非均匀Dzyaloshinskill-Moriya相互作用对量子Ising链热传导行为的影响
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摘要
基于Lindblad量子主方程方法,主要研究了交错、无序以及准周期Dzyaloshinskill-Moriya(DM)相互作用对量子Ising自旋链热传导行为的影响.通过计算局域能量密度和局域能流,发现对于这三类DM相互作用,当系统尺寸固定时,增大DM相互作用强度,流经量子Ising链的能流都将增多,但是能流随系统尺寸增大的标度行为却截然不同.因此,可以通过调节DM相互作用的强度与形式来控制量子Ising链的热传导行为.
Basing on the Lindblad master equation,we study the effect of the staggered,random,and the aperiodic Dzyaloshinskii-Moriya( DM) on the heat conductivity of quantum Ising chains. By calculating the average energy-density profile and the average energy current,the numerical results show that the DM interaction could increase the heat conduction of Ising chains for the fixed system size with the three kinds of DM interactions above. But the scaling behaviors of energy current with increasing system size for the Ising chain with staggered,random,Finonacci DM interactions show differently. Therefore,the heat transport behavior of Ising chain could be adjusted by controlling the strength and the forms of the DM interaction.
Basing on the Lindblad master equation,we study the effect of the staggered,random,and the aperiodic Dzyaloshinskii-Moriya( DM) on the heat conductivity of quantum Ising chains. By calculating the average energy-density profile and the average energy current,the numerical results show that the DM interaction could increase the heat conduction of Ising chains for the fixed system size with the three kinds of DM interactions above. But the scaling behaviors of energy current with increasing system size for the Ising chain with staggered,random,Finonacci DM interactions show differently. Therefore,the heat transport behavior of Ising chain could be adjusted by controlling the strength and the forms of the DM interaction.
引文
[1]DZYALOSHINSKY I.A thermodynamic theory of“Weak”ferromagnetism of antiferromagnetics[J].J Phys Chem Solids,1958,4(4):241-245.
[2]MORIYA T.Anisotropic superexchange interaction and weak ferromagnetism[J].Phys Rev,1960,120(1):91-98.
[3]ZHONG M,XU H,LIU X,et al.The effects of the Dzyaloshinskii-Moriya interaction on the ground-state properties of the XY Chain in a transverse field[J].Chinese physics B.2013,22(9):090313(1-7).
[4]MA F,LIU S,KONG X.Quantum entanglement and quantum phase transition in the the XY model with staggered DzyaloshinskiiMoriya interaction[J].Phys Rev A,2011,84(4):042302-042307.
[5]KARGARIAN M,JAFARI R,LANGARI A.Dzyaloshinskii-Moriya interaction and anisotropy effects on the entanglement of the Heisenberg model[J].Phy Rev A,2009,79(4):042319-042325.
[6]蔡卓,陆文彬,刘拥军.交错Dzyaloshinskill-Moriya相互作用对反铁磁Heisenberg链纠缠的影响[J].物理学报,2008,57(11):7 267-7 273.
[7]WANG X.Effects of anisotropy on thermal entanglement[J].Physics letters A,2001,28:101-104.
[8]DIVYAMANI B G.Thermal entanglement in a two-qubit Ising chain subjected to Dzyaloshinsky—Moriya interaction[J].Chinese physics letters,2013,30(12):120301(1-4).
[9]HU J,FANG J,QIAN LI,et al.Thermal entanglement of Ising model with Dzyaloshinskii-Moriya interaction in an inhomogeneous magnetic field[J].Chinese journal of quantum electronics,2011,28(3):229-334.
[10]LI D,LI X,LI H,et al.Thermal entanglement in the pure Dzyaloshinskii-Moriya model with magnetic field[J].Chinese physics letters,2015,32(5):050302(1-5).
[11]SHARMA K K,PANDEY S N.Dynamics of entanglement in qubit-qutrit with x-component of DM interaction[J].Comm Theor Phys,2016,65(3):278-284.
[12]JAFARPOUR M,ASHRAFPOUR M.Entanglement dynamics of a two-qutrit system under DM interaction and the relevance of the initial state[J].Quantum Inf Process,2013,12:761-772.
[13]LI W,ZHANG Z,TONG P.Effect of the Dzyaloshinskii-Moriya interaction on heat conductivity in one-dimensional quantum Ising chains[J].The European physical journal B,2012,85(73):20798(1-6).
[14]PROSEN T.Third quantization:a general method to solve master equations for quadratic open Fermi systems[J].New journal of physics,2008,10(4):43026(1-22).
[15]LI W,TONG P.Heat conduction in one-dimensional aperiodic quantum Ising chains[J].Phys Rev E,2011,83(3):031128-031133.
