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

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;insteadthe even-parity state |Ψ_e> and the odd-parity state |Ψ_o> constructed from them have the same long-range correlationsfor the parity non-conserved block operators.Moreover,the entanglement between a block of n contiguous spins and therest 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 thedifference of them approaches 1 monotonically and asymptotically from 0 as n increases from 1.These characteristicsindicate that MPS parity as a conserved physical quantity represents a kind of coherent collective quantum mode,andthat the parity conserved MPSs contain more correlation,coherence,and entanglement than the parity non-conservedones.

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

For the matrix product system of a one-dimensional spin-1/2 chain, we present a new model of quantum2 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 is2 described by the so-called N-qubit maximally entangled GHZ state ｜Ψpt =√2/2（｜1··· 1 ＋｜0··· 0）. At the critical point,2the physical quantities including the entanglement are not discontinuous and the matrix product system has longrange 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.

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

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 equM 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.