3-态量子Potts自旋链的负值度和有限标度理论
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摘要
利用量子重整化群变换方法研究了3-态量子Potts自旋链在临界点附近的负值度N(g)和系统的有限标度行为.利用元块—格点变换给出系统的重整化群方程,然后利用该方程研究了不同尺度Potts自旋链负值度N(g)随着有效磁场g的变化关系,发现负值度N(g)随着有效磁场g增大由1减小为0,并且在临界点附近系统尺度越大负值度N(g)下降越剧烈.进一步利用负值度导数绝对值|dN(g)/dg|的最大值随着系统尺度变化,给出在临界点附近不同尺度系统的负值度N(g)满足有限标度行为.
The negativity and finite scale behavior of 3-state quantum Potts spin chains are investigated using quantum renormalization group method.Quantum renormalization group functions are obtained using the block-site transformation.Using those functions the relation of negativity N(g)versus g is exhibited,which shows that the negativity N(g)decreases from 1 to 0 asincreases,and it decreases fast near the critical point as the size of system increases.The maximum of|dN(g)/dg|shows that the finite scale behavior is satisfied with the negativity of different size spin chains.
The negativity and finite scale behavior of 3-state quantum Potts spin chains are investigated using quantum renormalization group method.Quantum renormalization group functions are obtained using the block-site transformation.Using those functions the relation of negativity N(g)versus g is exhibited,which shows that the negativity N(g)decreases from 1 to 0 asincreases,and it decreases fast near the critical point as the size of system increases.The maximum of|dN(g)/dg|shows that the finite scale behavior is satisfied with the negativity of different size spin chains.
引文
[1]YAO Y,LI H W,ZHANG M,et al.Performance of various correlation measures in quantum phase transitions using the quantum renormalization-group method[J].Physical Review A,2012,86(4A),1-9.
[2]QIN M,REN Z Z,ZHANG X.Universal quantum correlation close to quantum critical phenomena[J].Scientific Reports,2016(6):26042.
[3]费少明.量子态的可分性与纠缠度量度[J].现代物理知识,2016(6):9-13.
[4]ELTSCHKA C,SIEWERT J.Negativity as an estimator of entanglement dimension[J].Physical Review Letters,2013,111:100503.
[5]邹维科,孔祥木,王春阳,等.三维钻石型等级晶格上量子Heisenberg系统的临界性质[J].物理学报,2010,59(7):4874-4879.
[6]XU Y L,WANG L S,KONG X M.Thermal entanglement between non-nearest-neighbor spins on fractal lattices[J].Physical Review A,2013,87(1A):1-5.
[7]KARGARIAN M,JAFARI R,LANGARI A.Renormalization of concurrence:The application of the quantum renormalization group to quantum-information systems[J].Physical Review A,2007,76(6):060304.
[8]KARGARIAN M,JAFARI R,LANGARI A.Dzyaloshinskii-Moriya interaction and anisotropy effects on the entanglement of the Heisenberg model[J].Physical Review A,2008,79(4):032346.
[9]XU Y L,KONG X M,LIU Z Q,et al.Quantum entanglement and quantum phase transition for the Ising model on a two-dimension square lattice[J].Physica A,2016,446:217-223.
[10]尹训昌,刘万芳,张平伟,等.外场下Sierpinski镂垫上Potts模型的临界特性[J].安庆师范大学学报,2017,23(4):36-61.
[11]LAJKO P,IGLOI F.Entanglement entropy of the Q≥4quantum Potts chain[J].Physical Review E,2017,95:012105.
[12]WU F Y.The Potts model[J].Reviews of Modern Physics,1982,54:235-268.
[2]QIN M,REN Z Z,ZHANG X.Universal quantum correlation close to quantum critical phenomena[J].Scientific Reports,2016(6):26042.
[3]费少明.量子态的可分性与纠缠度量度[J].现代物理知识,2016(6):9-13.
[4]ELTSCHKA C,SIEWERT J.Negativity as an estimator of entanglement dimension[J].Physical Review Letters,2013,111:100503.
[5]邹维科,孔祥木,王春阳,等.三维钻石型等级晶格上量子Heisenberg系统的临界性质[J].物理学报,2010,59(7):4874-4879.
[6]XU Y L,WANG L S,KONG X M.Thermal entanglement between non-nearest-neighbor spins on fractal lattices[J].Physical Review A,2013,87(1A):1-5.
[7]KARGARIAN M,JAFARI R,LANGARI A.Renormalization of concurrence:The application of the quantum renormalization group to quantum-information systems[J].Physical Review A,2007,76(6):060304.
[8]KARGARIAN M,JAFARI R,LANGARI A.Dzyaloshinskii-Moriya interaction and anisotropy effects on the entanglement of the Heisenberg model[J].Physical Review A,2008,79(4):032346.
[9]XU Y L,KONG X M,LIU Z Q,et al.Quantum entanglement and quantum phase transition for the Ising model on a two-dimension square lattice[J].Physica A,2016,446:217-223.
[10]尹训昌,刘万芳,张平伟,等.外场下Sierpinski镂垫上Potts模型的临界特性[J].安庆师范大学学报,2017,23(4):36-61.
[11]LAJKO P,IGLOI F.Entanglement entropy of the Q≥4quantum Potts chain[J].Physical Review E,2017,95:012105.
[12]WU F Y.The Potts model[J].Reviews of Modern Physics,1982,54:235-268.