After constructing the Bethe state of the XXZ Gaudin model with generic non-diagonal boundary terms,we analyze the properties of this state and obtain the determinant representations of the scalar products for this XX...After constructing the Bethe state of the XXZ Gaudin model with generic non-diagonal boundary terms,we analyze the properties of this state and obtain the determinant representations of the scalar products for this XXZ Gaudin model.展开更多
Quantum dynamics of many-body systems is a fascinating and significant subject for both theory and experiment.The question of how an isolated many-body system evolves to its steady state after a sudden perturbation or...Quantum dynamics of many-body systems is a fascinating and significant subject for both theory and experiment.The question of how an isolated many-body system evolves to its steady state after a sudden perturbation or quench still remains challenging.In this paper,using the Bethe ansatz wave function,we study the quantum dynamics of an inhomogeneous Gaudin magnet.We derive explicit analytical expressions for various local dynamic quantities with an arbitrary number of flipped bath spins,such as:the spin distribution function,the spin-spin correlation function,and the Loschmidt echo.We also numerically study the relaxation behavior of these dynamic properties,gaining considerable insight into coherence and entanglement between the central spin and the bath.In particular,we find that the spin-spin correlations relax to their steady value via a nearly logarithmic scaling,whereas the Loschmidt echo shows an exponential relaxation to its steady value.Our results advance the understanding of relaxation dynamics and quantum correlations of long-range interacting models of the Gaudin type.展开更多
We study the exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions.The energy and Bethe ansatz equations of the Gaudin model can be obtained via the off-d...We study the exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions.The energy and Bethe ansatz equations of the Gaudin model can be obtained via the off-diagonal Bethe ansatz method.Based on the off-diagonal Bethe ansatz solutions,we construct the Bethe states of the inhomogeneous XXX Heisenberg spin chain with the generic open boundaries.By taking a quasi-classical limit,we give explicit closed-form expression of the Bethe states of the Gaudin model.From the numerical simulations for the small-size system,it is shown that some Bethe roots go to infinity when the Gaudin model recovers the U(1)symmetry.Furthermore,it is found that the contribution of those Bethe roots to the Bethe states is a nonzero constant.This fact enables us to recover the Bethe states of the Gaudin model with the U(1)symmetry.These results provide a basis for the further study of the thermodynamic limit,correlation functions,and quantum dynamics of the Gaudin model.展开更多
We propose the eigenstates and eigenvalues of Hamiltonians of the rational SU(N)Gaudin model based on the quasi-classical limit of the SU(N)chain under the periodic boundary condition.Using the quantum inverse scatter...We propose the eigenstates and eigenvalues of Hamiltonians of the rational SU(N)Gaudin model based on the quasi-classical limit of the SU(N)chain under the periodic boundary condition.Using the quantum inverse scattering method,we also obtain the eigenvalues of the generation function of the rational SU(N)Gaudin model.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos.11075126,11031005,11375141the State Education Ministry of China under Grant No.20116101110017 and SRF for ROCS
文摘After constructing the Bethe state of the XXZ Gaudin model with generic non-diagonal boundary terms,we analyze the properties of this state and obtain the determinant representations of the scalar products for this XXZ Gaudin model.
基金support from NSAF(Grant No.U1930402)supported by the key NSFC grant No.12134015 and No.11874393+2 种基金the National Key R&D Program of China No.2017YFA0304500,the National Key R&D Program of China No.2016YFA0301200support from NSFC(Grants No.11974040 and No.12150610464),NSFC 11734002financial support from National Science Association Funds U1930402
文摘Quantum dynamics of many-body systems is a fascinating and significant subject for both theory and experiment.The question of how an isolated many-body system evolves to its steady state after a sudden perturbation or quench still remains challenging.In this paper,using the Bethe ansatz wave function,we study the quantum dynamics of an inhomogeneous Gaudin magnet.We derive explicit analytical expressions for various local dynamic quantities with an arbitrary number of flipped bath spins,such as:the spin distribution function,the spin-spin correlation function,and the Loschmidt echo.We also numerically study the relaxation behavior of these dynamic properties,gaining considerable insight into coherence and entanglement between the central spin and the bath.In particular,we find that the spin-spin correlations relax to their steady value via a nearly logarithmic scaling,whereas the Loschmidt echo shows an exponential relaxation to its steady value.Our results advance the understanding of relaxation dynamics and quantum correlations of long-range interacting models of the Gaudin type.
基金the National Natural Science Foundation of China(Grant Nos.11847245 and 11874393).
文摘We study the exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions.The energy and Bethe ansatz equations of the Gaudin model can be obtained via the off-diagonal Bethe ansatz method.Based on the off-diagonal Bethe ansatz solutions,we construct the Bethe states of the inhomogeneous XXX Heisenberg spin chain with the generic open boundaries.By taking a quasi-classical limit,we give explicit closed-form expression of the Bethe states of the Gaudin model.From the numerical simulations for the small-size system,it is shown that some Bethe roots go to infinity when the Gaudin model recovers the U(1)symmetry.Furthermore,it is found that the contribution of those Bethe roots to the Bethe states is a nonzero constant.This fact enables us to recover the Bethe states of the Gaudin model with the U(1)symmetry.These results provide a basis for the further study of the thermodynamic limit,correlation functions,and quantum dynamics of the Gaudin model.
基金Supported by the National Natural Science Foundation of China under Grant No.19975036.
文摘We propose the eigenstates and eigenvalues of Hamiltonians of the rational SU(N)Gaudin model based on the quasi-classical limit of the SU(N)chain under the periodic boundary condition.Using the quantum inverse scattering method,we also obtain the eigenvalues of the generation function of the rational SU(N)Gaudin model.
