We investigate the localization and topological properties of the Haldane model under the influence of random flux and Anderson disorder. Our localization analysis reveals that random flux induces a transition from in...We investigate the localization and topological properties of the Haldane model under the influence of random flux and Anderson disorder. Our localization analysis reveals that random flux induces a transition from insulating to metallic states, while Anderson localization only arises under the modulation of Anderson disorder. By employing real-space topological invariant methods, we demonstrates that the system undergoes topological phase transitions under different disorder manipulations, whereas random flux modulation uniquely induces topological Anderson insulator phases, with the potential to generate states with opposite Chern numbers. These findings highlight the distinct roles of disorder in shaping the interplay between topology and localization, providing insights into stabilizing topological states and designing robust topological quantum materials.展开更多
In this paper, in Section 1, we have described some equations and theorems concerning the Lebesgue integral and the Lebesgue measure. In Section 2, we have described the possible mathematical applications, of Lebesgue...In this paper, in Section 1, we have described some equations and theorems concerning the Lebesgue integral and the Lebesgue measure. In Section 2, we have described the possible mathematical applications, of Lebesgue integration, in some equations concerning various sectors of Chern-Simons theory and Yang-Mills gauge theory, precisely the two dimensional quantum Yang-Mills theory. In conclusion, in Section 3, we have described also the possible mathematical connections with some sectors of String Theory and Number Theory, principally with some equations concerning the Ramanujan’s modular equations that are related to the physical vibrations of the bosonic strings and of the superstrings, some Ramanujan’s identities concerning π and the zeta strings.展开更多
In this paper a gauge theory is proposed for the two-band model of Chern insulators.Based on the so-calle't Hooft monopole model,a U(1)Maxwell electromagnetic sub-field is constructed from an SU(2)gauge field,from...In this paper a gauge theory is proposed for the two-band model of Chern insulators.Based on the so-calle't Hooft monopole model,a U(1)Maxwell electromagnetic sub-field is constructed from an SU(2)gauge field,from which arise two types of topological defects,monopoles and e2 merons.We focus on the topological number in the Hall conductance σ_(xy)=e^(2)/hC,where C is the Chern number.It is discovered that in the monopole case C is indeterminate,while in the meron case C takes different values,due to a varying on-site energy m.As a typical example,we apply this method to the square lattice and compute the winding numbers(topological charges)of the defects;the C-evaluations we obtain reproduce the results of the usual literature.Furthermore,based on the gauge theory we propose a new model to obtain the high Chern numbers|C|=2,4.展开更多
This paper studies the induced Chern connection of submanifolds in a Finsler manifold and gets the relations between the induced Chern connection and the Chern connection of the induced Finsler metric. Then the author...This paper studies the induced Chern connection of submanifolds in a Finsler manifold and gets the relations between the induced Chern connection and the Chern connection of the induced Finsler metric. Then the authors point out a difference between Finsler submanifolds and Riemann submanifolds.展开更多
The Chern-Simons theory in two-space one-time dimensions is quantized on the light-front under appropriate gauge-fixing conditions using the Hamiltonian, path integral and BRST formulations.
Chern-Simon theory and the holographic principle as well as scale relativity are used to find out the exact value of cosmic ordinary and dark energy density. The result agrees completely with previously obtained ones ...Chern-Simon theory and the holographic principle as well as scale relativity are used to find out the exact value of cosmic ordinary and dark energy density. The result agrees completely with previously obtained ones as well as with accurate cosmic measurements.展开更多
This paper reconstructs,based on American and Chinese primary sources,the visits of Chinese mathematicians Shiing-shen Chern陈省身(Chen Xingshen)and Hua Luogeng华罗庚(Loo-Keng Hua)4 to the Institute for Advanced Study...This paper reconstructs,based on American and Chinese primary sources,the visits of Chinese mathematicians Shiing-shen Chern陈省身(Chen Xingshen)and Hua Luogeng华罗庚(Loo-Keng Hua)4 to the Institute for Advanced Study in Princeton in the United States in the 1940s,especially their interactions with Oswald Veblen and Hermann Weyl,two leading mathematicians at the IAS.It argues that Chern’s and Hua’s motivations and choices in regard to their transnational movements between China and the US were more nuanced and multifaceted than what is presented in existing accounts,and that socio-political factors combined with professional-personal ones to shape their decisions.The paper further uses their experiences to demonstrate the importance of transnational scientific interactions for the development of science in China,the US,and elsewhere in the twentieth century.展开更多
The Chern number is often used to distinguish different topological phases of matter in two-dimensional electron systems. A fast and efficient coupling-matrix method is designed to calculate the Chern number in finite...The Chern number is often used to distinguish different topological phases of matter in two-dimensional electron systems. A fast and efficient coupling-matrix method is designed to calculate the Chern number in finite crystalline and disordered systems. To show its effectiveness, we apply the approach to the Haldane model and the lattice Hofstadter model, and obtain the correct quantized Chern numbers. The disorder-induced topological phase transition is well reproduced, when the disorder strength is increased beyond the critical value. We expect the method to be widely applicable to the study of topological quantum numbers.展开更多
Using Feynman path integral method we calculate the Casimir force of Maxwell Chern Simons Abelian gauge field between perfectly conducting parallel lines.
