The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal-field is studied within the mean-field theory based on Bogoliubov inequality for the Gibbs free energy. The ground-state phase diagram and th...The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal-field is studied within the mean-field theory based on Bogoliubov inequality for the Gibbs free energy. The ground-state phase diagram and the tricritical point are obtained in the transverse field Ω/ zJ-longitudinal crystal D / zJ field plane. We find that there are the first order-order phase transitions in a very small range of D /zJ besides the usual first order-disorder phase transitions and the second order-disorder phase transitions,展开更多
The spin-1 Blume–Capel model with transverse and longitudinal external magnetic fields h, in addition to a longitudinal random crystal field D, is studied in the mean-field approximation. It is assumed that the cryst...The spin-1 Blume–Capel model with transverse and longitudinal external magnetic fields h, in addition to a longitudinal random crystal field D, is studied in the mean-field approximation. It is assumed that the crystal field is either turned on with probability p or turned off with probability 1 p on the sites of a square lattice. Phase diagrams are then calculated on the reduced temperature crystal field planes for given values of γ=Ω/J and p at zero h. Thus, the effect of changing γ and p are illustrated on the phase diagrams in great detail and interesting results are observed.展开更多
An improved transverse Ising model is proposed by taking the depolarization field effect into account. Within the framework of mean-held theory we investigate the behavior of the ferroelectric thin film. Our results s...An improved transverse Ising model is proposed by taking the depolarization field effect into account. Within the framework of mean-held theory we investigate the behavior of the ferroelectric thin film. Our results show that the influence of the depolarization field is to flatten the spontaneous polarization profile and make the films more homogeneous, which is consistent with Ginzburg Landau theory. This fact shows that this model can be taken as an effective model to deal with the ferroelectric film and can be further extended to refer to quantum effect. The competition between quantum effect and depolarization field induces some interesting phenomena on ferroelectric thin films.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
We study the structure of the continuous matrix product operator(cMPO)^([1]) for the transverse field Ising model(TFIM).We prove TFIM’s cMPO is solvable and has the form T=e^(-1/2H_(F)).H_(F) is a non-local free ferm...We study the structure of the continuous matrix product operator(cMPO)^([1]) for the transverse field Ising model(TFIM).We prove TFIM’s cMPO is solvable and has the form T=e^(-1/2H_(F)).H_(F) is a non-local free fermionic Hamiltonian on a ring with circumferenceβ,whose ground state is gapped and non-degenerate even at the critical point.The full spectrum of H_(F) is determined analytically.At the critical point,our results verify the state–operator-correspondence^([2]) in the conformal field theory(CFT).We also design a numerical algorithm based on Bloch state ansatz to calculate the lowlying excited states of general(Hermitian)cMPO.Our numerical calculations coincide with the analytic results of TFIM.In the end,we give a short discussion about the entanglement entropy of cMPO’s ground state.展开更多
The phase diagrams and the other crtical properties of S-3/2 Ising model in random longitudinal and transverse fields(RLIM) are dicussed with the approximate scheme combined by mean-field renormalization group theory(...The phase diagrams and the other crtical properties of S-3/2 Ising model in random longitudinal and transverse fields(RLIM) are dicussed with the approximate scheme combined by mean-field renormalization group theory(MFRG) and the discretized path-integral representation(DPIR).展开更多
A effective approximate scheme which is combined by cluster with the discrelized path-integral representation (DPIR) is used in the study on the random-bond Ising model in a transverse field (RTIM). The critical therm...A effective approximate scheme which is combined by cluster with the discrelized path-integral representation (DPIR) is used in the study on the random-bond Ising model in a transverse field (RTIM). The critical thermodynamical properties, such as the critical temperature, the critical transverse field, the average magnetization ,the susceptibility and the special heat atc.. are calculated, And some results have been improved.展开更多
The critical behaviors of a mixed spin-1/2 and spin-sB Ising system with a transverse crystal field are studiedby use of the effective-field theory with correlations. The effect of the transverse crystal field on tran...The critical behaviors of a mixed spin-1/2 and spin-sB Ising system with a transverse crystal field are studiedby use of the effective-field theory with correlations. The effect of the transverse crystal field on transition temperaturesis investigated numerically for the honeycomb (z = 3) and square (z = 4) lattices. The results show that there is notricritical point for the system.展开更多
Along the way initiated by Carleo and Troyer [G. Carleo and M. Troyer, Science 355(2017) 602], we construct the neural-network quantum state of transverse-field Ising model(TFIM) by an unsupervised machine learning me...Along the way initiated by Carleo and Troyer [G. Carleo and M. Troyer, Science 355(2017) 602], we construct the neural-network quantum state of transverse-field Ising model(TFIM) by an unsupervised machine learning method. Such a wave function is a map from the spin-configuration space to the complex number field determined by an array of network parameters. To get the ground state of the system, values of the network parameters are calculated by a Stochastic Reconfiguration(SR) method. We provide for this SR method an understanding from action principle and information geometry aspects. With this quantum state, we calculate key observables of the system, the energy,correlation function, correlation length, magnetic moment, and susceptibility. As innovations, we provide a high e?ciency method and use it to calculate entanglement entropy(EE) of the system and get results consistent with previous work very well.展开更多
The relationship between the transverse field Ising model and the Landau phenomenological theory for ferroelectrics is analyzed, and the Landau free energy expression for ferroelectrics having surfaces is derived. It ...The relationship between the transverse field Ising model and the Landau phenomenological theory for ferroelectrics is analyzed, and the Landau free energy expression for ferroelectrics having surfaces is derived. It is pointed out that the traditional expression in which the surface integral has only a term of the square polarization is valid only for special cases, in general a term of the polarization to the four should be included as well. By use of the newly derived free energy expression, the thickness-dependence of the spontaneous polarization and Curie temperature of ferroelectric films is calculated; thereby some experimental results incompatible with the traditional phenomenological theory are successfully explained.展开更多
文摘The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal-field is studied within the mean-field theory based on Bogoliubov inequality for the Gibbs free energy. The ground-state phase diagram and the tricritical point are obtained in the transverse field Ω/ zJ-longitudinal crystal D / zJ field plane. We find that there are the first order-order phase transitions in a very small range of D /zJ besides the usual first order-disorder phase transitions and the second order-disorder phase transitions,
文摘The spin-1 Blume–Capel model with transverse and longitudinal external magnetic fields h, in addition to a longitudinal random crystal field D, is studied in the mean-field approximation. It is assumed that the crystal field is either turned on with probability p or turned off with probability 1 p on the sites of a square lattice. Phase diagrams are then calculated on the reduced temperature crystal field planes for given values of γ=Ω/J and p at zero h. Thus, the effect of changing γ and p are illustrated on the phase diagrams in great detail and interesting results are observed.
