Quantum integrability and Bethe ansatz solution for interacting matter-radiation systems

Calculation of Atomic Number States: a Bethe Ansatz Approach

We analyze the conditions for producing atomic number states in a one-dimensional optical box using the Bethe ansatz method. This approach provides a general framework, enabling the study of number state production over a wide range of realistic experimental parameters.

The Algebraic Bethe Ansatz and Tensor Networks

We describe the Algebraic Bethe Ansatz for the spin-1/2 XXX and XXZ Heisenberg chains with open and periodic boundary conditions in terms of tensor networks. These Bethe eigenstates have the structure of Matrix Product States with a conserved number of down-spins. The tensor network formulation suggestes possible extensions of the Algebraic Bethe Ansatz to two dimensions.

Refinement of Bethe ansatz string and its alternative

The well known string solution to Bethe ansatz equations is shown to be inconsistent in its widely accepted form. A valid refinement demanding higher order corrections in subsequent roots is identified. A new alternative string solution is proposed for finite long chains, consistent with the non-Bethe strings observed earlier.

作为量子电路的Bethe Ansatz

The Bethe Ansatz as a Quantum Circuit

该研究针对Bethe ansatz量子电路形式缺乏量子门解析推导的问题，通过全面研究其转化过程得到电路门解析表达式，提出构建Bethe波函数的新型矩阵乘积态网络图解规则，为其坐标与代数版本等价性提供新视角。

Bethe Ansatz Solutions for Certain Periodic Quantum Circuits

I derived Bethe Ansatz equations for two model Periodic Quantum Circuits: 1) XXZ model; 2) Chiral Hubbard Model. I obtained explicit expressions for the spectra of the strings of any length. These analytic results may be useful for calibration and error mitigations in modern engineered quantum platforms.

Derivation of Matrix Product Ansatz for the Heisenberg Chain from Algebraic Bethe Ansatz

We derive a matrix product representation of the Bethe ansatz state for the XXX and XXZ spin-1/2 Heisenberg chains using the algebraic Bethe ansatz. In this representation, the components of the Bethe eigenstates are expressed as traces of products of matrices which act on ${\bar {\mathscr H}}$, the tensor product of auxiliary spaces. By changing the basis in ${\bar {\mathscr H}}$, we derive explicit finite-dimensional representations for the matrices. These matrices are the same as those appearing in the recently proposed matrix product ansatz by Alcaraz and Lazo [Alcaraz F C and Lazo M J 200…