Article
Physics, Particles & Fields
Xiang-Mao Ding, Tinglyer Zhang
Summary: This study extends previous research by demonstrating the one-to-one correspondence between supersymmetric vacua in three-dimensional N=2 gauge theories and the eigenstates of XXZ integrable spin chain Hamiltonians with open boundary conditions. The researchers explore the A2 quiver gauge theory and the sl3 open XXZ spin chain with diagonal boundary condition, and establish the correspondence between the vacuum equations of different gauge groups and Bethe Ansatz equations with different boundary parameters. Furthermore, they extend this research to the general Ar quiver gauge theory.
Article
Physics, Particles & Fields
Nikolay Gromov, Fedor Levkovich-Maslyuk, Paul Ryan
Summary: In this paper, we have made progress in developing the separation of variables program for integrable spin chains with gl symmetry by explicitly finding the matrix elements of the SoV measure for the first time. This enabled us to compute correlation functions and wave function overlaps in a simple determinant form. Our results also include the representation of overlaps between on-shell and off-shell algebraic Bethe states, as well as between Bethe states with different twists, in a determinant form, which is particularly relevant for AdS/CFT applications.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Particles & Fields
Rafael I. Nepomechie, Ana L. Retore
Summary: The effect of introducing a boundary inhomogeneity in the transfer matrix of an integrable open quantum spin chain was investigated, where a local Hamiltonian can be constructed and quantum group symmetry can be achieved. The boundary inhomogeneity has a profound effect on the Bethe ansatz solution.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Mechanics
Feng Pan, Yao-Zhong Zhang, Xiaohan Qi, Yue Liang, Yuqing Zhang, Jerry P. Draayer
Summary: The Bethe ansatz solution of the two-axis two-spin Hamiltonian is derived using the Jordan-Schwinger boson realization of the SU(2) algebra. The solution of the Bethe ansatz equations corresponds to zeros of the extended Heine-Stieltjes polynomials. Symmetry properties of excited levels and zeros of the polynomials are discussed, with a detailed study of the case of two equal spins showing symmetric levels and well-entangled excited states.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2021)
Article
Physics, Particles & Fields
Kang Lu
Summary: We study the gl(m|n) XXX spin chains defined on tensor products of highest weight gl(m|n)-modules. We show that the on-shell Bethe vectors are eigenvectors of higher transfer matrices and compute the corresponding eigenvalues. Then we take the classical limits and obtain the corresponding results for the gl(m|n) Gaudin models.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)
Article
Physics, Particles & Fields
Nikolay Gromov, Nicolo Primi, Paul Ryan
Summary: In this paper, we study integrable SI(N) spin chains, which are not only exemplary quantum integrable systems but also have a wide range of applications. Using the Functional Separation of Variables (FSoV) technique and a new tool called Character Projection, we calculate all matrix elements of a complete set of operators, called principal operators, in the basis diagonalizing the conserved charges. We then derive determinant forms for the form-factors of multiple principal operators between arbitrary factorizable states, proving that the set of principal operators generates the complete spin chain Yangian. We also obtain the representation of these operators in the SoV bases, allowing the computation of correlation functions with any number of principal operators.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Gwenaeel Ferrando, Rouven Frassek, Vladimir Kazakov
Summary: The authors propose the full system of Baxter Q-functions (QQ-system) for integrable spin chains with the symmetry of the D-r Lie algebra. They use this system to derive new Weyl-type formulas expressing transfer matrices in all symmetric and antisymmetric representations through r + 1 basic Q-functions, which are consistent with the Q-operators recently proposed by one of the authors and verified explicitly at small finite length on the level of operators.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Mathematical
Joao Caetano, Shota Komatsu
Summary: In this paper, we study crosscap states in integrable field theories and spin chains. We derive exact formulas for overlaps and entropies, and find that they generally decrease along the renormalization group flow. We also discuss the applications of crosscap states in quantum quench and their relations to other models.
JOURNAL OF STATISTICAL PHYSICS
(2022)
Article
Materials Science, Multidisciplinary
Parameshwar R. Pasnoori, Junhyun Lee, J. H. Pixley, Natan Andrei, Patrick Azaria
Summary: In this work, the spin-1/2 Heisenberg chain with boundary magnetic fields is studied using a combination of Bethe ansatz and density matrix renormalization group (DMRG) techniques. Different ground states and high-energy bound states are observed depending on the orientation and strength of the boundary magnetic fields. The number of towers in the Hilbert space also changes, indicating a boundary eigenstate phase transition (BEPT). The magnetization profile shows a qualitative change across the critical field. However, it is unclear if the observed phenomena correspond to a genuine phase transition in the ground state.
Article
Physics, Particles & Fields
Tamas Gombor
Summary: This study focuses on the integrable crosscap states of integrable quantum spin chains and classifies them for gl(N) symmetric models. It also provides a derivation for the exact overlaps between the integrable crosscap states and the Bethe states, showing that the normalized overlaps of multi-particle states are ratios of Gaudin-like determinants. Additionally, it collects integrable crosscap states that may be relevant in the AdS/CFT correspondence.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Miao He, Yunfeng Jiang
Summary: The notion of a crosscap state, first defined in 2d CFT, has been generalized to 2d massive integrable quantum field theories and integrable spin chains. It has been shown that the crosscap states preserve integrability. The exact overlap formula of the crosscap state and the on-shell Bethe states has been derived, and the conjectured overlap formula for integrable spin chains has been rigorously proven by coordinate Bethe ansatz. Furthermore, the quench dynamics and dynamical correlation functions of the crosscap state have been studied.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)
Article
Physics, Particles & Fields
Jiaju Zhang, M. A. Rajabpour
Summary: We study the entanglement content of magnon excited states in integrable spin chains and classify it in the scaling limit. We find that when the number of excited magnons is small compared to the system size, the entanglement content can be decomposed into the sum of entanglement of particular excited states in free fermionic or bosonic theories. We also conjecture a classification of the entanglement content of translational invariant free fermionic and bosonic Hamiltonians based on the entanglement content of fermionic and bosonic chains with the number operator as the Hamiltonian.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Multidisciplinary
Nafiz Ishtiaque, Seyed F. Moosavian, Surya Raghavendran, Junya Yagi
Summary: This study presents a correspondence between two-dimensional N = (2, 2) supersymmetric gauge theories and rational integrable gl(m | j) spin chains, mapping them through brane configurations in string theory. It also provides a string theory derivation of a similar correspondence for rational gl(m | n) spin chains proposed by Nekrasov.
Article
Astronomy & Astrophysics
Wei Wang, Yi Qiao, Rong-Hua Liu, Wu-Ming Liu, Junpeng Cao
Summary: This study focuses on the exact elementary excitations in a U(1) symmetry broken quantum integrable system, specifically the twisted J1-J2 spin chain with various spin interactions. The energy spectrum is quantified using zero roots of the transfer matrix, leading to the determination of ground state energy and elementary excitations in the thermodynamic limit. Additionally, nearly degenerate states and the possibility of gapless low-lying excitations and quantum phase transitions are observed in certain regimes of the system.
Article
Physics, Particles & Fields
Charlotte Kristjansen, Dennis Muller, Konstantin Zarembo
Summary: This paper discusses the integrable boundary states of the PSU(2,2|4) super spin chain underlying the AdS/CFT correspondence, as well as the overlaps between Bethe eigenstates and these boundary states encoding one-point functions of conformal operators. It also explores the relationships between different Dynkin diagrams of super Lie algebras and how overlap formulae transform between them.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
