The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.I...The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.In this paper,we introduce a Lie group that the Heisenberg group can be imbedded into and call it generalized complex Heisenberg.We investigate quaternionic analysis on the generalized complex Heisenberg.We also give the Penrose integral formula for k-CF functions and construct the tangential k-Cauchy-Fueter complex.展开更多
Motivated by the mathematical beauty and the recent experimental realizations of fractal systems,we study the spin-1/2 antiferromagnetic Heisenberg model on a Sierpiński gasket.The fractal porous feature generates ne...Motivated by the mathematical beauty and the recent experimental realizations of fractal systems,we study the spin-1/2 antiferromagnetic Heisenberg model on a Sierpiński gasket.The fractal porous feature generates new kinds of frustration to exhibit exotic quantum states.Using advanced tensor network techniques,we identify a quantum gapless-spin-liquid ground state in fractional spatial dimension.This fractal spin system also demonstrates nontrivial nonlocal properties.While the extremely short-range correlation causes a highly degenerate spin form factor,the entanglement in this fractal system suggests a long-range scaling behavior.We also study the dynamic structure factor and clearly identify the gapless excitation with a stable corner excitation emerged from the ground-state entanglement.Our results unambiguously point out multiple essential properties of this fractal spin system,and open a new route to explore spin liquid and frustrated magnetism.展开更多
Squaring the circle is one of the oldest challenges in mathematical geometry. In 1882, it was proven that π was transcendental, and the task of squaring the circle was considered impossible. Demonstrating that squari...Squaring the circle is one of the oldest challenges in mathematical geometry. In 1882, it was proven that π was transcendental, and the task of squaring the circle was considered impossible. Demonstrating that squaring the circle was not possible took place before discovering quantum mechanics. The purpose of this paper is to show that it is actually possible to square the circle when taking into account the Heisenberg uncertainty principle. The conclusion is clear: it is possible to square the circle when taking into account the Heisenberg uncertainty principle.展开更多
基金Supported by National Nature Science Foundation in China(12101564,11971425,11801508)Nature Science Foundation of Zhejiang province(LY22A010013)Domestic Visiting Scholar Teacher Professional Development Project(FX2021042)。
文摘The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.In this paper,we introduce a Lie group that the Heisenberg group can be imbedded into and call it generalized complex Heisenberg.We investigate quaternionic analysis on the generalized complex Heisenberg.We also give the Penrose integral formula for k-CF functions and construct the tangential k-Cauchy-Fueter complex.
基金the National Natural Science Foundation of China(Grant No.12274126)carried out during the virtual program“Tensor Networks in Many Body and Quantum Field Theory”held at the Institute for Nuclear Theory,University of Washington,Seattle(INT 21–1c)。
文摘Motivated by the mathematical beauty and the recent experimental realizations of fractal systems,we study the spin-1/2 antiferromagnetic Heisenberg model on a Sierpiński gasket.The fractal porous feature generates new kinds of frustration to exhibit exotic quantum states.Using advanced tensor network techniques,we identify a quantum gapless-spin-liquid ground state in fractional spatial dimension.This fractal spin system also demonstrates nontrivial nonlocal properties.While the extremely short-range correlation causes a highly degenerate spin form factor,the entanglement in this fractal system suggests a long-range scaling behavior.We also study the dynamic structure factor and clearly identify the gapless excitation with a stable corner excitation emerged from the ground-state entanglement.Our results unambiguously point out multiple essential properties of this fractal spin system,and open a new route to explore spin liquid and frustrated magnetism.
文摘Squaring the circle is one of the oldest challenges in mathematical geometry. In 1882, it was proven that π was transcendental, and the task of squaring the circle was considered impossible. Demonstrating that squaring the circle was not possible took place before discovering quantum mechanics. The purpose of this paper is to show that it is actually possible to square the circle when taking into account the Heisenberg uncertainty principle. The conclusion is clear: it is possible to square the circle when taking into account the Heisenberg uncertainty principle.
