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

Journal of Physics Conference Series

Spin chain under next nearest neighbor interaction

L. C. Kwek, Y Takahashi, Keng Wah Choo

Published Jan 7, 2009• 16 citations
Publisher

Abstract

We perform a numerical study on the concurrence of the ground state Heisenberg XXX with next-nearest-neighbor interaction with open and periodic boundary condition.
DOI
10.1088/1742-6596/143/1/012014

Related papers

Ground state of the antiferromagnetic Heisenberg chain with nearest-aand next-nearest-neighbor interactions

M. A. García‐Bach, Douglas J. Klein

Physics Letters A•Apr 1, 1982•7 citations

Ground state energies for a finite linear Heisenberg chain with nearest and next-nearest neighbor interactions

Ikuo Ono

Physics Letters A•Feb 1, 1972•17 citations

Ground-state of the linear anisotropic antiferromagnetic Heisenberg chain with nearest and next-nearest neighbor interactions

Jay D. Mancini, Janice D. Prie, William J. Massano

Solid State Communications•Feb 1, 1994•4 citations

Spin liquid ground state on the honeycomb Heisenberg spin 1/2 model with nearest and next nearest neighbor interaction

Zhenyue Zhu, Steven White, David A. Huse

Bulletin of the American Physical Society•Mar 2, 2012•0 citations

Entanglement in quantum network systems

Keng Wah Choo

Entanglement, according to the physicist Erwin Schrdinger, the essence of Quantum Mechanics, has been known for a long time now to be the source of paradoxes. The most remarkable one is called non-locality and it is at the heart of the Einstein-Podolsky-Rosen (EPR) paradox and of the fact that Quantum Mechanics violates Bell’s inequalities. Recent years, entanglement has emerged as the resource that makes quantum information science so successful. Indeed, based on entanglement, various informational tasks become feasible while they would be impossible using classical physics. Following this new trend in quantum information science, a growing community of scientists has started to investigate the resource entanglement, quantum algorithms, and the possibility of building a quantum computer that perform the quantum algorithms. However, the issue of quantum state interacting with the environment causes errors in the process of quantum computation. These errors arise mainly from decoherence, or the tendency of a quantum computer to decay from a given quantum state into an incoherent state as it interacts with the adjacent state of the environment. These interactions between the environment and quantum bits are unavoidable, and induce the breakdown of information stored in the quantum computer, and thus ended up with errors in computation. In order for quantum computer to be used to solve problems, decoherence and other potential sources of error must be reduced to an acceptable level. In this thesis, we study the various measures for quantifying bipartite and multipartite quantum entanglement for pure and mixed states. We look into the implementation of a quantum network as a universal quantum estimator where its use for estimation of state purity and entanglement are discussed in the first two chapters. The following chapters focus on quantum information processing, where one of the most useful algorithms is discussed, namely the Grover search algorithm. Based on our understanding of various entanglement measures, we study how concurrence changes over Grover search iterations. We further explore the use of this algorithm and quantum Fourier algorithm for applications in the field of bioinformatics. We then review in chapter 5 the progress made in semiconductor quantum dots systems, which have been used in many implementation for quantum information processing. We look into two applications where double quantum dots system can be exploited in chapter 6, namely the quantum teleportation and quantum state transfer. We investigate the various entanglement measures in a double quantum dots system. By introducing decoherence, we identify settings where such system can be used with acceptable performance in these applications. We conclude that quantum teleportation and quantum state transfer remain possible for a large range of external magnetic field and interdot distance under mild decoherence conditions. In chapter 7, we further investigate the nearest neighbor (NN) and nextnearest neighbor (NNN) interactions in the quantum network of one dimension structure. We perform comprehensive numerical studies on the ground state concurrence of both Heisenberg XXX model and Heisenberg XX model with periodic boundary and open boundary conditions. We found that although next-nearest-neighbor interaction does not enhance entanglement in nearest-neighbor pair in Heisenberg XXX model with periodic boundary condition, for Heisenberg XXX model with open boundary condition, nearest neighbor entanglement could be enhanced by next-nearest-neighbor nteraction. This feature is also present in Heisenberg XX model both in periodic and open boundary conditions. In the last chapter, we conclude on our research and provide some outlooks into the future development of quantum network systems.

