We investigate the t–W scheme for the anti-ferromagnetic X X X spin chain under both periodic and open boundary conditions. We propose a new parametrization of the eigenvalues of the transfer matrix. Based on it, we ...We investigate the t–W scheme for the anti-ferromagnetic X X X spin chain under both periodic and open boundary conditions. We propose a new parametrization of the eigenvalues of the transfer matrix. Based on it, we obtain the exact solution of the system. By analyzing the distribution of zero roots at the ground state, we obtain the explicit expressions of the eigenfunctions of the transfer matrix and the associated W operator(see Eqs.(10) and(70)) in the thermodynamic limit. We find that the ratio of the quantum determinant with the eigenvalue of W operator for the ground state exhibits exponential decay behavior. Thus this fact ensures that the so-called inversion relation(the t–W relation without the W-term) can be used to study the ground state properties of quantum integrable systems with/without U(1)-symmetry in the thermodynamic limit.展开更多
In this paper, we introduce the reduced matrix in kq representation and provide the reduced matrix elements of a projection operator P on the rational noncommutative orbifold T^2/Z_4.we give the closed form for the pr...In this paper, we introduce the reduced matrix in kq representation and provide the reduced matrix elements of a projection operator P on the rational noncommutative orbifold T^2/Z_4.we give the closed form for the projector by Jacobi elliptical functions. Since projectors correspond to soliton solutions of the field theory on the noncommutative orbifold, we thus present a corresponding soliton solution.展开更多
The second reference state of the open XYZ spin chain with non-diagonal boundary terms is studied. The associated Bethe states exactly yield the second set of eigenvalues proposed recently by functional Bethe Ansatz.
With the help of the F-basis provided by the Drinfeld twist or factorising F-matrix for the spatial optical soliton model associated with the eight-vertex model, we calculate the partition function for the eight-verte...With the help of the F-basis provided by the Drinfeld twist or factorising F-matrix for the spatial optical soliton model associated with the eight-vertex model, we calculate the partition function for the eight-vertex model on an N ×N square lattice with domain wall boundary condition.展开更多
We show that for Green-Schwarz superstring in AdS_(3)×S^(3),the one-parameter family of flat currents retains a zero-curvature condition and keeps the variation relations under is-symmetry,diffeomorphism,local Lo...We show that for Green-Schwarz superstring in AdS_(3)×S^(3),the one-parameter family of flat currents retains a zero-curvature condition and keeps the variation relations under is-symmetry,diffeomorphism,local Lorentz SO(1,2)×SO(3)and global PSU(1,1|2)^(2)symmetry transformations respectively.This indicates that the flat currents exist in all the n-symmetry gauge fixed cases.As a result,we find that the infinite conserved quantities are invariant under these transformations and independent of the gauge choice of the system.展开更多
We parameterize the Green–Schwarz IIB superstring in the AdS_(3)×S^(3) background under the light cone gauge by the method of Metsaev and Tseytlin in AdS3 and by the method of Rahmfeld and Rajaraman in S3.After ...We parameterize the Green–Schwarz IIB superstring in the AdS_(3)×S^(3) background under the light cone gauge by the method of Metsaev and Tseytlin in AdS3 and by the method of Rahmfeld and Rajaraman in S3.After some calculation,we obtain the corresponding Maurer–Cartan 1−forms and the action.Then we fix two bosonic variables x+=τand y^(5)=σ,perform the partial Legendre transformation of the remaining bosonic variables,and find a Lagrangian that is linear in velocity after eliminating the metric of the world sheet.We also give the Hamiltonian and prove that the system is local and the Poisson bracket of the theory can be well defined.Using these results,one can further study the properties of solution space,solution transformation and the structure of the flat current algebra of the superstring in the AdS_(3)×S^(3) background.展开更多
