The Precise Formula in a Sine Function Form of the norm of the Amplitude and the Necessary and Sufficient Phase Condition for Any Quantum Algorithm with Arbitrary Phase Rotations

Power of Sine Hamiltonian Operator for Estimating the Eigenstate Energies on Quantum Computers

Quantum computers have been shown to have tremendous potential in solving difficult problems in quantum chemistry. In this paper, we propose a new classical quantum hybrid method, named as power of sine Hamiltonian operator (PSHO), to evaluate the eigenvalues of a given Hamiltonian (H). In PSHO, for any reference state, the normalized energy of the sine Hamiltonian power state can be determined. With the increase of the power, the initial reference state can converge to the eigenstate with the largest absolute eigenvalue in the coefficients of the expansion of reference state, and the normaliz…

利用域变换和傅里叶正弦级数的高效局部化函数方法

Efficient method for localized functions using domain transformation and Fourier sine series

本文提出了一种在一维和三维空间中高效处理局部化状态的谱方法，通过将无限域转换为(0, π)域，并利用傅里叶正弦级数作为基函数，实现了高精度计算和高效性能，特别展示了对Hartree能量的高效计算。

Resurgence in sine-Gordon quantum mechanics: Exact agreement between multi-instantons and uniform WKB

We compute multi-instanton amplitudes in the sine-Gordon quantum mechanics (periodic cosine potential) by integrating out quasi-moduli parameters corresponding to separations of instantons and anti-instantons. We propose an extension of Bogomolnyi--Zinn-Justin prescription for multi-instanton configurations and an appropriate subtraction scheme. We obtain the multi-instanton contributions to the energy eigenvalue of the lowest band at the zeroth order of the coupling constant. For the configurations with only instantons (anti-instantons), we obtain unambiguous results. For those with both inst…

量子逆散射方法中的 sine-Gordon 模型在壳重整化

On-shell renormalization of sine-Gordon by the quantum inverse scattering method

该研究通过量子逆散射方法，利用盒子长度重标度与在壳条件定义 sine-Gordon 模型的重整化方案，吸收截断依赖，并导出孤子与呼吸子质量，揭示可积性与重整化的关联。

一维系统中量子临界点的正弦平方变形方法

A sine-square deformation approach to quantum critical points in one-dimensional systems

提出利用正弦平方变形（SSD）通过有限尺寸标度分析局域可观测量在热力学极限下的平移对称性来精确确定一维系统的量子临界点，并通过近邻和长程反铁磁伊辛链模型验证了方法的有效性。