Exact solution of Heisenberg model with site-dependent exchange couplings and Dzyloshinsky–Moriya interaction

We propose an integrable spin-1/2 Heisenberg model where the exchange couplings and Dzyloshinky–Moriya interactions are dependent on the sites. By employing the quantum inverse scattering method, we obtain the eigenvalues and the Bethe ansatz equation of the system with the periodic boundary condition. Furthermore, we obtain the exact solution and study the boundary effect of the system with the anti-periodic boundary condition via the off-diagonal Bethe ansatz. The operator identities of the transfer matrix at the inhomogeneous points are proved at the operator level. We construct the T –Q relation based on them. From which, we obtain the energy spectrum of the system. The corresponding eigenstates are also constructed. We find an interesting coherence state that is induced by the topological boundary.     

Exact solution of the Gaudin model with Dzyaloshinsky–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions

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 X X X 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.     

Exact solution of a topological spin ring with an impurity

The spin-1/2 Heisenberg chain coupled to a spin-S impurity moment with anti-periodic boundary condition is studied via the off-diagonal Bethe ansatz method. The twisted boundary breaks the U(1) symmetry of the system, which leads to that the spin ring with impurity can not be solved by the conventional Bethe ansatz methods. By combining the properties of the R-matrix, the transfer matrix, and the quantum determinant, we derive the T –Q relation and the corresponding Bethe ansatz equations. The residual magnetizations of the ground states and the impurity specific heat are investigated. It is found that the residual magnetizations in this model strongly depend on the constraint of the topological boundary condition, the inhomogeneity of the impurity comparing with the hosts could depress the impurity specific heat in the thermodynamic limit. This method can be expand to other integrable impurity models without U(1) symmetry.     

A New Method to Construct Integrable Coupling System for Burgers Equation Hierarchy by Kronecker Product

It is shown that the Kronecker product can be applied to construct a new integrable coupling system of soliton equation hierarchy in this paper. A direct application to the Burgers spectral problem leads to a novel soliton equation hierarchy of integrable coupling system. It indicates that the Kronecker product is an efficient and straightforward method to construct the integrable couplings.     

Exact Eigenstates for a Class of Model Describing Interactions Among Five Bosonic Modes with Multiphoton Process

We present an efficient approach to studying the spectra and eigenstates for the model describing interactions among five bosonic modes without using the assumption of the Bethe ansatz. The exact analytical results of all the eigenstates and eigenvalues are in terms of a parameter A for a class of models describing five-mode multiphoton process. The parameter is determined by the roots of a polynomial and is solvable analytically or numerically.     

Effective inhibit energetic cost in stimulated Raman shortcut-to-adiabatic passage

A shortcut to the adiabatic process is an effective method for quantum information processing.The fast and robust quantum information transfer can be implemented by this method.The energetic cost is an important measurement for the shortcut.In this paper,we investigate how to inhibit the energetic cost in stimulated Raman shortcut-to-adiabatic passage in a three-level system.The energetic cost can be manipulated by adjusting detuning of the system and the energetic cost takes the minimum with one-photon resonance condition.     

CONSTRUCTION OF THE SOLITON STATES OF THE QUANTUM NONLINEAR SCHR?DINGER EQUATION

The quantum nonlinear schr?dinger equation (QNSE) is exactly solved by Beth's ansatz method and we give a reasonable definition of the quantum soliton states. From the definition we construct the soliton states of the QNSE from its bound-state solutions. The dispersion effect of the quantum soliton is also exactly analysed.     

A new multi-component integrable coupling system for AKNS equation hierarchy with sixteen-potential functions

It is shown in this paper that the upper triangular strip matrix of Lie algebra can be used to construct a new integrable coupling system of soliton equation hierarchy. A direct application to the Ablowitz--Kaup--Newell-- Segur(AKNS) spectral problem leads to a novel multi-component soliton equation hierarchy of an integrable coupling system with sixteen-potential functions. It is indicated that the study of integrable couplings when using the upper triangular strip matrix of Lie algebra is an efficient and straightforward method.     

Point-contact tunneling spectroscopy between a Nb tip and an ideal topological insulator Sn-doped Bi1.1Sb0.9Te2S

We find that the quantum-classical correspondence in integrable systems is characterized by two time scales. One is the Ehrenfest time below which the system is classical; the other is the quantum revival time beyond which the system is fully quantum. In between, the quantum system can be well approximated by classical ensemble distribution in phase space. These results can be summarized in a diagram which we call Ehrenfest diagram. We derive an analytical expression for Ehrenfest time, which is proportional to h~(-1/2). According to our formula, the Ehrenfest time for the solar-earth system is about 10~(26) times of the age of the solar system. We also find an analytical expression for the quantum revival time, which is proportional to h~(-1). Both time scales involve ω(I), the classical frequency as a function of classical action. Our results are numerically illustrated with two simple integrable models. In addition, we show that similar results exist for Bose gases, where 1/N serves as an effective Planck constant.     

