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:1209.1523

Multisite Entanglement acts as a Better Indicator of Quantum Phase Transitions in Spin Models with Three-spin Interactions

Manabendra Nath Bera, R. Prabhu, Aditi Sen De, Ujjwal Sen

Published Sep 7, 2012• 5 citations
arXivHTMLPDF

Abstract

We employ a genuine multipartite entanglement measure, the generalized geometric measure, for investigating the quantum phase transition in an infinite quantum spin-1/2 chain with two-spin as well as three-spin interactions. We show that in contrast to bipartite entanglement of the ground state, the genuine multiparty one unerringly indicates the quantum phase transition in the system. The system lends itself to a complementary behavior between bipartite and genuine multipartite entanglements. We also investigate the trend of the multipartite entanglement in finite chains, in which we perform a finite-size scaling to confirm the signature of the quantum phase transition already in finite systems. The finite-size investigation renders the phenomenon to be observable in real systems.

DOI
10.48550/arxiv.1209.1523

Related papers

Genuine-multipartite-entanglement trends in gapless-to-gapped transitions of quantum spin systems

Anindya Biswas, R. Prabhu, Aditi Sen +1 more

We investigate the behavior of genuine multiparticle entanglement, as quantified by the generalized geometric measure, in gapless-to-gapped quantum transitions of one- and two-dimensional quantum spin models. The investigations are performed in the exactly solvable one-dimensional $XY$ models, as well as two-dimensional frustrated ${J}_{1}--{J}_{2}$ models, including the Shastry-Sutherland model. The generalized geometric measure shows nonmonotonic features near such transitions in the frustrated quantum systems. We also compare the features of the generalized geometric measure near the quantum critical points with the same for measures of bipartite quantum correlations. The multipartite quantum correlation measure turns out to be a better indicator of quantum critical points than the bipartite measures, especially for two-dimensional models.

arXiv:1211.3241•Physical Review A•Sep 2, 2014•49 citations

Tensor-network approach to compute genuine multisite entanglement in infinite quantum spin chains

Sudipto Singha Roy, Himadri Shekhar Dhar, Aditi Sen +1 more

We devise a method based on the tensor-network formalism to calculate genuine multisite entanglement in ground states of infinite spin chains containing spin-1/2 or spin-1 quantum particles. The ground state is obtained by employing an infinite time-evolving block decimation method acting upon an initial matrix product state for the infinite spin system. We explicitly show how such infinite matrix product states with translational invariance provide a natural framework to derive the generalized geometric measure, a computable measure of genuine multisite entanglement, in the thermodynamic limit of quantum many-body systems with both spin-1/2 and higher-spin particles.

arXiv:1807.04033•Physical Review A•Jun 6, 2019•6 citations

Multipartite entanglement and quantum phase transitions in the one-, two-, and three-dimensional transverse-field Ising model

Afshin Montakhab, Ali Asadian

In this paper we consider the quantum phase transition in the Ising model in the presence of a transverse field in one, two, and three dimensions from a multipartite entanglement point of view. Using exact numerical solutions, we are able to study such systems up to 25 qubits. The Meyer-Wallach measure of global entanglement is used to study the critical behavior of this model. The transition we consider is between a symmetric Greenberger-Horne-Zeilinger--like state to a paramagnetic product state. We find that global entanglement serves as a good indicator of quantum phase transition with interesting scaling behavior. We use finite-size scaling to extract the critical point as well as some critical exponents for the one- and two-dimensional models. Our results indicate that such multipartite measure of global entanglement shows universal features regardless of dimension $d$. Our results also provide evidence that multipartite entanglement is better suited for the study of quantum phase transitions than the much-studied bipartite measures.

arXiv:1009.1357•Physical Review A•Dec 14, 2010•40 citations

Entanglement in first excited states of some many-body quantum spin systems: indication of quantum phase transition in finite size systems

George Biswas, Anindya Biswas

Abstract We compute concurrence, a measure of bipartite entanglement, of the first excited state of the 1-D Heisenberg frustrated J 1 - J 2 spin-chain and observe a sudden change in the entanglement of the eigen state near the coupling strength α = J 2 / J 1 ≈ 0.241, where a quantum phase transition from spin-fluid phase to dimer phase has been previously reported. We numerically observe this phenomena for spin-chain with 8 sites to 16 sites, and the value of α at which the change in entanglement is observed, asymptotically tends to a value α c ≈ 0.24116. We have calculated the finite-size scaling exponents for spin chains with even and odd spins. It may be noted that bipartite as well as multipartite entanglement measures applied on the ground state of the system, fail to detect any quantum phase transition from the gapless to the gapped phase in the 1-D Heisenberg frustrated J 1 - J 2 spin-chain. Furthermore, we measure bipartite entanglement of first excited states for other spin models like 2-D Heisenberg J 1 - J 2 model and Shastry-Sutherland model and find similar indications of quantum phase transitions.

arXiv:1909.12531•Physica Scripta•Nov 26, 2020•7 citations

Bound Genuine Multisite Entanglement: Detector of Gapless-Gapped Quantum Transitions in Frustrated Systems

Aditi Sen De, Ujjwal Sen

We define a multiparty entanglement measure, called generalized geometric measure, that can detect and quantify genuine multiparty entanglement for any number of parties. The quantum phase transitions in exactly solvable models like the anisotropic XY model can be detected by this measure. We find that the multisite measure can be a useful tool to detect quantum phenomena in more complex systems like quasi 2D and 2D frustrated Heisenberg antiferromagnets. We propose an order parameter, called bound generalized geometric measure, in the spirit of bound quantum states, that can recognize the gapless and gapped phases of the frustrated models by its sign. The vanishing of the order parameter therefore signals the transition between such phases.

