In terms of reflection transformation of a matrix product state （MPS）, the parity of the MPS is defined. Based on the reflective parity non-conserved MPS pair we construct the even-parity state ｜ψe〉 and the odd-p...In terms of reflection transformation of a matrix product state （MPS）, the parity of the MPS is defined. Based on the reflective parity non-conserved MPS pair we construct the even-parity state ｜ψe〉 and the odd-parity state ｜ψσ〉. It is interesting to find that the parity non-conserved reflective MPS pair have no long-range correlations; instead the even-parity state ｜ψe〉 and the odd-parity state ｜ψo〉 constructed from them have the same long-range correlations for the parity non-conserved block operators. Moreover, the entanglement between a block of n contiguous spins and the rest of the spin chain for the states ｜ψe〉 and ｜ψo〉 is larger than that for the reflective MPS pair except for n = 1, and the difference of them approaches 1 monotonically and asymptotically from 0 as n increases from 1. These characteristics indicate that MPS parity as a conserved physical quantity represents a kind of coherent collective quantum mode, and that the parity conserved MPSs contain more correlation, coherence, and entanglement than the parity non-conserved ones.展开更多
We propose a method for calculating the nonradiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface(PES)in the Franck-Condon region.The method combines the n-mode rep...We propose a method for calculating the nonradiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface(PES)in the Franck-Condon region.The method combines the n-mode repre-sentation method to construct the ab initio PES and the nearly exact time-dependent density matrix renormalization group method(TD-DMRG)to simulate quantum dynamics.In addition,in the framework of TD-DMRG,we further develop an algorithm to calculate the final-state-resolved rate coefficient which is very useful to analyze the contribution from each vibrational mode to the transition process.We use this method to study the internal conversion(IC)process of azulene after taking into account the anharmonicity of the ground state PES.The results show that even for this semi-rigid molecule,the intramode anharmonicity enhances the IC rate significantly,and after considering the two-mode coupling effect,the rate increases even further.The reason is that the anharmonicity enables the C-H vibrations to receive electronic energy while C-H vibrations do not contribute on the harmonic PES as the Huang-Rhys factor is close to 0.展开更多
In a structural system reliability analysis that lacks probabilistic information, calculating the numerical characteristics of the state functions, especially the first four moments of the state functions, is necessar...In a structural system reliability analysis that lacks probabilistic information, calculating the numerical characteristics of the state functions, especially the first four moments of the state functions, is necessary. Based on that, the structural system reliability is analyzed with a fourth-order moment method. The reliability sensitivity is required to conduct the differential operation of the numerical characteristic functions. A reliability sensitivity analysis formula is then derived in combination with the relation of the differential operation. Based on the matrix theory and Kronecker algebra, this paper systematically derives a matrix expression of the first four moments of the state functions, and establishes the matrix relation between the first four moments of the state functions and those of the basic random variables. On this basis, a differential operation formula of the first four moments of the state functions is further derived against the first four moments of the basic random variables. The vector relation between the state functions and the multidimensional basic random variables is described by means of the matrix operation to extend the operation method. Finally, a concise and intuitive formula is obtained to explore the inherent essential relation between the numerical characteristics of the state functions and those of the basic random variables, leading to a universal equation for the two kinds of numerical characteristics.展开更多
For our proposed composite parity-conserved matrix product state(MPS), if only a spin block length is larger than 1, any two such spin blocks have correlation including classical correlation and quantum correlation. B...For our proposed composite parity-conserved matrix product state(MPS), if only a spin block length is larger than 1, any two such spin blocks have correlation including classical correlation and quantum correlation. Both the total correlation and the classical correlation become larger than that in any subcomponent; while the quantum correlations of the two nearest-neighbor spin blocks and the two next-nearest-neighbor spin blocks become smaller and for other conditions the quantum correlation becomes larger, i.e., the increase or the production of the long-range quantum correlation is at the cost of reducing the short-range quantum correlation, which deserves to be investigated in the future; and the ration of the quantum correlation to the total correlation monotonically decreases to a steady value as the spacing spin length increasing.展开更多