The Perk-Schultz model with SUq(m\n)spin boundary impurities is constructed by dressing the c-number reflecting K matrix with local L-matrix which acts non-trivially on an impurity Hilbert space.The eigenvalue of the ...The Perk-Schultz model with SUq(m\n)spin boundary impurities is constructed by dressing the c-number reflecting K matrix with local L-matrix which acts non-trivially on an impurity Hilbert space.The eigenvalue of the transfer matrix and the corresponding Bethe ansatz equations with different c-number reflecting K-matrices are obtained by using the nested Bethe ansatz method(m≠n).When m=1,n=2,our results come back to that of super-symmetric t-J model with SU_(q)(1\2)spin boundary impurities.展开更多
We find one parameter fiat currents of the sigma model on supercoset targets with Z2m grading given by Young satisfaction equations of motion and the Virasoro constraint. This means that one can generate a series of c...We find one parameter fiat currents of the sigma model on supercoset targets with Z2m grading given by Young satisfaction equations of motion and the Virasoro constraint. This means that one can generate a series of classical solutions from the original one. For these new solutions one can also construct fiat currents and conserved charges, which form the same set with the original one.展开更多
We study the reflection of a straight line or a billiard on a plane in an n-dimensional Minkowski space. It is found that the reflection law coincides with that defined with respect to confocal quadratic surfaces in p...We study the reflection of a straight line or a billiard on a plane in an n-dimensional Minkowski space. It is found that the reflection law coincides with that defined with respect to confocal quadratic surfaces in projective geometry. We then establish the full Poncelet theorem which holds in projective geometry in n-dimensional Minkowski space and in their quadratic surfaces including de Sitter and AdS spaces.展开更多
基金Project supported by the National Key R&D Program of China (Grant No. 2021YFA1402104)the National Natural Science Foundation of China (Grant Nos. 12247103,12305005, 12074410, 11934015, and 11975183)+3 种基金Major Basic Research Program of Natural Science of Shaanxi Province (Grant Nos. 2021JCW-19 and 2017ZDJC-32)Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB33000000)Young Talent Fund of Xi’an Association for Science and Technology (Grant No. 959202313086)Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No. 22JSZ005)。
文摘We investigate the t–W scheme for the anti-ferromagnetic X X X spin chain under both periodic and open boundary conditions. We propose a new parametrization of the eigenvalues of the transfer matrix. Based on it, we obtain the exact solution of the system. By analyzing the distribution of zero roots at the ground state, we obtain the explicit expressions of the eigenfunctions of the transfer matrix and the associated W operator(see Eqs.(10) and(70)) in the thermodynamic limit. We find that the ratio of the quantum determinant with the eigenvalue of W operator for the ground state exhibits exponential decay behavior. Thus this fact ensures that the so-called inversion relation(the t–W relation without the W-term) can be used to study the ground state properties of quantum integrable systems with/without U(1)-symmetry in the thermodynamic limit.
基金Supported by the Natural Science Foundation of China under Grant Nos. 10575080, 11047025, 11075126 the Project of Knowledge Innovation Program (PKIP) of Chinese Academy of Sciences
文摘In this paper, we introduce the reduced matrix in kq representation and provide the reduced matrix elements of a projection operator P on the rational noncommutative orbifold T^2/Z_4.we give the closed form for the projector by Jacobi elliptical functions. Since projectors correspond to soliton solutions of the field theory on the noncommutative orbifold, we thus present a corresponding soliton solution.
基金Supports by the National Natural Science Foundation of China under Grant Nos. 11075125 and 11031005
文摘The second reference state of the open XYZ spin chain with non-diagonal boundary terms is studied. The associated Bethe states exactly yield the second set of eigenvalues proposed recently by functional Bethe Ansatz.
