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

arXiv:quant-ph/0407226 · Physical Review A

Reexamination of entanglement and the quantum phase transition

Min-Fong Yang

Published Mar 28, 2005• 149 citations
arXivHTMLPDF

Abstract

We show that, for an exactly solvable quantum spin model, a discontinuity in the first derivative of the ground-state concurrence appears in the absence of a quantum phase transition. It is opposed to the popular belief that the nonanalyticity property of ground-state concurrence can be used to determine quantum phase transitions. We further point out that the analyticity property of the ground-state concurrence in general can be more intricate than that of the ground-state energy. Thus there is no one-to-one correspondence between quantum phase transitions and the nonanalyticity property of the concurrence. Moreover, we show that the von Neumann entropy, as another measure of entanglement, cannot reveal quantum phase transitions in the present model. Therefore, in order to link with quantum phase transitions, some other measures of entanglement are needed.

DOI
10.1103/physreva.71.030302

Related papers

Quantum phase transitions in fully connected spin models: An entanglement perspective

Michele Filippone, Sébastien Dusuel, Julien Vidal

We consider a set of fully connected spin models that display first- or second-order transitions and for which we compute the ground-state entanglement in the thermodynamical limit. We analyze several entanglement measures (concurrence, R\'enyi entropy, and negativity) and show that, in general, discontinuous transitions lead to a jump of these quantities at the transition point. Interestingly, we also find examples where this is not the case.

arXiv:1101.3654•Physical Review A•Feb 25, 2011•52 citations

Quantum Phase Transitions and Bipartite Entanglement

Lian-Ao Wu, M. S. Sarandy, Daniel A. Lidar

We develop a general theory of the relation between quantum phase transitions (QPTs) characterized by nonanalyticities in the energy and bipartite entanglement. We derive a functional relation between the matrix elements of two-particle reduced density matrices and the eigenvalues of general two-body Hamiltonians of d-level systems. The ground state energy eigenvalue and its derivatives, whose nonanalyticity characterizes a QPT, are directly tied to bipartite entanglement measures. We show that first-order QPTs are signaled by density matrix elements themselves and second-order QPTs by the first derivative of density matrix elements. Our general conclusions are illustrated via several quantum spin models.

arXiv:quant-ph/0407056•Physical Review Letters•Dec 15, 2004•484 citations

Genuine tripartite entanglement and quantum phase transition

Chang‐shui Yu, He‐Shan Song, H. T. Cui

A new formulation called as entanglement measure for simplification, is presented to characterize genuine tripartite entanglement of $(2\times 2\times n)-$dimensional quantum pure states. The formulation shows that the genuine tripartite entanglement can be described only on the basis of the local $(2\times 2)-$dimensional reduced density matrix. In particular, the two exactly solvable models of spin system studied by Yang (Phys. Rev. A \textbf{71}, 030302(R) (2005)) is reconsidered by employing the entanglement measure. The results show that a discontinuity in the first derivative of the entanglement measure or in the entanglement measure itself of the ground state just corresponds to the existence of quantum phase transition, which is obviously prior to concurrence. Hence, the given entanglement measure may become a new alternate candidate to help study the connection between quantum entanglement and quantum phase transitions.

arXiv:quant-ph/0611011•Nov 1, 2006•0 citations

Quantum Phase Transition and Entanglement of Bi-Spin System

Tosihide H. YOSIDA, Ji-Xuan Hou

In this paper we study the quantum phase transition and entanglement in s1=1/2 and s2=1 spin pair system by the exact diagonalization method. We show that, for this exactly solvable quantum bi-spin system, entanglement appears before quantum phase transition and disappears after it. Moreover, we show that the von Neumann entropy, as a measure of entanglement, can reveal quantum phase transition in this system.

