entanglement entropy of a block of spins for the ground state of the one-dimensional quantum Ising model with sufficiently strong transverse field. This is proved by a refinement of the stochastic geometric arguments in the earlier work by Grimmett et al. (J Stat Phys 131:305–339, 2008). The proof utilises a transformation to a model of classical probability called the continuum random-cluster model. Our method of proof is fairly robust, and applies also to certain disordered systems.
AB - A rigorous proof is presented of the boundedness of the entanglement entropy of a block of spins for the ground state of the one-dimensional quantum Ising model with sufficiently strong transverse field. This is proved by a refinement of the stochastic geometric arguments in the earlier work by Grimmett et al. (J Stat Phys 131:305–339, 2008). The proof utilises a transformation to a model of classical probability called the continuum random-cluster model. Our method of proof is fairly robust, and applies also to certain disordered systems.
KW - Area law
KW - Entanglement
KW - Entropy
KW - Quantum Ising model
KW - Random-cluster model
UR - http://www.scopus.com/inward/record.url?scp=85075955807&partnerID=8YFLogxK
U2 - 10.1007/s10955-019-02432-y
DO - 10.1007/s10955-019-02432-y
M3 - Article
AN - SCOPUS:85075955807
VL - 178
SP - 281
EP - 296
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
SN - 0022-4715
IS - 1
ER -