Quantization of the O（N） Nonlinear Sigma Model

The Hamilton-Jacobi method of quantizing singular systems is discussed.The equations of motion are obtained as total differential equations in many variables.It is shown that if the system is integrable,one can obtain the canonical phase space coordinates and set of canonical Hamilton-Jacobi partial differential equations without any need to introduce unphysical auxiliary fields.As an example we quantize the O(2) nonlinear sigma model using two different approaches:the functional Schrodinger method to obtain the wave functionals for the ground and the exited state and then we quantize the same model using the canonical path integral quantization as an integration over the canonical phase-space coordinates.     

Exact solution of an integrable quantum spin chain with competing interactions

We construct an integrable quantum spin chain that includes the nearest-neighbor, next-nearest-neighbor, chiral three-spin couplings, Dzyloshinsky-Moriya interactions and unparallel boundary magnetic fields. Although the interactions in bulk materials are isotropic, the spins nearby the boundary fields are polarized, which induce the anisotropic exchanging interactions of the first and last bonds. The U(1) symmetry of the system is broken because of the off-diagonal boundary reflections. Using the off-diagonal Bethe ansatz, we obtain an exact solution to the system. The inhomogeneous T-Q relation and Bethe ansatz equations are given explicitly. We also calculate the ground state energy. The method given in this paper provides a general way to construct new integrable models with certain interesting interactions.     

Elliptic Quantum Groups and Ruijsenaars Models

We construct symmetric and exterior powers of the vector representation of the elliptic quantum groupsE _Τ,η(slN). The corresponding transfer matrices give rise to various integrable difference equations which could be solved in principle by the nested Bethe ansatz method. In special cases we recover the Ruijsenaars systems of commuting difference operators.     

Exact Solution of a Non-Hermitian Generalized Rabi Model

An integrable non-Hermitian generalized Rabi model is constructed.A twist matrix is introduced to the construction of Hamiltonian and generates the non-Hermitian properties.The Yang-Baxter integrability of the system is proven.The exact energy spectrum and eigenstates are obtained using the Bethe ansatz.The method given in this study provides a general way to construct integrable spin-boson models.     

Quantum group invariant integrable n-state models with periodic boundary conditions

Using the methods of topological quantum field theory we construct aU _q [sl(n)] invariant integrable transfer matrix for the case ofq being a root of unity. It corresponds to a 2-dimensional vertex model on a torus with topological interaction w.r.t. its interior. By means of the nested Bethe ansatz method we analyse conformai properties and discuss the representational content of the Bethe ansatz solutions.     

An open-boundary integrable model of three coupled XY spin chains

The integrable open-boundary conditions for the model of three coupled one-dimensional XY spin chains are considered in the framework of the quantum inverse scattering method. The diagonal boundary K-matrices are found and a class of integrable boundary terms is determined. The boundary model Hamiltonian is solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are derived.     

Electrostatic Analogy for Integrable Pairing Force Hamiltonians

For the exactly solved reduced BCS model an electrostatic analogy exists; in particular it served to obtain the exact thermodynamic limit of the model from the Richardson Bethe ansatz equations. We present an electrostatic analogy for a wider class of integrable Hamiltonians with pairing force interactions. We apply it to obtain the exact thermodynamic limit of this class of models. To verify the analytical results, we compare them with numerical solutions of the Bethe ansatz equations for finite systems at half-filling for the ground state.     

Integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons

A general graded reflection equation algebra is proposed and the corresponding boundary quantum inverse scattering method is formulated. The formalism is applicable to all boundary lattice systems where an invertible R-matrix exists. As an application, the integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons are investigated. The diagonal boundary K-matrices are found and a class of integrable boundary terms are determined. The boundary system is solved by means of the coordinate space Bethe ansatz technique and the Bethe ansatz equations are derived. As a sideline, it is shown that all R-matrices associated with a quantum affine superalgebra enjoy the crossing-unitarity property.     

开边界条件下一类新Hubbard模型的精确解

用坐标Bethe ansatz方法详细研究了开边界条件下一类新Hubbard模型的可积性问题. 得到了系统的能谱、可积边界条件和Bethe ansatz方程.     

Integrable open boundary conditions for the Bariev model of three coupled XY spin chains

The integrable open-boundary conditions for the Bariev model of three coupled one-dimensional XY spin chains are studied in the framework of the boundary quantum inverse scattering method. Three kinds of diagonal boundary K-matrices leading to nine classes of possible choices of boundary fields are found and the corresponding integrable boundary terms are presented explicitly. The boundary Hamiltonian is solved by using the coordinate Bethe ansatz technique and the Bethe ansatz equations are derived.