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Bulletin of the American Physical Society

Even-odd parity effects of a spin-1 Heisenberg chain on long-range interaction and entanglement

Sangchul Oh, Mark G. Friesen, Xuedong Hu

Published Mar 22, 2011• 0 citations
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A strongly coupled Heisenberg chain provides an important channel for quantum communication through its many-body ground state. Yet, the nature of the effective interactions and the ability to mediate long-range entanglement differs significantly for chains of opposite parity. Here, we contrast the characters of even- and odd-size chains when they are coupled to external qubits. Additional parity effects emerge in both cases, depending on the positions of the attached qubits. Some striking results include (i) the emergence of maximal entanglement and (ii) spin-chain Ruderman-Kittel-Kasuya-Yosida interactions for qubits attached to an even chain, and (iii) the ability of chains of either parity to mediate qubit entanglement that is undiminished by distance.

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

Jing-Min Zhu

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 |Φ e ⟩ and the odd-parity state |Φ o ⟩. It is interesting to find that the parity non-conserved reflective MPS pair have no long-range correlations; instead the even-parity state |Φ e ⟩ and the odd-parity state |Φ o ⟩ constructed from them have the same long-range correlations for the parity non-conserved block operators. Moreover, the entanglement between a block of n contiguous spins and the rest of the spin chain for the states |Φ e ⟩ and |Φ o ⟩ is larger than that for the reflective MPS pair except for n = 1, and the difference of them approaches 1 monotonically and asymptotically from 0 as n increases from 1. These characteristics indicate that MPS parity as a conserved physical quantity represents a kind of coherent collective quantum mode, and that the parity conserved MPSs contain more correlation, coherence, and entanglement than the parity non-conserved ones.

Communications in Theoretical Physics•Aug 1, 2010•11 citations
A strongly coupled Heisenberg chain provides an important channel for quantum communication through its many-body ground state. Yet, the nature of the effective interactions and the ability to mediate long-range entanglement differs significantly for chains of opposite parity. Here, we contrast the characters of even- and odd-size chains when they are coupled to external qubits. Additional parity effects emerge in both cases, depending on the positions of the attached qubits. Some striking results include (i) the emergence of maximal entanglement and (ii) spin-chain Ruderman-Kittel-Kasuya-Yosida interactions for qubits attached to an even chain, and (iii) the ability of chains of either parity to mediate qubit entanglement that is undiminished by distance.
It is well known that the notions of spatial locality are often lost in quantum systems with long-range interactions, as exhibited by the emergence of phases with exotic long-range order and faster propagation of quantum correlations. We demonstrate here that such induced ``quasinonlocal'' effects do not necessarily translate to growth of global entanglement in the quantum system. By investigating the ground and quenched states of the variable-range, spin-1/2 Heisenberg Hamiltonian, we observe that the genuine multiparty entanglement in the system can either increase or counterintuitively diminish with a growing range of interactions. The behavior is reflective of the underlying phase structure of the quantum system and provides key insights for generation of multipartite entanglement in experimental atomic, molecular, and optical physics where such variable-range interactions have been implemented.
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 |Φ e ⟩ and the odd-parity state |Φ o ⟩. It is interesting to find that the parity non-conserved reflective MPS pair have no long-range correlations; instead the even-parity state |Φ e ⟩ and the odd-parity state |Φ o ⟩ constructed from them have the same long-range correlations for the parity non-conserved block operators. Moreover, the entanglement between a block of n contiguous spins and the rest of the spin chain for the states |Φ e ⟩ and |Φ o ⟩ is larger than that for the reflective MPS pair except for n = 1, and the difference of them approaches 1 monotonically and asymptotically from 0 as n increases from 1. These characteristics indicate that MPS parity as a conserved physical quantity represents a kind of coherent collective quantum mode, and that the parity conserved MPSs contain more correlation, coherence, and entanglement than the parity non-conserved ones.