With the Becchi-Rouet-Stora-Tyutin(BRST) quantization of gauge theory,we solve the long-standing difficult problem of the local constraint conditions,i.e.the single occupation of a slave particle per site,in the slave...With the Becchi-Rouet-Stora-Tyutin(BRST) quantization of gauge theory,we solve the long-standing difficult problem of the local constraint conditions,i.e.the single occupation of a slave particle per site,in the slave particle theory.This difficulty is actually caused by inconsistently dealing with the local Lagrange multiplier λ_(i) which ensures the constraint:in the Hamiltonian formalism of the theory,λ_(i) is time-independent and commutes with the Hamiltonian while in the Lagrangian formalism,λ_(i)(t) becomes time-dependent and plays a role of gauge field.This implies that the redundant degrees of freedom of λ_(i)(t) are introduced and must be removed by the additional constraint,the gauge fixing condition(GFC) ?_tλ_(i)(t)= 0.In literature,this GFC was missed.We add this GFC and use the BRST quantization of gauge theory for Dirac's first-class constraints in the slave particle theory.This GFC endows λ_(i)(t) with dynamics and leads to important physical results.As an example,we study the Hubbard model at half-filling and find that the spinon is gapped in the weak U and the system is indeed a conventional metal,which resolves the paradox that the weak coupling state is a superconductor in the previous slave boson mean field(MF) theory.For the t-J model,we find that the dynamic effect of λ_(i)(t) substantially suppresses the d-wave pairing gap and then the superconducting critical temperature may be lowered at least a factor of one-fifth of the MF value which is of the order of 1000 K.The renormalized T_c is then close to that in cuprates.展开更多
The EPR parameters of trivalent Er（3＋） ions doped in hexagonal Ga N crystal have been studied by diagonalizing the 364×364 complete energy matrices. The results indicate that the resonance ground states may be...The EPR parameters of trivalent Er（3＋） ions doped in hexagonal Ga N crystal have been studied by diagonalizing the 364×364 complete energy matrices. The results indicate that the resonance ground states may be derived from the Kramers doublet Γ6. The EPR g-factors may be ascribed to the stronger covalent bonding and nephelauxetic effects compared with other rare-earth doped complexes, as a result of the mismatch of ionic radii of the impurity Er（3＋）ion and the replaced Ga（3＋） ion apart from the intrinsic covalency of host Ga N. Furthermore, the J–J mixing effects on the EPR parameters from the high-lying manifolds have been evaluated. It is found that the dominant J–J mixing contribution is from the manifold 2K（15/2）, which accounts for about 2.5%. The next important J–J contribution arises from the crystal–field mixture between the ground state 4I（15/2） and the first excited state4I（13/2）, and is usually less than 0.2%. The contributions from the rest states may be ignored.展开更多
Restricted Boltzmann machine(RBM)has been proposed as a powerful variational ansatz to represent the ground state of a given quantum many-body system.On the other hand,as a shallow neural network,it is found that the ...Restricted Boltzmann machine(RBM)has been proposed as a powerful variational ansatz to represent the ground state of a given quantum many-body system.On the other hand,as a shallow neural network,it is found that the RBM is still hardly able to capture the characteristics of systems with large sizes or complicated interactions.In order to find a way out of the dilemma,here,we propose to adopt the Green's function Monte Carlo(GFMC)method for which the RBM is used as a guiding wave function.To demonstrate the implementation and effectiveness of the proposal,we have applied the proposal to study the frustrated J_(1)-J_(2)Heisenberg model on a square lattice,which is considered as a typical model with sign problem for quantum Monte Carlo simulations.The calculation results demonstrate that the GFMC method can significantly further reduce the relative error of the ground-state energy on the basis of the RBM variational results.This encourages to combine the GFMC method with other neural networks like convolutional neural networks for dealing with more models with sign problem in the future.展开更多
文摘With the Becchi-Rouet-Stora-Tyutin(BRST) quantization of gauge theory,we solve the long-standing difficult problem of the local constraint conditions,i.e.the single occupation of a slave particle per site,in the slave particle theory.This difficulty is actually caused by inconsistently dealing with the local Lagrange multiplier λ_(i) which ensures the constraint:in the Hamiltonian formalism of the theory,λ_(i) is time-independent and commutes with the Hamiltonian while in the Lagrangian formalism,λ_(i)(t) becomes time-dependent and plays a role of gauge field.This implies that the redundant degrees of freedom of λ_(i)(t) are introduced and must be removed by the additional constraint,the gauge fixing condition(GFC) ?_tλ_(i)(t)= 0.In literature,this GFC was missed.We add this GFC and use the BRST quantization of gauge theory for Dirac's first-class constraints in the slave particle theory.This GFC endows λ_(i)(t) with dynamics and leads to important physical results.As an example,we study the Hubbard model at half-filling and find that the spinon is gapped in the weak U and the system is indeed a conventional metal,which resolves the paradox that the weak coupling state is a superconductor in the previous slave boson mean field(MF) theory.For the t-J model,we find that the dynamic effect of λ_(i)(t) substantially suppresses the d-wave pairing gap and then the superconducting critical temperature may be lowered at least a factor of one-fifth of the MF value which is of the order of 1000 K.The renormalized T_c is then close to that in cuprates.
基金Project supported by the Foundation of Education Department of Shaanxi Province,China(Grant No.16JK1402)
文摘The EPR parameters of trivalent Er（3＋） ions doped in hexagonal Ga N crystal have been studied by diagonalizing the 364×364 complete energy matrices. The results indicate that the resonance ground states may be derived from the Kramers doublet Γ6. The EPR g-factors may be ascribed to the stronger covalent bonding and nephelauxetic effects compared with other rare-earth doped complexes, as a result of the mismatch of ionic radii of the impurity Er（3＋）ion and the replaced Ga（3＋） ion apart from the intrinsic covalency of host Ga N. Furthermore, the J–J mixing effects on the EPR parameters from the high-lying manifolds have been evaluated. It is found that the dominant J–J mixing contribution is from the manifold 2K（15/2）, which accounts for about 2.5%. The next important J–J contribution arises from the crystal–field mixture between the ground state 4I（15/2） and the first excited state4I（13/2）, and is usually less than 0.2%. The contributions from the rest states may be ignored.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11934020 and 11874421)the Natural Science Foundation of Beijing(Grant No.Z180013)。
文摘Restricted Boltzmann machine(RBM)has been proposed as a powerful variational ansatz to represent the ground state of a given quantum many-body system.On the other hand,as a shallow neural network,it is found that the RBM is still hardly able to capture the characteristics of systems with large sizes or complicated interactions.In order to find a way out of the dilemma,here,we propose to adopt the Green's function Monte Carlo(GFMC)method for which the RBM is used as a guiding wave function.To demonstrate the implementation and effectiveness of the proposal,we have applied the proposal to study the frustrated J_(1)-J_(2)Heisenberg model on a square lattice,which is considered as a typical model with sign problem for quantum Monte Carlo simulations.The calculation results demonstrate that the GFMC method can significantly further reduce the relative error of the ground-state energy on the basis of the RBM variational results.This encourages to combine the GFMC method with other neural networks like convolutional neural networks for dealing with more models with sign problem in the future.