For the matrix product system of a one-dimensional spin-1/2 chain, we present a new model of quantum2 phase transitions and find that in the thermodynamic limit, both sides of the critical point are respectively descr...For the matrix product system of a one-dimensional spin-1/2 chain, we present a new model of quantum2 phase transitions and find that in the thermodynamic limit, both sides of the critical point are respectively described by phases ｜Ψa 〉=｜1··· 1 representing all particles spin up and ｜Ψb 〉=｜0··· 0 representing all particles spin down, while the phase transition point is an isolated intermediate-coupling point where√ the two phases coexist equally, which is2 described by the so-called N-qubit maximally entangled GHZ state ｜Ψpt =√2/2（｜1··· 1 ＋｜0··· 0）. At the critical point,2the physical quantities including the entanglement are not discontinuous and the matrix product system has longrange correlation and N-qubit maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of potential directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-qubit maximal entanglement.展开更多
We present a new model of quantum phase transitions in matrix product systems of one-dimensional spin-1 chains and study the phases coexistence phenomenon. We find that in the thermodynamic limit the proposed system h...We present a new model of quantum phase transitions in matrix product systems of one-dimensional spin-1 chains and study the phases coexistence phenomenon. We find that in the thermodynamic limit the proposed system has three different quantum phases and by adjusting the control parameters we are able to realize any phase, any two phases equal coexistence and the three phases equM coexistence. At every critical point the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N-spin maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of certain directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-spin maximal entanglement.展开更多
The matrix product state （MPS） is utilized to investigate the ground state properties and quantum phase transitions （OPTs） of the dimerized antiferromagnetic Heisenberg （DAH） model. The ground state MPS wavefunc...The matrix product state （MPS） is utilized to investigate the ground state properties and quantum phase transitions （OPTs） of the dimerized antiferromagnetic Heisenberg （DAH） model. The ground state MPS wavefunctions determined by the infinite time-evolving block decimation （iTEBD） algorithm are shown to be very efficient descriptions of DAH model. In the thermodynamic limit, the quantum entanglement, the bond energy~ and the nearest-neighbor correlations are calculated. It is revealed that the singular behavior of the bipartite entanglement can detect the QPTs directly. The critical point J2c= 1.0 is determined evidently, and the quantum phase transition is argued to belong to the second-order category. At the critical point, logarithmic divergent character of the block entanglement is observed, and the system can be described by a free bosonic field theory.展开更多
基金Supported by the Scientific Research Foundation of CUIT under Grant No.KYTZ201024the National Natural Science Foundation of China under Grant Nos.10775100,10974137 the Fund of Theoretical Nuclear Center of HIRFL of China
文摘In terms of reflection transformation of a matrix product state （MPS）, the parity of the MPS is defined. Based on the reflective parity non-conserved MPS pair we construct the even-parity state ｜ψe〉 and the odd-parity state ｜ψσ〉. It is interesting to find that the parity non-conserved reflective MPS pair have no long-range correlations; instead the even-parity state ｜ψe〉 and the odd-parity state ｜ψo〉 constructed from them have the same long-range correlations for the parity non-conserved block operators. Moreover, the entanglement between a block of n contiguous spins and the rest of the spin chain for the states ｜ψe〉 and ｜ψo〉 is larger than that for the reflective MPS pair except for n = 1, and the difference of them approaches 1 monotonically and asymptotically from 0 as n increases from 1. These characteristics indicate that MPS parity as a conserved physical quantity represents a kind of coherent collective quantum mode, and that the parity conserved MPSs contain more correlation, coherence, and entanglement than the parity non-conserved ones.
基金supported by the National Natural Science Foundation of China through the Project "Science Center for Luminescence from Molecular Aggregates(SCELMA)" (No.21788102)the Ministry of Science and Technology of China through the National Key R&D Plan (No.2017YFA0204501)supported by the National Natural Science Foundation of China (No.22003029)
文摘We propose a method for calculating the nonradiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface(PES)in the Franck-Condon region.The method combines the n-mode repre-sentation method to construct the ab initio PES and the nearly exact time-dependent density matrix renormalization group method(TD-DMRG)to simulate quantum dynamics.In addition,in the framework of TD-DMRG,we further develop an algorithm to calculate the final-state-resolved rate coefficient which is very useful to analyze the contribution from each vibrational mode to the transition process.We use this method to study the internal conversion(IC)process of azulene after taking into account the anharmonicity of the ground state PES.The results show that even for this semi-rigid molecule,the intramode anharmonicity enhances the IC rate significantly,and after considering the two-mode coupling effect,the rate increases even further.The reason is that the anharmonicity enables the C-H vibrations to receive electronic energy while C-H vibrations do not contribute on the harmonic PES as the Huang-Rhys factor is close to 0.
