Commensurate and incommensurate Haldane phases for a spin-1 bilinear-biquadratic model are investigated using an infinite matrix product state algorithm.The bipartite entanglement entropy can detect a transition point...Commensurate and incommensurate Haldane phases for a spin-1 bilinear-biquadratic model are investigated using an infinite matrix product state algorithm.The bipartite entanglement entropy can detect a transition point between the two phases.In both phases,the entanglement spectrum shows double degeneracy.We calculate the nonlocal order parameter of the bond-centered inversion in both phases,which rapidly approaches a saturation value of-1 as the segment length increases.The nonlocal order parameter of the bond-centered inversion with a saturation value-1 and the nonzero value string order indicate that the Haldane phase is a symmetry-protected topological phase.To distinguish the commensurate and incommensurate Haldane phases,the transversal spin correlation and corresponding momentum distribution of the structure factor are analyzed.As a result,the transversal spin correlations exhibit different decay forms in both phases.展开更多
A new procedure of trial variational wave functional is proposed for investigating the mass renormalization and the local structure of the ground state of a one-dimensional quantum sine-Gordon model with linear spatia...A new procedure of trial variational wave functional is proposed for investigating the mass renormalization and the local structure of the ground state of a one-dimensional quantum sine-Gordon model with linear spatial modulation, whose ground state differs from that without modulation. The phase diagram obtained in parameters plane shows that the vertical part of the boundary between soliton lattice phase and incommensurate (IC) phase with vanishing gap sticks at , the IC phase can only appear for and the IC phase regime is enlarged with increasing spatial modulation in the case of definite parameter . The transition is of the continuous type on the vertical part of the boundary, while it is of the first order on the boundary for .展开更多
Measurements by using the ultrasonic technique together for electric resistance verified that the first sound velocity valley on cooling is mainly due to the soft-mode of driving the com- mensurate phase transition,an...Measurements by using the ultrasonic technique together for electric resistance verified that the first sound velocity valley on cooling is mainly due to the soft-mode of driving the com- mensurate phase transition,and the second one due to the soft-mode of driving the martensitic transformation.The starting point,R_s,and finishing point,R_f,of the commensurate phase transition of the alloy have been determined.展开更多
The calculations of low-energy phonon dispersion relations in lead zirconate(PZ)have been carried out using the Vaks model.This model takes into account only five low-energy phonon modes and their interactions.It has ...The calculations of low-energy phonon dispersion relations in lead zirconate(PZ)have been carried out using the Vaks model.This model takes into account only five low-energy phonon modes and their interactions.It has been shown that this model allows to achieve good agreement not only between calculated and experimental transverse acoustic phonon dispersion but also between their temperature dependences.It has been shown 5-mode system,which describes low-energy phonon dispersion in PZ,is close to unstable state.Even a little change of interaction parameter can lead to lattice instability with nonzero wave vector qcrit.Wave vector qcrit could have any value,including irrational one.In this case,system will undergo an incommensurate phase transition.展开更多
基金the National Natural Science Foundation of China(Grant No.11805285)the Natural Science Foundation of Shaanxi Province of China(Grant No.2022JM-033)the Science and Technology Research Program of Chongqing Municipal Education Commission(Grant No.KJQN 201900703)。
文摘Commensurate and incommensurate Haldane phases for a spin-1 bilinear-biquadratic model are investigated using an infinite matrix product state algorithm.The bipartite entanglement entropy can detect a transition point between the two phases.In both phases,the entanglement spectrum shows double degeneracy.We calculate the nonlocal order parameter of the bond-centered inversion in both phases,which rapidly approaches a saturation value of-1 as the segment length increases.The nonlocal order parameter of the bond-centered inversion with a saturation value-1 and the nonzero value string order indicate that the Haldane phase is a symmetry-protected topological phase.To distinguish the commensurate and incommensurate Haldane phases,the transversal spin correlation and corresponding momentum distribution of the structure factor are analyzed.As a result,the transversal spin correlations exhibit different decay forms in both phases.
文摘A new procedure of trial variational wave functional is proposed for investigating the mass renormalization and the local structure of the ground state of a one-dimensional quantum sine-Gordon model with linear spatial modulation, whose ground state differs from that without modulation. The phase diagram obtained in parameters plane shows that the vertical part of the boundary between soliton lattice phase and incommensurate (IC) phase with vanishing gap sticks at , the IC phase can only appear for and the IC phase regime is enlarged with increasing spatial modulation in the case of definite parameter . The transition is of the continuous type on the vertical part of the boundary, while it is of the first order on the boundary for .
文摘Measurements by using the ultrasonic technique together for electric resistance verified that the first sound velocity valley on cooling is mainly due to the soft-mode of driving the com- mensurate phase transition,and the second one due to the soft-mode of driving the martensitic transformation.The starting point,R_s,and finishing point,R_f,of the commensurate phase transition of the alloy have been determined.
文摘The calculations of low-energy phonon dispersion relations in lead zirconate(PZ)have been carried out using the Vaks model.This model takes into account only five low-energy phonon modes and their interactions.It has been shown that this model allows to achieve good agreement not only between calculated and experimental transverse acoustic phonon dispersion but also between their temperature dependences.It has been shown 5-mode system,which describes low-energy phonon dispersion in PZ,is close to unstable state.Even a little change of interaction parameter can lead to lattice instability with nonzero wave vector qcrit.Wave vector qcrit could have any value,including irrational one.In this case,system will undergo an incommensurate phase transition.