基金Project supported by the National Key Research and Development Program of China (Grant Nos. 2021YFA1400900, 2021YFA0718300, and 2021YFA1402100)the National Natural Science Foundation of China (Grant Nos. 12174461, 12234012, 12334012, and 52327808)。
文摘We investigate the localization and topological properties of the Haldane model under the influence of random flux and Anderson disorder. Our localization analysis reveals that random flux induces a transition from insulating to metallic states, while Anderson localization only arises under the modulation of Anderson disorder. By employing real-space topological invariant methods, we demonstrates that the system undergoes topological phase transitions under different disorder manipulations, whereas random flux modulation uniquely induces topological Anderson insulator phases, with the potential to generate states with opposite Chern numbers. These findings highlight the distinct roles of disorder in shaping the interplay between topology and localization, providing insights into stabilizing topological states and designing robust topological quantum materials.
文摘In this paper, in Section 1, we have described some equations and theorems concerning the Lebesgue integral and the Lebesgue measure. In Section 2, we have described the possible mathematical applications, of Lebesgue integration, in some equations concerning various sectors of Chern-Simons theory and Yang-Mills gauge theory, precisely the two dimensional quantum Yang-Mills theory. In conclusion, in Section 3, we have described also the possible mathematical connections with some sectors of String Theory and Number Theory, principally with some equations concerning the Ramanujan’s modular equations that are related to the physical vibrations of the bosonic strings and of the superstrings, some Ramanujan’s identities concerning π and the zeta strings.
基金The authors XL and ZC acknowledge the financial support from the Natural Science Foundation of Beijing Grant No.Z180007the National Science Foundation of China Grant No.11572005WH acknowledges the support from the National Science Foundation of China Grant No.11874003 and Grant No.51672018.
文摘In this paper a gauge theory is proposed for the two-band model of Chern insulators.Based on the so-calle't Hooft monopole model,a U(1)Maxwell electromagnetic sub-field is constructed from an SU(2)gauge field,from which arise two types of topological defects,monopoles and e2 merons.We focus on the topological number in the Hall conductance σ_(xy)=e^(2)/hC,where C is the Chern number.It is discovered that in the monopole case C is indeterminate,while in the meron case C takes different values,due to a varying on-site energy m.As a typical example,we apply this method to the square lattice and compute the winding numbers(topological charges)of the defects;the C-evaluations we obtain reproduce the results of the usual literature.Furthermore,based on the gauge theory we propose a new model to obtain the high Chern numbers|C|=2,4.
文摘This paper studies the induced Chern connection of submanifolds in a Finsler manifold and gets the relations between the induced Chern connection and the Chern connection of the induced Finsler metric. Then the authors point out a difference between Finsler submanifolds and Riemann submanifolds.
文摘The Chern-Simons theory in two-space one-time dimensions is quantized on the light-front under appropriate gauge-fixing conditions using the Hamiltonian, path integral and BRST formulations.
文摘Chern-Simon theory and the holographic principle as well as scale relativity are used to find out the exact value of cosmic ordinary and dark energy density. The result agrees completely with previously obtained ones as well as with accurate cosmic measurements.
文摘This paper reconstructs,based on American and Chinese primary sources,the visits of Chinese mathematicians Shiing-shen Chern陈省身(Chen Xingshen)and Hua Luogeng华罗庚(Loo-Keng Hua)4 to the Institute for Advanced Study in Princeton in the United States in the 1940s,especially their interactions with Oswald Veblen and Hermann Weyl,two leading mathematicians at the IAS.It argues that Chern’s and Hua’s motivations and choices in regard to their transnational movements between China and the US were more nuanced and multifaceted than what is presented in existing accounts,and that socio-political factors combined with professional-personal ones to shape their decisions.The paper further uses their experiences to demonstrate the importance of transnational scientific interactions for the development of science in China,the US,and elsewhere in the twentieth century.
基金Project supported by the National Basic Research Program of China(Grant Nos.2009CB929504,2011CB922103,and 2010CB923400)the National Natural Science Foundation of China(Grant Nos.11225420,11074110,11174125,11074109,11074111,and 91021003)+3 种基金the Priority Academic Program Development of Jiangsu Higher Education Institutions,Chinathe Natural Science Foundation of Jiangsu Province,China(Grant No.BK2010364)the US NSF(Grant Nos.DMR-0906816 and DMR-1205734)he Princeton MRSEC(Grant No.DMR-0819860)
文摘The Chern number is often used to distinguish different topological phases of matter in two-dimensional electron systems. A fast and efficient coupling-matrix method is designed to calculate the Chern number in finite crystalline and disordered systems. To show its effectiveness, we apply the approach to the Haldane model and the lattice Hofstadter model, and obtain the correct quantized Chern numbers. The disorder-induced topological phase transition is well reproduced, when the disorder strength is increased beyond the critical value. We expect the method to be widely applicable to the study of topological quantum numbers.
文摘Using Feynman path integral method we calculate the Casimir force of Maxwell Chern Simons Abelian gauge field between perfectly conducting parallel lines.