基金Project supported by the National Natural Science Foundation of China(Nos.51135003 and U1234208)the Major State Basic Research Development Program of China(973 Program)(No.2014CB046303)
文摘In a structural system reliability analysis that lacks probabilistic information, calculating the numerical characteristics of the state functions, especially the first four moments of the state functions, is necessary. Based on that, the structural system reliability is analyzed with a fourth-order moment method. The reliability sensitivity is required to conduct the differential operation of the numerical characteristic functions. A reliability sensitivity analysis formula is then derived in combination with the relation of the differential operation. Based on the matrix theory and Kronecker algebra, this paper systematically derives a matrix expression of the first four moments of the state functions, and establishes the matrix relation between the first four moments of the state functions and those of the basic random variables. On this basis, a differential operation formula of the first four moments of the state functions is further derived against the first four moments of the basic random variables. The vector relation between the state functions and the multidimensional basic random variables is described by means of the matrix operation to extend the operation method. Finally, a concise and intuitive formula is obtained to explore the inherent essential relation between the numerical characteristics of the state functions and those of the basic random variables, leading to a universal equation for the two kinds of numerical characteristics.
基金Supported by the National Natural Science Foundation of China under Grant No.10974137the Major Natural Science Foundation of the Educational Department of Sichuan Province under Grant No.14ZA0167
文摘For our proposed composite parity-conserved matrix product state(MPS), if only a spin block length is larger than 1, any two such spin blocks have correlation including classical correlation and quantum correlation. Both the total correlation and the classical correlation become larger than that in any subcomponent; while the quantum correlations of the two nearest-neighbor spin blocks and the two next-nearest-neighbor spin blocks become smaller and for other conditions the quantum correlation becomes larger, i.e., the increase or the production of the long-range quantum correlation is at the cost of reducing the short-range quantum correlation, which deserves to be investigated in the future; and the ration of the quantum correlation to the total correlation monotonically decreases to a steady value as the spacing spin length increasing.
基金Supported by National Natural Science Foundation of China(10974137)by Educational Commission of Sichuan Province of China(14ZA0167)
文摘For the matrix product system of a one-dimensional spin-1/2 chain, we present a new model of quantum2 phase transitions and find that in the thermodynamic limit, both sides of the critical point are respectively described by phases ｜Ψa 〉=｜1··· 1 representing all particles spin up and ｜Ψb 〉=｜0··· 0 representing all particles spin down, while the phase transition point is an isolated intermediate-coupling point where√ the two phases coexist equally, which is2 described by the so-called N-qubit maximally entangled GHZ state ｜Ψpt =√2/2（｜1··· 1 ＋｜0··· 0）. At the critical point,2the physical quantities including the entanglement are not discontinuous and the matrix product system has longrange correlation and N-qubit maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of potential directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-qubit maximal entanglement.
基金Supported by National Natural Science Foundation of China(10974137)Major Natural Science Foundation of Educational Department of Sichuan Province(14ZA0167)
文摘We present a new model of quantum phase transitions in matrix product systems of one-dimensional spin-1 chains and study the phases coexistence phenomenon. We find that in the thermodynamic limit the proposed system has three different quantum phases and by adjusting the control parameters we are able to realize any phase, any two phases equal coexistence and the three phases equM coexistence. At every critical point the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N-spin maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of certain directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-spin maximal entanglement.
基金Supported by the Chinese National Science Foundation under Grant Nos.11047160 and 10874003It is also partially supported by the National Basic Research Program of China under Grant No.2009CB939901
文摘The matrix product state （MPS） is utilized to investigate the ground state properties and quantum phase transitions （OPTs） of the dimerized antiferromagnetic Heisenberg （DAH） model. The ground state MPS wavefunctions determined by the infinite time-evolving block decimation （iTEBD） algorithm are shown to be very efficient descriptions of DAH model. In the thermodynamic limit, the quantum entanglement, the bond energy~ and the nearest-neighbor correlations are calculated. It is revealed that the singular behavior of the bipartite entanglement can detect the QPTs directly. The critical point J2c= 1.0 is determined evidently, and the quantum phase transition is argued to belong to the second-order category. At the critical point, logarithmic divergent character of the block entanglement is observed, and the system can be described by a free bosonic field theory.
基金supported by the National Natural Science Foundation of China(11504283)Scientific Research Program Fundation of Shaanxi Provincial Education Department(16JK1335)