基金Project supported by the National Natural Science Foundation of China Grant Nos.11075126 and 11031005)
文摘With the help of the F-basis provided by the Drinfeld twist or factorising F-matrix for the spatial optical soliton model associated with the eight-vertex model, we calculate the partition function for the eight-vertex model on an N ×N square lattice with domain wall boundary condition.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10575080 and 11047179the NWU Graduate Cross-discipline Funds(09YJC25)+1 种基金the Youth Foundation of Xi’an Institute of Posts and Telecommunications(ZL2007-18)the Special Fund for Basic Scientific Research of Central Colleges,Chang’an University and supported by the Special Foundation for Basic Research Program of Chang’an University,Open Fund of Key Laboratory for Special Area Highway Engineering(Chang’an University)(Ministry of Education)under Grant No CHD2009JC030.
文摘We show that for Green-Schwarz superstring in AdS_(3)×S^(3),the one-parameter family of flat currents retains a zero-curvature condition and keeps the variation relations under is-symmetry,diffeomorphism,local Lorentz SO(1,2)×SO(3)and global PSU(1,1|2)^(2)symmetry transformations respectively.This indicates that the flat currents exist in all the n-symmetry gauge fixed cases.As a result,we find that the infinite conserved quantities are invariant under these transformations and independent of the gauge choice of the system.
基金by the National Natural Science Foundation of China under Grant Nos 11047179,11075126,11031005 and 10575080the Special Fund for Basic Scientific Research of Central Colleges,Chang’an University+4 种基金the Special Foundation for Basic Research Program of Chang’an Universitythe Open Fund of Key Laboratory for Special Area Highway Engineering(Chang’an University)the Ministry of Education under Grant No CHD2009JC030the Xi’an Shiyou University Science and Technology Foundation under Grant No 2010QN018the NWU Graduate Cross-Discipline Funds under Grant No 09YJC25.
文摘We parameterize the Green–Schwarz IIB superstring in the AdS_(3)×S^(3) background under the light cone gauge by the method of Metsaev and Tseytlin in AdS3 and by the method of Rahmfeld and Rajaraman in S3.After some calculation,we obtain the corresponding Maurer–Cartan 1−forms and the action.Then we fix two bosonic variables x+=τand y^(5)=σ,perform the partial Legendre transformation of the remaining bosonic variables,and find a Lagrangian that is linear in velocity after eliminating the metric of the world sheet.We also give the Hamiltonian and prove that the system is local and the Poisson bracket of the theory can be well defined.Using these results,one can further study the properties of solution space,solution transformation and the structure of the flat current algebra of the superstring in the AdS_(3)×S^(3) background.
基金Supported by the National Natural Science Foundation of China under Grant No.19975036the Science Fund of Northwest University,China.
文摘The Perk-Schultz model with SUq(m\n)spin boundary impurities is constructed by dressing the c-number reflecting K matrix with local L-matrix which acts non-trivially on an impurity Hilbert space.The eigenvalue of the transfer matrix and the corresponding Bethe ansatz equations with different c-number reflecting K-matrices are obtained by using the nested Bethe ansatz method(m≠n).When m=1,n=2,our results come back to that of super-symmetric t-J model with SU_(q)(1\2)spin boundary impurities.
基金Supported by the National Natural Science Foundation of China under Grant Nos 90403019 and 10575080, and the Xi＇an Shiyou University Science and Technology Foundation under Grant No 2006-43.
文摘We find one parameter fiat currents of the sigma model on supercoset targets with Z2m grading given by Young satisfaction equations of motion and the Virasoro constraint. This means that one can generate a series of classical solutions from the original one. For these new solutions one can also construct fiat currents and conserved charges, which form the same set with the original one.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10674162 and 10575080, and the National Basic Research Programme of China under Grant No 2006CB921107.
文摘We study the reflection of a straight line or a billiard on a plane in an n-dimensional Minkowski space. It is found that the reflection law coincides with that defined with respect to confocal quadratic surfaces in projective geometry. We then establish the full Poncelet theorem which holds in projective geometry in n-dimensional Minkowski space and in their quadratic surfaces including de Sitter and AdS spaces.
