一维量子XXZD模型的量子临界现象
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摘要
采用矩阵乘积态算法对不同单粒子各向异性系数(D=-0. 6,-0. 3,0,0. 3,0. 6)和类伊辛参数(Jz=-0. 5)的一维量子XXZD模型的基态进行模拟,基于基态波函数中纠缠的概念,计算冯诺依曼熵和平移算子之间的标度关系,从而确定中心荷和相比普适类。任意选取临界区域内的单粒子各向异性参数,研究了一维量子XXZD模型的单点几何纠缠的有限尺寸修正项系数与Luttinger液体紧致半径之间的关系。结果表明,单点几何纠缠的有限尺寸修正的方法是一种普适的研究量子临界性的方法,可以简捷的计算出Luttinger液体的紧致半径值。
The ground state wavefunction is simulated by matrix product state algorithm of one-dimensional XXZD model with different single-particle anisotropy coefficients( D =-0. 6,-0. 3,0,0. 3,0. 6) and Ising-like parameters( Jz=-0. 5). Based on the concept of entanglement,the central charge and the relative universal class will be determined by the scaling relation between von Neumann entropy and translation operator. Arbitrary selection of single particle anisotropic parameters within the critical region. We researched The relationship between the finite-size correction coefficient of geometric entanglement per site and the compact radius of Luttinger liquid in one-dimensional quantum XXZD model. The researched results shows that the compact radius of Luttinger liquid can be calculated simply and the finite-size correction method of geometric entanglement per site is an universal method to study quantum criticality.
The ground state wavefunction is simulated by matrix product state algorithm of one-dimensional XXZD model with different single-particle anisotropy coefficients( D =-0. 6,-0. 3,0,0. 3,0. 6) and Ising-like parameters( Jz=-0. 5). Based on the concept of entanglement,the central charge and the relative universal class will be determined by the scaling relation between von Neumann entropy and translation operator. Arbitrary selection of single particle anisotropic parameters within the critical region. We researched The relationship between the finite-size correction coefficient of geometric entanglement per site and the compact radius of Luttinger liquid in one-dimensional quantum XXZD model. The researched results shows that the compact radius of Luttinger liquid can be calculated simply and the finite-size correction method of geometric entanglement per site is an universal method to study quantum criticality.
引文
[1]LIU C C,WANG D,SUN W Y,et al. Quantum Fisher information,quantum entanglement and correlation close to quantum critical phenomena[J]. Quantum Inf Process,2017,16:219.
[2]MA S K. Modern theory of critical phenomena[M]. California:Westview Press,1976.
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[4] MA Y Q,CHEN S. Geometric phase and quantum phase transition in an inhomogenous periodic XY spin model[J]. Phys Rev A,2009,79:022116-022122.
[5] HU B Q,LIU X J,LIU J H,et al. Geometric entanglement from matrix product state representations[J]. New J Phys,2011,13:093041-093049.
[6] STEPHAN J M,MISGUICH G,ALET F. Geometric entanglement and Affleck-Ludwig boundary entropies in critical XXZ and Ising chains[J]. Phys Rev B,2010,82:180406-180409.
[7]WEI T C,GOLDBART P M. Geometric measure of entanglement and applications to bipartite and multipartite quantum states[J]. Phy Rev A,2003,68:04280-04291.
[8]WEI T C,DAS D,MUKHOPADYAY S,et al. Global entanglement and quantum criticality in spin chains[J].Phys Rev A,2005,71:060305-060308.
[9]WEI T C. Quantum entanglement:geometric quantification and applications to multi-partite states and quantum phase transitions[J]. 2009 ar Xiv:0905. 2467 v1.
[10]CHAKRAVARTY S,HALPERIN B I,NELSON D R. LowTemperature Behavior of Two-Dimensional Quantum Antiferromagnets[J]. Phys Rev Lett,1988,60:1057-1060.
[11]CHAKRAVARTY S,HALPERIN B I,NELSON D R. Twodimensional quantum Heisenberg antiferromagnet at low temperatures[J]. Phys Rev B,1989,39:2344-2371.
[12]DEGLI ESPOSTI BOSCHI C,ERCOLESSI E,ORTOLANI F. On c=1 critical phases in anisotropic spin-1 chains[J]. Eur Phys J B,2003,35:465-473.
[13]CHEN W,HIDA K,SANCTUARY B C. Ground-state phase diagram of S=1 XXZ chains with uniaxial singleion-type anisotropy[J]. Phys Rev B,2003,67:104401-104407.
[2]MA S K. Modern theory of critical phenomena[M]. California:Westview Press,1976.
[3] GOLDENFELD N. Lectures on phase transitions and the Renormalization group[M]. Reading:Addison-Wesley,1992.
[4] MA Y Q,CHEN S. Geometric phase and quantum phase transition in an inhomogenous periodic XY spin model[J]. Phys Rev A,2009,79:022116-022122.
[5] HU B Q,LIU X J,LIU J H,et al. Geometric entanglement from matrix product state representations[J]. New J Phys,2011,13:093041-093049.
[6] STEPHAN J M,MISGUICH G,ALET F. Geometric entanglement and Affleck-Ludwig boundary entropies in critical XXZ and Ising chains[J]. Phys Rev B,2010,82:180406-180409.
[7]WEI T C,GOLDBART P M. Geometric measure of entanglement and applications to bipartite and multipartite quantum states[J]. Phy Rev A,2003,68:04280-04291.
[8]WEI T C,DAS D,MUKHOPADYAY S,et al. Global entanglement and quantum criticality in spin chains[J].Phys Rev A,2005,71:060305-060308.
[9]WEI T C. Quantum entanglement:geometric quantification and applications to multi-partite states and quantum phase transitions[J]. 2009 ar Xiv:0905. 2467 v1.
[10]CHAKRAVARTY S,HALPERIN B I,NELSON D R. LowTemperature Behavior of Two-Dimensional Quantum Antiferromagnets[J]. Phys Rev Lett,1988,60:1057-1060.
[11]CHAKRAVARTY S,HALPERIN B I,NELSON D R. Twodimensional quantum Heisenberg antiferromagnet at low temperatures[J]. Phys Rev B,1989,39:2344-2371.
[12]DEGLI ESPOSTI BOSCHI C,ERCOLESSI E,ORTOLANI F. On c=1 critical phases in anisotropic spin-1 chains[J]. Eur Phys J B,2003,35:465-473.
[13]CHEN W,HIDA K,SANCTUARY B C. Ground-state phase diagram of S=1 XXZ chains with uniaxial singleion-type anisotropy[J]. Phys Rev B,2003,67:104401-104407.