Quantum integrability provides a unique and powerful framework for accurately understanding quantum magnetism.In this review,we focus specifically on several quantum integrable low-dimensional quantum Ising models.We ...Quantum integrability provides a unique and powerful framework for accurately understanding quantum magnetism.In this review,we focus specifically on several quantum integrable low-dimensional quantum Ising models.We begin with the transverse field Ising chain(TFIC)at quantum critical point and examine how it evolves under perturbations,such as an applied longitudinal field or weak coupling to another quantum critical TFIC.展开更多
In this article,a Generalized Calogero-Bogoyavlenskii-Schiff(CBS)equation is studied,serving as an extended shallow water wave model in higher dimensions.Firstly,utilizing the Bell polynomial method,the bilinear form ...In this article,a Generalized Calogero-Bogoyavlenskii-Schiff(CBS)equation is studied,serving as an extended shallow water wave model in higher dimensions.Firstly,utilizing the Bell polynomial method,the bilinear form of the equation,bilinear Bäcklund transformation,Lax pair and infinite conservation laws are derived,confirming the equation’s complete integrability in the context of the Lax pair.Subsequently,the nonlinear superposition formula of the equation is constructed based on the derived bilinear Bäcklund transformation and an array of infinite superposition soliton solutions of the equation are formulated using this nonlinear superposition formula.Lastly,leveraging the obtained bilinear equation,infinite superposition solutions of various functional types are constructed.Their dynamic characteristics are analyzed through illustrated solution images.It is noteworthy that this paper not only uncovers a multitude of properties through the Bell polynomial method but also derives both infinite linear and nonlinear superposition solutions,enriching the diversity of solutions,these aspects have not been previously explored in existing literature.展开更多
基金supported by the National Natural Science Foundation of China Grant Nos.12450004,12274288the Innovation Program for Quantum Science and Technology Grant No.2021ZD0301900。
文摘Quantum integrability provides a unique and powerful framework for accurately understanding quantum magnetism.In this review,we focus specifically on several quantum integrable low-dimensional quantum Ising models.We begin with the transverse field Ising chain(TFIC)at quantum critical point and examine how it evolves under perturbations,such as an applied longitudinal field or weak coupling to another quantum critical TFIC.
基金the Natural Science Foundation of Inner Mongolia Autonomous Region(Grant No.2024MS01003)the First-Class Disciplines Project,Inner Mongolia Autonomous Region,China(Grant Nos.YLXKZX-NSD-001 and YLXKZX-NSD-009)the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region(Grant No.NMGIRT2414).
文摘In this article,a Generalized Calogero-Bogoyavlenskii-Schiff(CBS)equation is studied,serving as an extended shallow water wave model in higher dimensions.Firstly,utilizing the Bell polynomial method,the bilinear form of the equation,bilinear Bäcklund transformation,Lax pair and infinite conservation laws are derived,confirming the equation’s complete integrability in the context of the Lax pair.Subsequently,the nonlinear superposition formula of the equation is constructed based on the derived bilinear Bäcklund transformation and an array of infinite superposition soliton solutions of the equation are formulated using this nonlinear superposition formula.Lastly,leveraging the obtained bilinear equation,infinite superposition solutions of various functional types are constructed.Their dynamic characteristics are analyzed through illustrated solution images.It is noteworthy that this paper not only uncovers a multitude of properties through the Bell polynomial method but also derives both infinite linear and nonlinear superposition solutions,enriching the diversity of solutions,these aspects have not been previously explored in existing literature.
