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Related papers: Exact solution of an su(n) spin torus

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We consider a unitary circuit where the underlying gates are chosen to be R-matrices satisfying the Yang-Baxter equation and correlation functions can be expressed through a transfer matrix formalism. These transfer matrices are no longer…

Quantum Physics · Physics 2022-01-12 Pieter W. Claeys , Jonah Herzog-Arbeitman , Austen Lamacraft

The nested off-diagonal Bethe ansatz method is proposed to diagonalize multi-component integrable models with generic integrable boundaries. As an example, the exact solutions of the su(n)-invariant spin chain model with both periodic and…

High Energy Physics - Theory · Physics 2015-06-18 Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

The general expression for the local matrix $L(\theta)$ of a quantum chain with the site space in any representation of $su(3)$ is obtained. This is made by generalizing $L(\theta)$ from the fundamental representation and imposing the…

Condensed Matter · Physics 2016-08-31 J. Abad , M. Rios

We prove an inversion identity for the open AdS/CFT SU(1|1) quantum spin chain which is exact for finite size. We use this identity, together with an analytic ansatz, to determine the eigenvalues of the transfer matrix and the corresponding…

High Energy Physics - Theory · Physics 2009-02-05 Rafael I. Nepomechie , Eric Ragoucy

We consider the case of an integrable quantum spin chain with "soliton non-peserving" boundary conditions. This is the first time that such boundary conditions have been considered in the spin chain framework. We construct the transfer…

High Energy Physics - Theory · Physics 2008-11-26 Anastasia Doikou

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…

High Energy Physics - Theory · Physics 2010-04-05 Wen-Li Yang , Rafael I. Nepomechie , Yao-Zhong Zhang

We propose an expression for the eigenvalues of the transfer matrix for the $U_q(B_n)$-invariant open quantum spin chain associated with the fundamental representation of $A^{(2)}_{2n}$. By assumption, the Bethe Ansatz equations are…

High Energy Physics - Theory · Physics 2015-06-26 Simone Artz , Luca Mezincescu , Rafael I. Nepomechie

The off-diagonal Bethe Ansatz method [1] is used to revisit the periodic XXX Heisenberg spin-1/2 chain. It is found that the spectrum of the transfer matrix can be characterized by an inhomogeneous T-Q relation, a natural but nontrivial…

Mathematical Physics · Physics 2015-06-09 Yupeng Wang , Wen-Li Yang , Junpeng Cao , Kangjie Shi

We employ the analytic Bethe Anzats to construct eigenvalues of transfer matrices with finite-dimensional atypical representations in the auxiliary space for the putative long-range spin chain encoding anomalous dimensions of all composite…

High Energy Physics - Theory · Physics 2008-11-26 A. V. Belitsky

We study an integrable noncompact superspin chain model that emerged in recent studies of the dilatation operator in the N=1 super-Yang-Mills theory. It was found that the latter can be mapped into a homogeneous Heisenberg magnet with the…

High Energy Physics - Theory · Physics 2011-02-16 A. V. Belitsky , S. E. Derkachov , G. P. Korchemsky , A. N. Manashov

We investigate the $t$-$W$ scheme for the anti-ferromagnetic XXX spin chain under both periodic and open boundary conditions. We propose a new parametrization of the eigenvalues of transfer matrix. Based on it, we obtain the exact solution…

Mathematical Physics · Physics 2023-12-08 Yi Qiao , Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

We review recent results on the Bethe Ansatz solutions for the eigenvalues of the transfer matrix of an integrable open XXZ quantum spin chain using functional relations which the transfer matrix obeys at roots of unity. First, we consider…

High Energy Physics - Theory · Physics 2008-11-26 Rajan Murgan

We study the exact solutions of quantum integrable model associated with the $C_n$ Lie algebra, with either a periodic or an open one with off-diagonal boundary reflections, by generalizing the nested off-diagonal Bethe ansatz method.…

Mathematical Physics · Physics 2021-02-25 Guang-Liang Li , Panpan Xue , Pei Sun , Hulin Yang , Xiaotian Xu , Junpeng Cao , Tao Yang , Wen-Li Yang

Generic inhomogeneous integrable XXZ chains with arbitrary spins are studied by means of the quantum separation of variables (SOV) method. Within this framework, a complete description of the spectrum (eigenvalues and eigenstates) of the…

Mathematical Physics · Physics 2014-11-25 G. Niccoli , V. Terras

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…

High Energy Physics - Theory · Physics 2008-11-26 Vladimir Kazakov , Alexander Sorin , Anton Zabrodin

The $SU_{q}(n)$ generators are obtained as large spectral parameter limit of the Yang-Baxter operators in the integrable $SU_{q}(n)$ invariant vertex model. The commutation relations, including Serre relations, are obtained as limits of the…

High Energy Physics - Theory · Physics 2009-10-28 H. J. de Vega , A. González--Ruiz

The Nested Bethe Ansatz is generalized to open boundary conditions. This is used to find the exact eigenvectors and eigenvalues of the $A_{n-1}$ vertex model with fixed open boundary conditions and the corresponding $SU_{q}(n)$ invariant…

High Energy Physics - Theory · Physics 2009-10-22 H. J. de Vega , A. González--Ruiz

The antiperiodic transfer matrix associated to higher spin representations of the rational 6-vertex Yang-Baxter algebra is analyzed by generalizing the approach introduced recently in [1], for the cyclic representations, in [2], for the…

Mathematical Physics · Physics 2013-06-04 G. Niccoli

Based on the inhomogeneous T-Q relation and the associated Bethe Ansatz equations obtained via the off-diagonal Bethe Ansatz, we construct the Bethe-type eigenstates of the SU(2)-invariant spin-s chain with generic non-diagonal boundaries…

Mathematical Physics · Physics 2016-08-18 Lijun Yang , Xin Zhang , Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

With the off-diagonal Bethe ansatz method proposed recently by the present authors, we exactly diagonalize the $XXX$ spin chain with arbitrary boundary fields. By constructing a functional relation between the eigenvalues of the transfer…

Mathematical Physics · Physics 2015-06-16 Junpeng Cao , Wenli Yang , Kangjie Shi , Yupeng Wang