文摘An improved transverse Ising model is proposed by taking the depolarization field effect into account. Within the framework of mean-held theory we investigate the behavior of the ferroelectric thin film. Our results show that the influence of the depolarization field is to flatten the spontaneous polarization profile and make the films more homogeneous, which is consistent with Ginzburg Landau theory. This fact shows that this model can be taken as an effective model to deal with the ferroelectric film and can be further extended to refer to quantum effect. The competition between quantum effect and depolarization field induces some interesting phenomena on ferroelectric thin films.
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supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB30000000)the National Natural Science Foundation of China(Grant Nos.11774398 and T2121001)。
文摘We study the structure of the continuous matrix product operator(cMPO)^([1]) for the transverse field Ising model(TFIM).We prove TFIM’s cMPO is solvable and has the form T=e^(-1/2H_(F)).H_(F) is a non-local free fermionic Hamiltonian on a ring with circumferenceβ,whose ground state is gapped and non-degenerate even at the critical point.The full spectrum of H_(F) is determined analytically.At the critical point,our results verify the state–operator-correspondence^([2]) in the conformal field theory(CFT).We also design a numerical algorithm based on Bloch state ansatz to calculate the lowlying excited states of general(Hermitian)cMPO.Our numerical calculations coincide with the analytic results of TFIM.In the end,we give a short discussion about the entanglement entropy of cMPO’s ground state.
文摘The phase diagrams and the other crtical properties of S-3/2 Ising model in random longitudinal and transverse fields(RLIM) are dicussed with the approximate scheme combined by mean-field renormalization group theory(MFRG) and the discretized path-integral representation(DPIR).
文摘A effective approximate scheme which is combined by cluster with the discrelized path-integral representation (DPIR) is used in the study on the random-bond Ising model in a transverse field (RTIM). The critical thermodynamical properties, such as the critical temperature, the critical transverse field, the average magnetization ,the susceptibility and the special heat atc.. are calculated, And some results have been improved.
基金The project supported by Science Foundation of the Ministry of Education of China under Grant No.99026
文摘The critical behaviors of a mixed spin-1/2 and spin-sB Ising system with a transverse crystal field are studiedby use of the effective-field theory with correlations. The effect of the transverse crystal field on transition temperaturesis investigated numerically for the honeycomb (z = 3) and square (z = 4) lattices. The results show that there is notricritical point for the system.
基金Supported by the Natural Science Foundation of China under Grant No.11875082
文摘Along the way initiated by Carleo and Troyer [G. Carleo and M. Troyer, Science 355(2017) 602], we construct the neural-network quantum state of transverse-field Ising model(TFIM) by an unsupervised machine learning method. Such a wave function is a map from the spin-configuration space to the complex number field determined by an array of network parameters. To get the ground state of the system, values of the network parameters are calculated by a Stochastic Reconfiguration(SR) method. We provide for this SR method an understanding from action principle and information geometry aspects. With this quantum state, we calculate key observables of the system, the energy,correlation function, correlation length, magnetic moment, and susceptibility. As innovations, we provide a high e?ciency method and use it to calculate entanglement entropy(EE) of the system and get results consistent with previous work very well.
基金Project partly supported by the Laboratory of Function Inorganic Materials of the Chinese Academy of Sciences.
文摘The relationship between the transverse field Ising model and the Landau phenomenological theory for ferroelectrics is analyzed, and the Landau free energy expression for ferroelectrics having surfaces is derived. It is pointed out that the traditional expression in which the surface integral has only a term of the square polarization is valid only for special cases, in general a term of the polarization to the four should be included as well. By use of the newly derived free energy expression, the thickness-dependence of the spontaneous polarization and Curie temperature of ferroelectric films is calculated; thereby some experimental results incompatible with the traditional phenomenological theory are successfully explained.
