Motivated by recent developments in quantum fidelity and fidelity susceptibility, we study relations among Lie algebra, fidelity susceptibility and quantum phase transition for a two-state system and the Lipkin-Meshko...Motivated by recent developments in quantum fidelity and fidelity susceptibility, we study relations among Lie algebra, fidelity susceptibility and quantum phase transition for a two-state system and the Lipkin-Meshkov Glick model. We obtain the fidelity susceptibilities for SU（2） and SU（1, 1） algebraic structure models. From this relation, the validity of the fidelity susceptibility to signal for the quantum phase transition is also verified in these two systems. At the same time, we obtain the geometric phases in these two systems by calculating the fidelity susceptibility. In addition, the new method of calculating fidelity susceptibility is used to explore the two-dimensional XXZ model and the Bose-Einstein condensate （BEC）.展开更多
We study geometric phases of the ground states of inhomogeneous XY spin chains in transverse fields with Dzyaloshinski--Moriya （DM） interaction, and investigate the effect of the DM interaction on the quantum phase ...We study geometric phases of the ground states of inhomogeneous XY spin chains in transverse fields with Dzyaloshinski--Moriya （DM） interaction, and investigate the effect of the DM interaction on the quantum phase transition （QPT） of such spin chains. The results show that the DM interaction could influence the distribution of the regions of QPTs but could not produce new critical points for the spin-chain. This study extends the relation between geometric phases and QPTs.展开更多
We investigate quantum phase transitions for q-state quantum Potts models(q=2,3,4)on a square lattice and for the Ising model on a honeycomb lattice by using the infinite projected entangled-pair state algorithm with ...We investigate quantum phase transitions for q-state quantum Potts models(q=2,3,4)on a square lattice and for the Ising model on a honeycomb lattice by using the infinite projected entangled-pair state algorithm with a simplified updating scheme.We extend the universal order parameter to a two-dimensional lattice system,which allows us to explore quantum phase transitions with symmetry-broken order for any translation-invariant quantum lattice system of the symmetry group G.The universal order parameter is zero in the symmetric phase,and it ranges from zero to unity in the symmetry-broken phase.The ground-state fidelity per lattice site is computed,and a pinch point is identified on the fidelity surface near the critical point.The results offer another example highlighting the connection between(i)critical points for a quantum many-body system undergoing a quantum phase-transition and(ii)pinch points on a fidelity surface.In addition,we discuss three quantum coherence measures:the quantum Jensen–Shannon divergence,the relative entropy of coherence,and the l1norm of coherence,which are singular at the critical point,thereby identifying quantum phase transitions.展开更多
We consider a qubit symmetrically and transversely coupled to an XY spin chain with Dzyaloshinsky-Moriya（DM） interaction in the presence of a transverse magnetic field.An analytical expression for the geometric phas...We consider a qubit symmetrically and transversely coupled to an XY spin chain with Dzyaloshinsky-Moriya（DM） interaction in the presence of a transverse magnetic field.An analytical expression for the geometric phase of the qubit is obtained in the weak coupling limit.We find that the modification of the geometrical phase induced by the spin chain environment is greatly enhanced by DM interaction in the weak coupling limit around the quantum phase transition point of the spin chain.展开更多
We obtained the ground-state energy level and associated geometric phase in the Dicke model with the dipoledipole interactions analytically by the Holstein-Primakoff transformation and the boson expansion approach in ...We obtained the ground-state energy level and associated geometric phase in the Dicke model with the dipoledipole interactions analytically by the Holstein-Primakoff transformation and the boson expansion approach in the thermodynamic limit. The nonadiabatic geometric phase induced by the photon field was derived with the time-dependent unitary transformation. It is shown that dipole-dipole interactions have a deep influence on scaled behavior of the geometric phase at the critical point.展开更多
We consider a two-qubit system described by the Heisenberg XY model with Dzyaloshinski Moriya （DM） anisotropic interaction in a perpendicular magnetic field to investigate the relation between entanglement, geometri...We consider a two-qubit system described by the Heisenberg XY model with Dzyaloshinski Moriya （DM） anisotropic interaction in a perpendicular magnetic field to investigate the relation between entanglement, geometric phase and quantum phase transition （QPT）. It is shown that the DM interaction has an effect on the critical boundary. The combination of entanglement and geometric phase may characterize QPT completely. Their jumps mean that the occurrence of QPT and inversely the QPT at the critical point at least corresponds to a jump of one of them.展开更多
We study critical behaviors of the reduced fidelity susceptibility for two neighboring sites in the onedimensional transverse field Ising model. It is found that the divergent behaviors of the susceptibility take the ...We study critical behaviors of the reduced fidelity susceptibility for two neighboring sites in the onedimensional transverse field Ising model. It is found that the divergent behaviors of the susceptibility take the form of square of logarithm, in contrast with the global ground-state fidelity susceptibility which is power divergence. In order to perform a scaling analysis, we take the square root of the susceptibility and determine the scaling exponent analytically and the result is further confirmed by numerical calculations.展开更多
A scheme to perfectly preserve an initial qubit state in geometric quantum computation is proposed for a single- qubit geometric quantum gate in a nuclear magnetic resonance system. At first, by adjusting some magneti...A scheme to perfectly preserve an initial qubit state in geometric quantum computation is proposed for a single- qubit geometric quantum gate in a nuclear magnetic resonance system. At first, by adjusting some magnetic field parameters, one can let the dynamic phase be proportional to the geometric phase. Then, by controlling the azimuthal angle in the initial state, we may realize a geometric quantum gate whose fidelity is equal to one under cyclic evolution. This means that the quantum information is no distortion in the process of geometric quantum computation.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 11075101)the Shanghai Leading Academic Discipline Project,China (Grant No. S30105)the Shanghai Research Foundation,China (Grant No. 07d222020)
文摘Motivated by recent developments in quantum fidelity and fidelity susceptibility, we study relations among Lie algebra, fidelity susceptibility and quantum phase transition for a two-state system and the Lipkin-Meshkov Glick model. We obtain the fidelity susceptibilities for SU（2） and SU（1, 1） algebraic structure models. From this relation, the validity of the fidelity susceptibility to signal for the quantum phase transition is also verified in these two systems. At the same time, we obtain the geometric phases in these two systems by calculating the fidelity susceptibility. In addition, the new method of calculating fidelity susceptibility is used to explore the two-dimensional XXZ model and the Bose-Einstein condensate （BEC）.