•Jan 1, 2008•0 citations

Entanglement of the Heisenberg chain with the next-nearest-neighbor interaction

Shi-Jian Gu, Haibin Li, You‐Quan Li +1 more

The features of the concurrences between the nearest-neighbors and that of the next-nearest-neighbors for the one-dimensional Heisenberg model with next-nearest-neighbor coupling $J$ are studied as functions of temperature and $J$. The two concurrences exhibit a different dependence on $J$ at the ground state, which could be interpreted from the point of view of the correlation functions. The threshold temperature at which the concurrence is zero and the temperature effect on the two concurrences for systems up to 12 sites are studied numerically.

arXiv:quant-ph/0403026•Physical Review A•Nov 1, 2004•65 citations
Entanglement, according to the physicist Erwin Schrdinger, the essence of Quantum Mechanics, has been known for a long time now to be the source of paradoxes. The most remarkable one is called non-locality and it is at the heart of the Einstein-Podolsky-Rosen (EPR) paradox and of the fact that Quantum Mechanics violates Bell’s inequalities. Recent years, entanglement has emerged as the resource that makes quantum information science so successful. Indeed, based on entanglement, various informational tasks become feasible while they would be impossible using classical physics. Following this new trend in quantum information science, a growing community of scientists has started to investigate the resource entanglement, quantum algorithms, and the possibility of building a quantum computer that perform the quantum algorithms. However, the issue of quantum state interacting with the environment causes errors in the process of quantum computation. These errors arise mainly from decoherence, or the tendency of a quantum computer to decay from a given quantum state into an incoherent state as it interacts with the adjacent state of the environment. These interactions between the environment and quantum bits are unavoidable, and induce the breakdown of information stored in the quantum computer, and thus ended up with errors in computation. In order for quantum computer to be used to solve problems, decoherence and other potential sources of error must be reduced to an acceptable level. In this thesis, we study the various measures for quantifying bipartite and multipartite quantum entanglement for pure and mixed states. We look into the implementation of a quantum network as a universal quantum estimator where its use for estimation of state purity and entanglement are discussed in the first two chapters. The following chapters focus on quantum information processing, where one of the most useful algorithms is discussed, namely the Grover search algorithm. Based on our understanding of various entanglement measures, we study how concurrence changes over Grover search iterations. We further explore the use of this algorithm and quantum Fourier algorithm for applications in the field of bioinformatics. We then review in chapter 5 the progress made in semiconductor quantum dots systems, which have been used in many implementation for quantum information processing. We look into two applications where double quantum dots system can be exploited in chapter 6, namely the quantum teleportation and quantum state transfer. We investigate the various entanglement measures in a double quantum dots system. By introducing decoherence, we identify settings where such system can be used with acceptable performance in these applications. We conclude that quantum teleportation and quantum state transfer remain possible for a large range of external magnetic field and interdot distance under mild decoherence conditions. In chapter 7, we further investigate the nearest neighbor (NN) and nextnearest neighbor (NNN) interactions in the quantum network of one dimension structure. We perform comprehensive numerical studies on the ground state concurrence of both Heisenberg XXX model and Heisenberg XX model with periodic boundary and open boundary conditions. We found that although next-nearest-neighbor interaction does not enhance entanglement in nearest-neighbor pair in Heisenberg XXX model with periodic boundary condition, for Heisenberg XXX model with open boundary condition, nearest neighbor entanglement could be enhanced by next-nearest-neighbor nteraction. This feature is also present in Heisenberg XX model both in periodic and open boundary conditions. In the last chapter, we conclude on our research and provide some outlooks into the future development of quantum network systems.
The features of the concurrences between the nearest-neighbors and that of the next-nearest-neighbors for the one-dimensional Heisenberg model with next-nearest-neighbor coupling JJJ are studied as functions of temperature and JJJ. The two concurrences exhibit a different dependence on JJJ at the ground state, which could be interpreted from the point of view of the correlation functions. The threshold temperature at which the concurrence is zero and the temperature effect on the two concurrences for systems up to 12 sites are studied numerically.