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

Communications in Theoretical Physics

Quantum Correlation in Matrix Product States of One-Dimensional Spin Chains*

Jing-Min Zhu

Published Sep 1, 2015• 3 citations
Publisher

Abstract

Abstract For our proposed composite parity-conserved matrix product state (MPS), if only a spin block length is larger than 1, any two such spin blocks have correlation including classical correlation and quantum correlation. Both the total correlation and the classical correlation become larger than that in any subcomponent; while the quantum correlations of the two nearest-neighbor spin blocks and the two next-nearest-neighbor spin blocks become smaller and for other conditions the quantum correlation becomes larger, i.e., the increase or the production of the long-range quantum correlation is at the cost of reducing the short-range quantum correlation, which deserves to be investigated in the future; and the ration of the quantum correlation to the total correlation monotonically decreases to a steady value as the spacing spin length increasing.

DOI
10.1088/0253-6102/64/3/356

Related papers

Properties of Parity Non-conserved and Parity Conserved States in Matrix Product Systems

Jing Zhu

In terms of reflection transformation of a matrix product state (MPS),the parity of the MPS is defined. Based on the reflective parity non-conserved MPS pair we construct the even-parity state |Ψ_e and the odd-parity state |Ψ_o.It is interesting to find that the parity non-conserved reflective MPS pair have no long-range correlations;instead the even-parity state |Ψ_e and the odd-parity state |Ψ_o constructed from them have the same long-range correlations for the parity non-conserved block operators.Moreover,the entanglement between a block of n contiguous spins and the rest of the spin chain for the states |Ψ_e and |Ψ_o is larger than that for the reflective MPS pair except for n = 1,and the difference of them approaches 1 monotonically and asymptotically from 0 as n increases from 1.These characteristics indicate that MPS parity as a conserved physical quantity represents a kind of coherent collective quantum mode,and that the parity conserved MPSs contain more correlation,coherence,and entanglement than the parity non-conserved ones.

理论物理通讯：英文版•Jan 1, 2010•0 citations

Properties of Parity Non-conserved and Parity Conserved States in Matrix Product Systems

Jing-Min Zhu

In terms of reflection transformation of a matrix product state (MPS), the parity of the MPS is defined. Based on the reflective parity non-conserved MPS pair we construct the even-parity state |Φ e ⟩ and the odd-parity state |Φ o ⟩. It is interesting to find that the parity non-conserved reflective MPS pair have no long-range correlations; instead the even-parity state |Φ e ⟩ and the odd-parity state |Φ o ⟩ constructed from them have the same long-range correlations for the parity non-conserved block operators. Moreover, the entanglement between a block of n contiguous spins and the rest of the spin chain for the states |Φ e ⟩ and |Φ o ⟩ is larger than that for the reflective MPS pair except for n = 1, and the difference of them approaches 1 monotonically and asymptotically from 0 as n increases from 1. These characteristics indicate that MPS parity as a conserved physical quantity represents a kind of coherent collective quantum mode, and that the parity conserved MPSs contain more correlation, coherence, and entanglement than the parity non-conserved ones.

Communications in Theoretical Physics•Aug 1, 2010•11 citations

Quantum phase transitions in composite matrix product states of one-dimensional spin-1/2 chains

Jing-Min Zhu

For matrix product states of one-dimensional spin-1/2 chains, we investigate the properties of quantum phase transition of the proposed composite system. We find that the system has three different ferromagnetic phases, one line of the two ferromagnetic phases coexisting equally describes the paramagnetic state, and the other two lines of two ferromagnetic phases coexisting equally describe the ferrimagnetic states, while the three phases coexisting equally point describes the ferromagnetic state. Whether on phase transition lines or at the phase transition point, the system is always in an isolated mediate-coupling state, the physical quantities are discontinuous and the system has long-range correlation and has long-range classical correlation and long-range quantum correlation. We believe that our work is helpful for comprehensively and profoundly understanding the quantum phase transitions, and of some certain guidance and enlightening on the classification and measure of quantum correlation of quantum many-body systems.

