Details
| Original language | English |
|---|---|
| Article number | 032110 |
| Pages (from-to) | 321101-321114 |
| Number of pages | 14 |
| Journal | Physical Review A - Atomic, Molecular, and Optical Physics |
| Volume | 66 |
| Issue number | 3 |
| Publication status | Published - 23 Sept 2002 |
| Externally published | Yes |
Abstract
What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems that can be solved. An example of such a system is the one-dimensional infinite-lattice anisotropic [Formula Presented] model. This model is exactly solvable using the Jordan-Wigner transform, and it is possible to calculate the two-site reduced density matrix for all pairs of sites. Using the two-site density matrix, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. We also study the entanglement in the transverse Ising model, a special case of the [Formula Presented] model, which exhibits a quantum phase transition. It is found that the next-nearest-neighbor entanglement (though not the nearest-neighbor entanglement) is a maximum at the critical point. Furthermore, we show that the critical point in the transverse Ising model corresponds to a transition in the behavior of the entanglement between a single site and the remainder of the lattice.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics
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In: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 66, No. 3, 032110, 23.09.2002, p. 321101-321114.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Entanglement in a simple quantum phase transition
AU - Osborne, Tobias J.
AU - Nielsen, Michael A.
N1 - Copyright: Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2002/9/23
Y1 - 2002/9/23
N2 - What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems that can be solved. An example of such a system is the one-dimensional infinite-lattice anisotropic [Formula Presented] model. This model is exactly solvable using the Jordan-Wigner transform, and it is possible to calculate the two-site reduced density matrix for all pairs of sites. Using the two-site density matrix, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. We also study the entanglement in the transverse Ising model, a special case of the [Formula Presented] model, which exhibits a quantum phase transition. It is found that the next-nearest-neighbor entanglement (though not the nearest-neighbor entanglement) is a maximum at the critical point. Furthermore, we show that the critical point in the transverse Ising model corresponds to a transition in the behavior of the entanglement between a single site and the remainder of the lattice.
AB - What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems that can be solved. An example of such a system is the one-dimensional infinite-lattice anisotropic [Formula Presented] model. This model is exactly solvable using the Jordan-Wigner transform, and it is possible to calculate the two-site reduced density matrix for all pairs of sites. Using the two-site density matrix, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. We also study the entanglement in the transverse Ising model, a special case of the [Formula Presented] model, which exhibits a quantum phase transition. It is found that the next-nearest-neighbor entanglement (though not the nearest-neighbor entanglement) is a maximum at the critical point. Furthermore, we show that the critical point in the transverse Ising model corresponds to a transition in the behavior of the entanglement between a single site and the remainder of the lattice.
UR - http://www.scopus.com/inward/record.url?scp=84871894919&partnerID=8YFLogxK
U2 - arXiv:quant-ph/0202162
DO - arXiv:quant-ph/0202162
M3 - Article
AN - SCOPUS:0036757880
VL - 66
SP - 321101
EP - 321114
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
SN - 1050-2947
IS - 3
M1 - 032110
ER -