arXiv:1002.1253•Feb 5, 2010•11 citations

Genuine tripartite entanglement monotone of (2⊗2⊗n) -dimensional systems

Chang‐shui Yu, Ling Zhou, He‐Shan Song

A genuine tripartite entanglement monotone is presented for $(2\ensuremath{\bigotimes}2\ensuremath{\bigotimes}n)$-dimensional tripartite pure states, obtained by introducing an entanglement measure for bipartite pure states. As an application, we consider the genuine tripartite entanglement of the ground state of the exactly solvable isotropic spin-$1/2$ chain with three-spin interaction. It is shown that the singular behavior of the genuine tripartite entanglement exactly signals a quantum phase transition.

arXiv:0802.1975•Physical Review A•Feb 13, 2008•12 citations
We employ a genuine multipartite entanglement measure, the generalized geometric measure, for investigating the quantum phase transition in an infinite quantum spin-1/2 chain with two-spin as well as three-spin interactions. We show that in contrast to bipartite entanglement of the ground state, the genuine multiparty one unerringly indicates the quantum phase transition in the system. The system lends itself to a complementary behavior between bipartite and genuine multipartite entanglements. We also investigate the trend of the multipartite entanglement in finite chains, in which we perform a finite-size scaling to confirm the signature of the quantum phase transition already in finite systems. The finite-size investigation renders the phenomenon to be observable in real systems.
We investigate the behavior of genuine multiparticle entanglement, as quantified by the generalized geometric measure, in gapless-to-gapped quantum transitions of one- and two-dimensional quantum spin models. The investigations are performed in the exactly solvable one-dimensional XYXYXY models, as well as two-dimensional frustrated J1−−J2{J}_{1}--{J}_{2}J1​−−J2​ models, including the Shastry-Sutherland model. The generalized geometric measure shows nonmonotonic features near such transitions in the frustrated quantum systems. We also compare the features of the generalized geometric measure near the quantum critical points with the same for measures of bipartite quantum correlations. The multipartite quantum correlation measure turns out to be a better indicator of quantum critical points than the bipartite measures, especially for two-dimensional models.
We devise a method based on the tensor-network formalism to calculate genuine multisite entanglement in ground states of infinite spin chains containing spin-1/2 or spin-1 quantum particles. The ground state is obtained by employing an infinite time-evolving block decimation method acting upon an initial matrix product state for the infinite spin system. We explicitly show how such infinite matrix product states with translational invariance provide a natural framework to derive the generalized geometric measure, a computable measure of genuine multisite entanglement, in the thermodynamic limit of quantum many-body systems with both spin-1/2 and higher-spin particles.
In this paper we consider the quantum phase transition in the Ising model in the presence of a transverse field in one, two, and three dimensions from a multipartite entanglement point of view. Using exact numerical solutions, we are able to study such systems up to 25 qubits. The Meyer-Wallach measure of global entanglement is used to study the critical behavior of this model. The transition we consider is between a symmetric Greenberger-Horne-Zeilinger--like state to a paramagnetic product state. We find that global entanglement serves as a good indicator of quantum phase transition with interesting scaling behavior. We use finite-size scaling to extract the critical point as well as some critical exponents for the one- and two-dimensional models. Our results indicate that such multipartite measure of global entanglement shows universal features regardless of dimension ddd. Our results also provide evidence that multipartite entanglement is better suited for the study of quantum phase transitions than the much-studied bipartite measures.
Abstract We compute concurrence, a measure of bipartite entanglement, of the first excited state of the 1-D Heisenberg frustrated J 1 - J 2 spin-chain and observe a sudden change in the entanglement of the eigen state near the coupling strength α = J 2 / J 1 ≈ 0.241, where a quantum phase transition from spin-fluid phase to dimer phase has been previously reported. We numerically observe this phenomena for spin-chain with 8 sites to 16 sites, and the value of α at which the change in entanglement is observed, asymptotically tends to a value α c ≈ 0.24116. We have calculated the finite-size scaling exponents for spin chains with even and odd spins. It may be noted that bipartite as well as multipartite entanglement measures applied on the ground state of the system, fail to detect any quantum phase transition from the gapless to the gapped phase in the 1-D Heisenberg frustrated J 1 - J 2 spin-chain. Furthermore, we measure bipartite entanglement of first excited states for other spin models like 2-D Heisenberg J 1 - J 2 model and Shastry-Sutherland model and find similar indications of quantum phase transitions.
We define a multiparty entanglement measure, called generalized geometric measure, that can detect and quantify genuine multiparty entanglement for any number of parties. The quantum phase transitions in exactly solvable models like the anisotropic XY model can be detected by this measure. We find that the multisite measure can be a useful tool to detect quantum phenomena in more complex systems like quasi 2D and 2D frustrated Heisenberg antiferromagnets. We propose an order parameter, called bound generalized geometric measure, in the spirit of bound quantum states, that can recognize the gapless and gapped phases of the frustrated models by its sign. The vanishing of the order parameter therefore signals the transition between such phases.
A genuine tripartite entanglement monotone is presented for $(2\ensuremath{\bigotimes}2\ensuremath{\bigotimes}n)$-dimensional tripartite pure states, obtained by introducing an entanglement measure for bipartite pure states. As an application, we consider the genuine tripartite entanglement of the ground state of the exactly solvable isotropic spin-1/21/21/2 chain with three-spin interaction. It is shown that the singular behavior of the genuine tripartite entanglement exactly signals a quantum phase transition.