基金Project supported by National Natural Science Foundation of China (Grant Nos. 10847108 and 10775023)
文摘We study geometric phases of the ground states of inhomogeneous XY spin chains in transverse fields with Dzyaloshinski--Moriya （DM） interaction, and investigate the effect of the DM interaction on the quantum phase transition （QPT） of such spin chains. The results show that the DM interaction could influence the distribution of the regions of QPTs but could not produce new critical points for the spin-chain. This study extends the relation between geometric phases and QPTs.
基金the National Natural Science Foundation of China(Grant No.11805285)Natural Science Foundation of Chongqing of China(Grant No.cstc2020jcyjmsxmX0034)the Science and Technology Research Program of Chongqing Municipal Education Commission(Grant No.KJQN 201900703)。
文摘We investigate quantum phase transitions for q-state quantum Potts models(q=2,3,4)on a square lattice and for the Ising model on a honeycomb lattice by using the infinite projected entangled-pair state algorithm with a simplified updating scheme.We extend the universal order parameter to a two-dimensional lattice system,which allows us to explore quantum phase transitions with symmetry-broken order for any translation-invariant quantum lattice system of the symmetry group G.The universal order parameter is zero in the symmetric phase,and it ranges from zero to unity in the symmetry-broken phase.The ground-state fidelity per lattice site is computed,and a pinch point is identified on the fidelity surface near the critical point.The results offer another example highlighting the connection between(i)critical points for a quantum many-body system undergoing a quantum phase-transition and(ii)pinch points on a fidelity surface.In addition,we discuss three quantum coherence measures:the quantum Jensen–Shannon divergence,the relative entropy of coherence,and the l1norm of coherence,which are singular at the critical point,thereby identifying quantum phase transitions.
基金Project supported by the National Basic Research Program of China (Grant No. 2010CB923102)the Special Prophase Project on the National Basic Research Program of China (Grant No. 2011CB311807)the National Natural Science Foundation of China (Grant No. 11074199)
文摘We consider a qubit symmetrically and transversely coupled to an XY spin chain with Dzyaloshinsky-Moriya（DM） interaction in the presence of a transverse magnetic field.An analytical expression for the geometric phase of the qubit is obtained in the weak coupling limit.We find that the modification of the geometrical phase induced by the spin chain environment is greatly enhanced by DM interaction in the weak coupling limit around the quantum phase transition point of the spin chain.
文摘We obtained the ground-state energy level and associated geometric phase in the Dicke model with the dipoledipole interactions analytically by the Holstein-Primakoff transformation and the boson expansion approach in the thermodynamic limit. The nonadiabatic geometric phase induced by the photon field was derived with the time-dependent unitary transformation. It is shown that dipole-dipole interactions have a deep influence on scaled behavior of the geometric phase at the critical point.
基金Project supported by the Natural Science Foundation for Young Scientists of Shanxi Province of China (Grant No. 2007021001)the Science and Technology Key Item of Chinese Ministry of Education (Grant No. 207017)+1 种基金National Fundamental Fund of Personnel Training (Grant No. J0730317)the National Natural Science Foundation of China (Grant No. 10774094)
文摘We consider a two-qubit system described by the Heisenberg XY model with Dzyaloshinski Moriya （DM） anisotropic interaction in a perpendicular magnetic field to investigate the relation between entanglement, geometric phase and quantum phase transition （QPT）. It is shown that the DM interaction has an effect on the critical boundary. The combination of entanglement and geometric phase may characterize QPT completely. Their jumps mean that the occurrence of QPT and inversely the QPT at the critical point at least corresponds to a jump of one of them.
基金Supported by National Natural Science Foundation of China under Grant Nos. 10874151 and 10935010National Fundamental Research Program of China under Grant No. 2006CB921205+1 种基金Program for New Century Excellent Talents in University (NCET)Science Foundation of Chinese University
文摘We study critical behaviors of the reduced fidelity susceptibility for two neighboring sites in the onedimensional transverse field Ising model. It is found that the divergent behaviors of the susceptibility take the form of square of logarithm, in contrast with the global ground-state fidelity susceptibility which is power divergence. In order to perform a scaling analysis, we take the square root of the susceptibility and determine the scaling exponent analytically and the result is further confirmed by numerical calculations.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10864002)
文摘A scheme to perfectly preserve an initial qubit state in geometric quantum computation is proposed for a single- qubit geometric quantum gate in a nuclear magnetic resonance system. At first, by adjusting some magnetic field parameters, one can let the dynamic phase be proportional to the geometric phase. Then, by controlling the azimuthal angle in the initial state, we may realize a geometric quantum gate whose fidelity is equal to one under cyclic evolution. This means that the quantum information is no distortion in the process of geometric quantum computation.