International Journal of Modern Physics B•Feb 16, 2015•5 citations

Long-range multipartite quantum correlations and factorization in a one-dimensional spin-1/2 XY chain

Lin-Lin Su, Junfeng Ren, Z. D. Wang +1 more

We study the properties of multipartite quantum correlation (MQC) in a one-dimensional spin-1/2 $XY$ chain, where the three-spin reduced states are focused on and the four introduced MQC measures are based on entanglement negativity and entanglement of formation. It is found that, even in the Ising case, the three-spin subsystems have long-range MQCs and the tripartite quantum correlations beyond the nearest-neighbor three spins can detect the quantum phase transition and obey the finite-size scaling around the critical point. Furthermore, in the $XY$ model, we show that the two selected MQCs can indicate exactly the factorization point of the ground state for the anisotropic model in the thermodynamic and finite-size cases. Moreover, the spatial distribution of MQC based on entanglement negativity can attain a much larger range by tuning the anisotropic parameter, and the newly defined MQC based on entanglement of formation can detect the bound entanglement in the three-spin subsystems when the entanglement negativity loses its efficacy.

arXiv:2207.14332•Physical Review A•Oct 19, 2022•9 citations

Matrix product states for su (2) invariant quantum spin chains

Rubina Zadourian, Andreas Fledderjohann, Andreas Klümper

Abstract A systematic and compact treatment of arbitrary su (2) invariant spin- s quantum chains with nearest-neighbour interactions is presented. The ground-state is derived in terms of matrix product states (MPS). The fundamental MPS calculations consist of taking products of basic tensors of rank 3 and contractions thereof. The algebraic su (2) calculations are carried out completely by making use of Wigner calculus. As an example of application, the spin-1 bilinear-biquadratic quantum chain is investigated. Various physical quantities are calculated with high numerical accuracy of up to 8 digits. We obtain explicit results for the ground-state energy, entanglement entropy, singlet operator correlations and the string order parameter. We find an interesting crossover phenomenon in the correlation lengths.

arXiv:1603.07769•Journal of Statistical Mechanics Theory and Experiment•Aug 1, 2016•3 citations

Sequentially generated entanglement, macroscopicity, and squeezing in a spin chain

Tahereh Abad, Klaus Mølmer, Vahid Karimipour

We study quantum states generated by a sequence of nearest neighbor bipartite entangling operations along a one-dimensional chain of spin qubits. After a single sweep of such a set of operations, the system is effectively described by a matrix product state (MPS) with the same virtual dimension as the spin qubits. We employ the explicit form of the MPS to calculate expectation values and two-site correlation functions of local observables, and we use the results to study fluctuations of collective observables. Through the so-called macroscopicity and the squeezing properties of the collective spin variables they witness the quantum correlations and multiparticle entanglement within the chain. Macroscopicity only occurs over the entire chain if the nearest neighbor interaction is maximally entangling, while a finite, sequential interaction between nearest neighbor particles leads to squeezing of the collective spin.

