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;> and the odd-parity state|Ψ;>.It is interesting to find that the parity non-conserved reflective MPS pair have no long-range correlations;insteadthe even-parity state |Ψ;> and the odd-parity state |Ψ;> 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;> and |Ψ;> 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.