相关论文: Rational Q-systems at Root of Unity I. Closed Chai…

We propose an effective Bethe ansatz for solving quantum many-body systems near an integrable point. Our approach retains the functional form of the Bethe wave function while renormalizing the Bethe roots to account for…

The modified algebraic Bethe ansatz, introduced by Cramp\'e and the author [8], is used to characterize the spectral problem of the Heisenberg XXZ spin-$\frac{1}{2}$ chain on the segment with lower and upper triangular boundaries. The…

We propose that the Baxter $Q$-operator for the spin-1/2 XXZ quantum spin chain is given by the $j\to \infty$ limit of the transfer matrix with spin-$j$ (i.e., $(2j+1)$-dimensional) auxiliary space. Applying this observation to the open…

We prove that physical solutions to the Heisenberg spin chain Bethe ansatz equations are exactly obtained by imposing two zero-remainder conditions. This bridges the gap between different criteria, yielding an alternative proof of a…

Since a long-time, the quantum integrable systems have remained an area where modern mathematical methods have given an access to interesting results in the study of physical systems. The exact computations, both numerical and asymptotic,…

We generalize our recent explicit construction of the full hierarchy of Baxter Q-operators of compact spin chains with su(n) symmetry to the supersymmetric case su(n|m). The method is based on novel degenerate solutions of the graded…

Using the Baxter's T-Q relation derived from the transfer matrix technique, we consider the diagonalization problem of discrete quantum pendulum and discrete quantum sine-Gordon Hamiltonian from the algebraic geometry aspect. For a finite…

In this paper we investigate an integrable loop model and its connection with a supersymmetric spin chain. The Bethe Ansatz solution allows us to study some properties of the ground state. When the loop fugacity $q$ lies in the physical…

Several quantum many-body models in one dimension possess exact solutions via the Bethe ansatz method, which has been highly successful for understanding their behavior. Nevertheless, there remain physical properties of such models for…

We solve the spectrum pf the closed Temperley-Lieb quantum spin chains using the coordinate Bethe ansatz. These Hamiltonians are invariante under the quantum group $U_{q}[sl(2)]$

The open spin-1/2 XXZ spin chain with diagonal boundary magnetic fields is the paradigmatic example of a quantum integrable model with open boundary conditions. We formulate a quantum algorithm for preparing Bethe states of this model,…

We study integrable vertex models and quantum spin chains with toroidal boundary conditions. An interesting class of such boundaries is associated with non-diagonal twist matrices. For such models there are no trivial reference states upon…

Baxter's TQ-equation is solved for the six-vertex model using the representation theory of quantum groups at roots of unity. A novel simplified construction of the Q-operator is given depending on a new free parameter. Specializing this…

We consider the preparation of all the eigenstates of spin chains using quantum circuits. It is known that generic eigenstates of free-fermionic spin chains can be prepared with circuits whose depth grows only polynomially with the length…

The spin-1/2 Heisenberg antiferromagnetic chain is the canonical example of an integrable quantum many-body model. Despite its exact solvability, explicit finite-size solutions are typically only accessible via numerical evaluation of the…

We show that eigenvalues of the family of Baxter Q-operators for supersymmetric integrable spin chains constructed with the gl(K|M)-invariant $R$-matrix obey the Hirota bilinear difference equation. The nested Bethe ansatz for super spin…

We propose that the Baxter's $Q$-operator for the XYZ quantum spin chain with open boundary conditions is given by the $j\to \infty$ limit of the corresponding transfer matrix with spin-$j$ (i.e., $(2j+1)$-dimensional) auxiliary space. The…

In this article we have discovered a close relationship between the (algebraic) Bethe Ansatz equations of the spin $s$ XXZ model of a finite size and the $q$-Sturm-Liouville problem. We have demonstrated that solutions of the Bethe Ansatz…

We give a brief review on the use of Bethe ansatz techniques to construct solutions of recursive functional equations which emerged in a bootstrap approach to the quantum Ernst system. The construction involves two particular limits of a…

The Bethe equations for the isotropic periodic spin-1/2 Heisenberg chain with N sites have solutions containing i/2, -i/2 that are singular: both the corresponding energy and the algebraic Bethe ansatz vector are divergent. Such solutions…