[16]YAN Y,WU C Q,CASATI G,et al.Nonballistic heat conduction in an integrable random-exchange Ising chain studied with quantum master equations[J].Phys Rev B,2008,77:172411-172414.
[17]SUN K,WANG C,CHEN Q.Heat transport in an open transverse-field Ising chain[J].Europhys Lett,2010,92:24002(1-6).
[18]BUTTIKER M.Four-terminal phase-coherent conductance[J].Phys Rev Lett,1986,57:1 761-1 764.
[19]LEPRI S,LIVI R,POLITI A.Thermal conduction in classical low-dimensional lattices[J].Phys Rep,2003,377(1):1-80.
[20]LI B,WANG J.Anomalous heat conduction and anomalous diffusion in one-dimensional systems[J].Phys Rev Lett,2003,91:044301-044304.
[21]BONETTO F,LEBOWITZ J L,REY B L.Fourier’s law:a challenge to theorists[M].London:Imperial College Press,2000.
[2]MORIYA T.Anisotropic superexchange interaction and weak ferromagnetism[J].Phys Rev,1960,120(1):91-98.
[3]ZHONG M,XU H,LIU X,et al.The effects of the Dzyaloshinskii-Moriya interaction on the ground-state properties of the XY Chain in a transverse field[J].Chinese physics B.2013,22(9):090313(1-7).
[4]MA F,LIU S,KONG X.Quantum entanglement and quantum phase transition in the the XY model with staggered DzyaloshinskiiMoriya interaction[J].Phys Rev A,2011,84(4):042302-042307.
[5]KARGARIAN M,JAFARI R,LANGARI A.Dzyaloshinskii-Moriya interaction and anisotropy effects on the entanglement of the Heisenberg model[J].Phy Rev A,2009,79(4):042319-042325.
[6]蔡卓,陆文彬,刘拥军.交错Dzyaloshinskill-Moriya相互作用对反铁磁Heisenberg链纠缠的影响[J].物理学报,2008,57(11):7 267-7 273.
[7]WANG X.Effects of anisotropy on thermal entanglement[J].Physics letters A,2001,28:101-104.
[8]DIVYAMANI B G.Thermal entanglement in a two-qubit Ising chain subjected to Dzyaloshinsky—Moriya interaction[J].Chinese physics letters,2013,30(12):120301(1-4).
[9]HU J,FANG J,QIAN LI,et al.Thermal entanglement of Ising model with Dzyaloshinskii-Moriya interaction in an inhomogeneous magnetic field[J].Chinese journal of quantum electronics,2011,28(3):229-334.
[10]LI D,LI X,LI H,et al.Thermal entanglement in the pure Dzyaloshinskii-Moriya model with magnetic field[J].Chinese physics letters,2015,32(5):050302(1-5).
[11]SHARMA K K,PANDEY S N.Dynamics of entanglement in qubit-qutrit with x-component of DM interaction[J].Comm Theor Phys,2016,65(3):278-284.
[12]JAFARPOUR M,ASHRAFPOUR M.Entanglement dynamics of a two-qutrit system under DM interaction and the relevance of the initial state[J].Quantum Inf Process,2013,12:761-772.
[13]LI W,ZHANG Z,TONG P.Effect of the Dzyaloshinskii-Moriya interaction on heat conductivity in one-dimensional quantum Ising chains[J].The European physical journal B,2012,85(73):20798(1-6).
[14]PROSEN T.Third quantization:a general method to solve master equations for quadratic open Fermi systems[J].New journal of physics,2008,10(4):43026(1-22).
[15]LI W,TONG P.Heat conduction in one-dimensional aperiodic quantum Ising chains[J].Phys Rev E,2011,83(3):031128-031133.
[16]YAN Y,WU C Q,CASATI G,et al.Nonballistic heat conduction in an integrable random-exchange Ising chain studied with quantum master equations[J].Phys Rev B,2008,77:172411-172414.
[17]SUN K,WANG C,CHEN Q.Heat transport in an open transverse-field Ising chain[J].Europhys Lett,2010,92:24002(1-6).
[18]BUTTIKER M.Four-terminal phase-coherent conductance[J].Phys Rev Lett,1986,57:1 761-1 764.
[19]LEPRI S,LIVI R,POLITI A.Thermal conduction in classical low-dimensional lattices[J].Phys Rep,2003,377(1):1-80.
[20]LI B,WANG J.Anomalous heat conduction and anomalous diffusion in one-dimensional systems[J].Phys Rev Lett,2003,91:044301-044304.
[21]BONETTO F,LEBOWITZ J L,REY B L.Fourier’s law:a challenge to theorists[M].London:Imperial College Press,2000.