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Exact solutions of quantum lattice models serve as useful guides for interpreting physical phenomena in condensed matter systems. Prominent examples of integrability appear in one dimension, including the Heisenberg chain, where the Bethe…

Strongly Correlated Electrons · Physics 2025-01-27 Ronald Melendrez , Bhaskar Mukherjee , Marcin Szyniszewski , Christopher J. Turner , Arijeet Pal , Hitesh J. Changlani

We propose a hole decomposition scheme to exactly solve a class of spin-1 quantum Ising models with transverse or longitudinal single-ion anisotropy. In this scheme, the spin-1 model is mapped onto a family of the $S=1/2$ transverse Ising…

Strongly Correlated Electrons · Physics 2009-07-17 Zhi-Hua Yang , Li-Ping Yang , Hai-Na Wu , Jianhui Dai , Tao Xiang

We consider solutions of the $2\times 2$ matrix Hamiltonian of physical systems within the context of the asymptotic iteration method. Our technique is based on transformation of the associated Hamiltonian in the form of the first order…

Quantum Physics · Physics 2009-11-13 R. Koc , O. Ozer , H. Tutunculer , R. G. Yildirim

We study S=1/2 quantum spin chains with shift-invariant and inversion-symmetric next-nearest-neighbor interaction, also known as zigzag spin chains. We completely classify the integrability and non-integrability of the above class of spin…

Statistical Mechanics · Physics 2026-04-13 Naoto Shiraishi

A general method is proposed for constructing the Bethe ansatz equations of integrable models without U(1) symmetry. As an example, the exact spectrum of the XXZ spin ring with M{\" o}bius like topological boundary condition is derived by…

Statistical Mechanics · Physics 2015-06-16 Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

We revisit the so-called folded XXZ model, which was treated earlier by two independent research groups. We argue that this spin-1/2 chain is one of the simplest quantum integrable models, yet it has quite remarkable physical properties.…

Statistical Mechanics · Physics 2021-10-13 Balázs Pozsgay , Tamás Gombor , Arthur Hutsalyuk , Yunfeng Jiang , Levente Pristyák , Eric Vernier

The high spin ultracold atom models with a special form of contact interactions, i.e., the scattering lengthes in the total spin-$2,4 \cdots$ channels are equal but may be different from that in the spin-0 channel, is studied. It is found…

Strongly Correlated Electrons · Physics 2011-08-23 Yuzhu Jiang , Junpeng Cao , Yupeng Wang

In the case of polynomial potentials all solutions to 1-D Schroedinger equation are entire functions totally determined by loci of their roots and their behaviour at infinity. In this paper a description of the first of the two properties…

Mathematical Physics · Physics 2009-11-13 Stefan Giller

It is known that for the Heisenberg XXZ spin-$\frac{1}{2}$ chain in the critical regime, the scaling limit of the vacuum Bethe roots yields an infinite set of numbers that coincide with the energy spectrum of the quantum mechanical 3D…

Mathematical Physics · Physics 2024-07-23 Sascha Gehrmann , Gleb A. Kotousov , Sergei L. Lukyanov

We define a variant of the Seiberg-Witten equations using the Rarita-Schwinger operators for closed simply connected spin smooth 4-manifold X. The moduli space of solutions to the system of non-linear differential equations consist of…

Differential Geometry · Mathematics 2023-06-08 Minh Lam Nguyen

The construction of analytic solutions for quasi-exactly solvable systems is an interesting problem. We revisit a class of models for which the odd solutions were largely missed previously in the literature: the anharmonic oscillator, the…

Mathematical Physics · Physics 2024-09-17 Siyu Li , Ian Marquette , Yao-Zhong Zhang

We complete the description of the circular, elliptic three spin string on AdS_5 x S^5 having three large angular momenta (J_1,J_2,J_3) on S^5 in the language of the integrable SU(3) spin chain. First, we recover the string solution…

High Energy Physics - Theory · Physics 2009-11-10 C. Kristjansen , T. Mansson

We consider the problem of a central spin with arbitrary spin s that interacts pairwise and uniformly with a bath of N spins with s=1/2. We present two approaches for determining the exact spectrum of this model, one based on properties of…

Quantum Physics · Physics 2018-11-14 Rafael I. Nepomechie , Xi-Wen Guan

The spin chains originating from large-N conformal gauge theories are of a special kind: The Hamiltonian is not invariant under the symmetry algebra, it is rather a part of it. This leads to interesting properties within the asymptotic…

High Energy Physics - Theory · Physics 2011-03-23 Niklas Beisert

The $Q$-system is an efficient method for finding complete physical solutions of Bethe ansatz equations, but so far its application has been confined to systems possessing $U(1)$ symmetry. We extend the rational $Q$-system framework to…

High Energy Physics - Theory · Physics 2025-12-02 Yunfeng Jiang , Yi-Chao Liu , Yuan Miao , Zi-Xi Tan

As part of a study that investigates the dynamics of the s=1/2 XXZ model in the planar regime |Delta|<1, we discuss the singular nature of the Bethe ansatz equations for the case Delta=0 (XX model). We identify the general structure of the…

Strongly Correlated Electrons · Physics 2009-11-10 Daniel Biegel , Michael Karbach , Gerhard Muller , Klaus Wiele

Dynamical correlation functions contain important physical information on correlated spin models. Here a dynamical theory suitable suitable to the isotropic spin-1/2 Heisenberg chain in a longitudinal magnetic field is extended to…

Strongly Correlated Electrons · Physics 2021-11-29 José M. P. Carmelo , Pedro D. Sacramento

We argue that the Hamiltonians for A_{2n}^(2) open quantum spin chains corresponding to two choices of integrable boundary conditions have the symmetries U_q(B_n) and U_q(C_n), respectively. We find a formula for the Dynkin labels of the…

Mathematical Physics · Physics 2017-06-20 Ibrahim Ahmed , Rafael I. Nepomechie , Chunguang Wang

The XXX spin-$\frac{1}{2}$ Heisenberg chain with non-diagonal boundary fields represents a cornerstone model in the study of integrable systems with open boundaries. Despite its significance, solving this model exactly has remained a…

Strongly Correlated Electrons · Physics 2026-01-21 Holger Frahm , Andreas Klümper , Dennis Wagner , Xin Zhang

We construct the exact solution for a family of one-half spin chains explicitly. The spin chains Hamiltonian corresponds to an isotropic Heisenberg Hamiltonian, with staggered exchange couplings that take only two different values. We work…

Quantum Physics · Physics 2022-10-07 Pablo Serra , Alejandro Ferrón , Omar Osenda