•May 1, 2007•0 citations

Entanglement across a transition to quantum chaos

Carlos Mejía-Monasterio, Giuliano Benenti, Gabriel G. Carlo +1 more

We study the relation between entanglement and quantum chaos in one- and two-dimensional spin-$1∕2$ lattice models, which exhibit mixing of the noninteracting eigenfunctions and transition from integrability to quantum chaos. Contrary to what occurs in a quantum phase transition, the onset of quantum chaos is not a property of the ground state but takes place for any typical many-spin quantum state. We study bipartite and pairwise entanglement measures---namely, the reduced von Neumann entropy and the concurrence---and discuss quantum entanglement sharing. Our results suggest that the behavior of the entanglement is related to the mixing of the eigenfunctions rather than to the transition to chaos.

arXiv:quant-ph/0410246•Physical Review A•Jun 1, 2005•75 citations

Concurrence in collective models

Julien Vidal

We review the entanglement properties in collective models and their relationship with quantum phase transitions. Focusing on the concurrence, which characterizes the two-spin entanglement, we show that for first-order transitions, this quantity is singular but continuous at the transition point, contrary to the common belief. We also propose a conjecture for the concurrence of arbitrary symmetric states which connects it with a recently proposed criterion for bipartite entanglement.

arXiv:quant-ph/0603108•Physical Review A•Jun 13, 2006•82 citations
We show that, for an exactly solvable quantum spin model, a discontinuity in the first derivative of the ground-state concurrence appears in the absence of a quantum phase transition. It is opposed to the popular belief that the nonanalyticity property of ground-state concurrence can be used to determine quantum phase transitions. We further point out that the analyticity property of the ground-state concurrence in general can be more intricate than that of the ground-state energy. Thus there is no one-to-one correspondence between quantum phase transitions and the nonanalyticity property of the concurrence. Moreover, we show that the von Neumann entropy, as another measure of entanglement, cannot reveal quantum phase transitions in the present model. Therefore, in order to link with quantum phase transitions, some other measures of entanglement are needed.
We develop a general theory of the relation between quantum phase transitions (QPTs) characterized by nonanalyticities in the energy and bipartite entanglement. We derive a functional relation between the matrix elements of two-particle reduced density matrices and the eigenvalues of general two-body Hamiltonians of d-level systems. The ground state energy eigenvalue and its derivatives, whose nonanalyticity characterizes a QPT, are directly tied to bipartite entanglement measures. We show that first-order QPTs are signaled by density matrix elements themselves and second-order QPTs by the first derivative of density matrix elements. Our general conclusions are illustrated via several quantum spin models.
A new formulation called as entanglement measure for simplification, is presented to characterize genuine tripartite entanglement of (2×2×n)−(2\times 2\times n)-(2×2×n)−dimensional quantum pure states. The formulation shows that the genuine tripartite entanglement can be described only on the basis of the local (2×2)−(2\times 2)-(2×2)−dimensional reduced density matrix. In particular, the two exactly solvable models of spin system studied by Yang (Phys. Rev. A \textbf{71}, 030302(R) (2005)) is reconsidered by employing the entanglement measure. The results show that a discontinuity in the first derivative of the entanglement measure or in the entanglement measure itself of the ground state just corresponds to the existence of quantum phase transition, which is obviously prior to concurrence. Hence, the given entanglement measure may become a new alternate candidate to help study the connection between quantum entanglement and quantum phase transitions.
We study the relation between entanglement and quantum chaos in one- and two-dimensional spin-1∕21∕21∕2 lattice models, which exhibit mixing of the noninteracting eigenfunctions and transition from integrability to quantum chaos. Contrary to what occurs in a quantum phase transition, the onset of quantum chaos is not a property of the ground state but takes place for any typical many-spin quantum state. We study bipartite and pairwise entanglement measures---namely, the reduced von Neumann entropy and the concurrence---and discuss quantum entanglement sharing. Our results suggest that the behavior of the entanglement is related to the mixing of the eigenfunctions rather than to the transition to chaos.