Multipartite quantum nonlocality in two-dimensional transverse-field Ising models on N × N square lattices
We propose a procedure to transform two-dimensional (2D) tensor network states into one-dimensional (1D) tensor network states. With the help of the technique, we are able to investigate multipartite quantum nonlocality (characterized by Bell-type inequalities and Bell correlation function) of the g...
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| Veröffentlicht in: | The European physical journal. B, Condensed matter physics Condensed matter physics, 2019-04, Vol.92 (4), p.1-12, Article 75 |
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| container_title | The European physical journal. B, Condensed matter physics |
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| creator | Sun, Zhao-Yu Guo, Xiao Wang, Mei |
| description | We propose a procedure to transform two-dimensional (2D) tensor network states into one-dimensional (1D) tensor network states. With the help of the technique, we are able to investigate multipartite quantum nonlocality (characterized by Bell-type inequalities and Bell correlation function) of the ground states of 2D transverse-field Ising models on
N
×
N
square lattices. We find that in the thermodynamic limit, in a quite narrow region near the critical field
λ
c
, the hierarchy of the multipartite nonlocality increases dramatically, and the ground state transmutes into a highly correlated state. Furthermore, we study quantum correlations of several typical subregions on the square lattices, and disclose some direct numerical evidences for the competition between (1) the entanglement entropy which a subregion shares with its environment block and (2) the multipartite nonlocality which reserves in the subregion.
Graphical abstract |
| doi_str_mv | 10.1140/epjb/e2019-90617-9 |
| format | Article |
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N
×
N
square lattices. We find that in the thermodynamic limit, in a quite narrow region near the critical field
λ
c
, the hierarchy of the multipartite nonlocality increases dramatically, and the ground state transmutes into a highly correlated state. Furthermore, we study quantum correlations of several typical subregions on the square lattices, and disclose some direct numerical evidences for the competition between (1) the entanglement entropy which a subregion shares with its environment block and (2) the multipartite nonlocality which reserves in the subregion.
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N
×
N
square lattices. We find that in the thermodynamic limit, in a quite narrow region near the critical field
λ
c
, the hierarchy of the multipartite nonlocality increases dramatically, and the ground state transmutes into a highly correlated state. Furthermore, we study quantum correlations of several typical subregions on the square lattices, and disclose some direct numerical evidences for the competition between (1) the entanglement entropy which a subregion shares with its environment block and (2) the multipartite nonlocality which reserves in the subregion.
Graphical abstract</description><subject>Bell's inequality</subject><subject>Complex Systems</subject><subject>Condensed Matter Physics</subject><subject>Correlation analysis</subject><subject>Critical field (superconductivity)</subject><subject>Fluid- and Aerodynamics</subject><subject>Ground state</subject><subject>Ising model</subject><subject>Lattices (mathematics)</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum entanglement</subject><subject>Quantum theory</subject><subject>Regular Article</subject><subject>Solid State Physics</subject><subject>Tensors</subject><subject>Two dimensional models</subject><issn>1434-6028</issn><issn>1434-6036</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp9kMtOwzAQRS0EEqXwA6wssQ71K68lqnhUKrCBteUkk8rFsVPbAfVL-CB-jLRFsGMzM4tzr0YHoUtKrikVZAb9upoBI7RMSpLRPCmP0IQKLpKM8Oz492bFKToLYU0IoRkVE_T2OJioe-WjjoA3g7Jx6LB11rhaGR23WFscP1zS6A5s0M4qg6NXNryDD5C0GkyDF0HbFe5cAyZgZ_ET_vocRxj7PGCjYtQ1hHN00ioT4OJnT9Hr3e3L_CFZPt8v5jfLpGZclAmjgla0alTG2qpVtG2KMm0allcgUgGKkUaVvAJekYKmBSec523FFM1yJiBVfIquDr29d5sBQpRrN_jx8SAZIzwvM5axkWIHqvYuBA-t7L3ulN9KSuROqtxJlXupci9VlmOIH0JhhO0K_F_1P6lvzW1-bw</recordid><startdate>20190401</startdate><enddate>20190401</enddate><creator>Sun, Zhao-Yu</creator><creator>Guo, Xiao</creator><creator>Wang, Mei</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20190401</creationdate><title>Multipartite quantum nonlocality in two-dimensional transverse-field Ising models on N × N square lattices</title><author>Sun, Zhao-Yu ; Guo, Xiao ; Wang, Mei</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2349-2141b1bda62fbfa1fd895dd27be454ea20da93be3b0815830337fb2a16724e5a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Bell's inequality</topic><topic>Complex Systems</topic><topic>Condensed Matter Physics</topic><topic>Correlation analysis</topic><topic>Critical field (superconductivity)</topic><topic>Fluid- and Aerodynamics</topic><topic>Ground state</topic><topic>Ising model</topic><topic>Lattices (mathematics)</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum entanglement</topic><topic>Quantum theory</topic><topic>Regular Article</topic><topic>Solid State Physics</topic><topic>Tensors</topic><topic>Two dimensional models</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Sun, Zhao-Yu</creatorcontrib><creatorcontrib>Guo, Xiao</creatorcontrib><creatorcontrib>Wang, Mei</creatorcontrib><collection>CrossRef</collection><jtitle>The European physical journal. B, Condensed matter physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Sun, Zhao-Yu</au><au>Guo, Xiao</au><au>Wang, Mei</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Multipartite quantum nonlocality in two-dimensional transverse-field Ising models on N × N square lattices</atitle><jtitle>The European physical journal. B, Condensed matter physics</jtitle><stitle>Eur. Phys. J. B</stitle><date>2019-04-01</date><risdate>2019</risdate><volume>92</volume><issue>4</issue><spage>1</spage><epage>12</epage><pages>1-12</pages><artnum>75</artnum><issn>1434-6028</issn><eissn>1434-6036</eissn><abstract>We propose a procedure to transform two-dimensional (2D) tensor network states into one-dimensional (1D) tensor network states. With the help of the technique, we are able to investigate multipartite quantum nonlocality (characterized by Bell-type inequalities and Bell correlation function) of the ground states of 2D transverse-field Ising models on
N
×
N
square lattices. We find that in the thermodynamic limit, in a quite narrow region near the critical field
λ
c
, the hierarchy of the multipartite nonlocality increases dramatically, and the ground state transmutes into a highly correlated state. Furthermore, we study quantum correlations of several typical subregions on the square lattices, and disclose some direct numerical evidences for the competition between (1) the entanglement entropy which a subregion shares with its environment block and (2) the multipartite nonlocality which reserves in the subregion.
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| subjects | Bell's inequality Complex Systems Condensed Matter Physics Correlation analysis Critical field (superconductivity) Fluid- and Aerodynamics Ground state Ising model Lattices (mathematics) Mathematical analysis Mathematical models Physics Physics and Astronomy Quantum entanglement Quantum theory Regular Article Solid State Physics Tensors Two dimensional models |
| title | Multipartite quantum nonlocality in two-dimensional transverse-field Ising models on N × N square lattices |
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