Quantum phase transitions in matrix product states ofone-dimensional spin-1/2 chains

  • For the matrix product system of a one-dimensional spin-1/2 chain, we present a new model of quantum phase transitions and find that in the thermodynamic limit, both sides of the critical point are respectively described by phases |Ψa>=|1…1> representing all particles spin up and |Ψb>=|0…0> representing all particles spin down, while the phase transition point is an isolated intermediate-coupling point where the two phases coexist equally, which is described by the so-called N-qubit maximally entangled GHZ state |Ψpt>=√2/2(|1…1>+|0…0>). At the critical point, the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N-qubit maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of potential directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-qubit maximal entanglement.
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ZHU Jing-Min. Quantum phase transitions in matrix product states ofone-dimensional spin-1/2 chains[J]. Chinese Physics C, 2014, 38(12): 123102. doi: 10.1088/1674-1137/38/12/123102
ZHU Jing-Min. Quantum phase transitions in matrix product states ofone-dimensional spin-1/2 chains[J]. Chinese Physics C, 2014, 38(12): 123102.  doi: 10.1088/1674-1137/38/12/123102 shu
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Received: 2014-01-10
Revised: 2014-04-15
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Quantum phase transitions in matrix product states ofone-dimensional spin-1/2 chains

  • College of Optoelectronic Technology, Chengdu University of Information Technology, Chengdu 610225, China

Abstract: For the matrix product system of a one-dimensional spin-1/2 chain, we present a new model of quantum phase transitions and find that in the thermodynamic limit, both sides of the critical point are respectively described by phases |Ψa>=|1…1> representing all particles spin up and |Ψb>=|0…0> representing all particles spin down, while the phase transition point is an isolated intermediate-coupling point where the two phases coexist equally, which is described by the so-called N-qubit maximally entangled GHZ state |Ψpt>=√2/2(|1…1>+|0…0>). At the critical point, the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N-qubit maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of potential directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-qubit maximal entanglement.

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