arXiv:1707.09396•Physical Review A•Oct 26, 2017•3 citations
Abstract For our proposed composite parity-conserved matrix product state (MPS), if only a spin block length is larger than 1, any two such spin blocks have correlation including classical correlation and quantum correlation. Both the total correlation and the classical correlation become larger than that in any subcomponent; while the quantum correlations of the two nearest-neighbor spin blocks and the two next-nearest-neighbor spin blocks become smaller and for other conditions the quantum correlation becomes larger, i.e., the increase or the production of the long-range quantum correlation is at the cost of reducing the short-range quantum correlation, which deserves to be investigated in the future; and the ration of the quantum correlation to the total correlation monotonically decreases to a steady value as the spacing spin length increasing.
In terms of reflection transformation of a matrix product state (MPS),the parity of the MPS is defined. Based on the reflective parity non-conserved MPS pair we construct the even-parity state |Ψ_e and the odd-parity state |Ψ_o.It is interesting to find that the parity non-conserved reflective MPS pair have no long-range correlations;instead the even-parity state |Ψ_e and the odd-parity state |Ψ_o constructed from them have the same long-range correlations for the parity non-conserved block operators.Moreover,the entanglement between a block of n contiguous spins and the rest of the spin chain for the states |Ψ_e and |Ψ_o is larger than that for the reflective MPS pair except for n = 1,and the difference of them approaches 1 monotonically and asymptotically from 0 as n increases from 1.These characteristics indicate that MPS parity as a conserved physical quantity represents a kind of coherent collective quantum mode,and that the parity conserved MPSs contain more correlation,coherence,and entanglement than the parity non-conserved ones.
In terms of reflection transformation of a matrix product state (MPS), the parity of the MPS is defined. Based on the reflective parity non-conserved MPS pair we construct the even-parity state |Φ e ⟩ and the odd-parity state |Φ o ⟩. It is interesting to find that the parity non-conserved reflective MPS pair have no long-range correlations; instead the even-parity state |Φ e ⟩ and the odd-parity state |Φ o ⟩ constructed from them have the same long-range correlations for the parity non-conserved block operators. Moreover, the entanglement between a block of n contiguous spins and the rest of the spin chain for the states |Φ e ⟩ and |Φ o ⟩ is larger than that for the reflective MPS pair except for n = 1, and the difference of them approaches 1 monotonically and asymptotically from 0 as n increases from 1. These characteristics indicate that MPS parity as a conserved physical quantity represents a kind of coherent collective quantum mode, and that the parity conserved MPSs contain more correlation, coherence, and entanglement than the parity non-conserved ones.
For matrix product states of one-dimensional spin-1/2 chains, we investigate the properties of quantum phase transition of the proposed composite system. We find that the system has three different ferromagnetic phases, one line of the two ferromagnetic phases coexisting equally describes the paramagnetic state, and the other two lines of two ferromagnetic phases coexisting equally describe the ferrimagnetic states, while the three phases coexisting equally point describes the ferromagnetic state. Whether on phase transition lines or at the phase transition point, the system is always in an isolated mediate-coupling state, the physical quantities are discontinuous and the system has long-range correlation and has long-range classical correlation and long-range quantum correlation. We believe that our work is helpful for comprehensively and profoundly understanding the quantum phase transitions, and of some certain guidance and enlightening on the classification and measure of quantum correlation of quantum many-body systems.
We study the properties of multipartite quantum correlation (MQC) in a one-dimensional spin-1/2 XYXYXY chain, where the three-spin reduced states are focused on and the four introduced MQC measures are based on entanglement negativity and entanglement of formation. It is found that, even in the Ising case, the three-spin subsystems have long-range MQCs and the tripartite quantum correlations beyond the nearest-neighbor three spins can detect the quantum phase transition and obey the finite-size scaling around the critical point. Furthermore, in the XYXYXY model, we show that the two selected MQCs can indicate exactly the factorization point of the ground state for the anisotropic model in the thermodynamic and finite-size cases. Moreover, the spatial distribution of MQC based on entanglement negativity can attain a much larger range by tuning the anisotropic parameter, and the newly defined MQC based on entanglement of formation can detect the bound entanglement in the three-spin subsystems when the entanglement negativity loses its efficacy.
Abstract A systematic and compact treatment of arbitrary su (2) invariant spin- s quantum chains with nearest-neighbour interactions is presented. The ground-state is derived in terms of matrix product states (MPS). The fundamental MPS calculations consist of taking products of basic tensors of rank 3 and contractions thereof. The algebraic su (2) calculations are carried out completely by making use of Wigner calculus. As an example of application, the spin-1 bilinear-biquadratic quantum chain is investigated. Various physical quantities are calculated with high numerical accuracy of up to 8 digits. We obtain explicit results for the ground-state energy, entanglement entropy, singlet operator correlations and the string order parameter. We find an interesting crossover phenomenon in the correlation lengths.
We study quantum states generated by a sequence of nearest neighbor bipartite entangling operations along a one-dimensional chain of spin qubits. After a single sweep of such a set of operations, the system is effectively described by a matrix product state (MPS) with the same virtual dimension as the spin qubits. We employ the explicit form of the MPS to calculate expectation values and two-site correlation functions of local observables, and we use the results to study fluctuations of collective observables. Through the so-called macroscopicity and the squeezing properties of the collective spin variables they witness the quantum correlations and multiparticle entanglement within the chain. Macroscopicity only occurs over the entire chain if the nearest neighbor interaction is maximally entangling, while a finite, sequential interaction between nearest neighbor particles leads to squeezing of the collective spin.