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

We present a new model of quantum phase transitions in matrix product systems of one-dimensional spin-1 chains and study the phases coexistence phenomenon. We find that in the thermodynamic limit the proposed system has three different quantum phases and by adjusting the control parameters we are able to realize any phase, any two phases equal coexistence and the three phases equal coexistence. At every critical point the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N -spin 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 certain directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N -spin maximal entanglement.

Section: The Entanglement Propertymentioning

confidence: 99%

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

Zhu¹

2014

“…There are many kinds of methods to measure entanglement, such as the quantification characteristic function of quantum nonlocality [18], Bell inequality [19,20], quantum discord [21], averaged entropy [22] and so on. For our system, we shall adopt the von Neumann entropy which [23][24][25][26][27][28][29][30] according to the bipartition parameterization by the adjacent spin number n of a B n spin block is,…”

Section: The Entanglement Propertymentioning

confidence: 99%

Quantum phase transitions in matrix product states of one-dimensional spin-½ chains

Zhu

2014

For the matrix product system of a one-dimensional spin-½ 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 . 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.

“…the upper limit value 2 from 1.58496 as n increases from 1, which is consistent with the result from the above section about the entanglement entropy S fp of the fixed point. The different entanglement entropy S n of a spin block as a function of its size n, is responsible for different MPS entanglement, which accounts for the different collective quantum phenomena and quantum-phase transition phenomena at the same time, in the fields of condensed matter [19][20][21][22][23][24].…”

Section: Here We Consider the Mps |ψ With Representation Matricesmentioning

confidence: 99%

Entanglement property in matrix product spin systems

Zhu¹

2012

We study the entanglement property in matrix product spin-ring systems systemically by von Neumann entropy. We find that: (i) the Hilbert space dimension of one spin determines the upper limit of the maximal value of the entanglement entropy of one spin, while for multiparticle entanglement entropy, the upper limit of the maximal value depends on the dimension of the representation matrices. Based on the theory, we can realize the maximum of the entanglement entropy of any spin block by choosing the appropriate control parameter values. (ii) When the entanglement entropy of one spin takes its maximal value, the entanglement entropy of an asymptotically large spin block, i.e. the renormalization group fixed point, is not likely to take its maximal value, and so only the entanglement entropy Sn of a spin block that varies with size n can fully characterize the spin-ring entanglement feature. Finally, we give the entanglement dynamics, i.e. the Hamiltonian of the matrix product system.