Title: Signatures of Majorana Zero-Modes in an isolated one-dimensional superconductor Show Chinese title

Title: 孤立一维超导体中马约拉纳零模的签名

Abstract: We examine properties of the mean-field wave function of the one-dimensional Kitaev model supporting Majorana Zero Modes (MZMs) \emph{when restricted} to a fixed number of particles. Such wave functions can in fact be realized as exact ground states of interacting number-conserving Hamiltonians and amount to a more realistic description of the finite isolated superconductors. Akin to their mean-field parent, the fixed-number wave functions encode a single electron spectral function at zero energy that decays exponentially away from the edges, with a localization length that agrees with the mean-field value. Based purely on the structure of the number-projected ground states, we construct the fixed particle number generalization of the MZM operators. They can be used to compute the edge tunneling conductance; however, notably the value of the zero-bias conductance remains the same as in the mean-field case, quantized to $2e^2/h$. We also compute the topological entanglement entropy for the number-projected wave functions and find that it contains a `robust' $\log(2)$ component as well as a logarithmic correction to the mean field result, which depends on the precise partitioning used to compute it. The presence of the logarithmic term in the entanglement entropy indicates the absence of a spectral gap above the ground state; as one introduces fluctuations in the number of particles, the correction vanishes smoothly. Show Chinese abstract

Abstract: 我们研究了一维Kitaev模型的平均场波函数在固定粒子数下的性质，该模型支持马约拉纳零模（MZMs）\emph{当受限时}。这样的波函数实际上可以作为相互作用的粒子数守恒哈密顿量的精确基态，并且更真实地描述了有限孤立超导体。与它们的平均场父态类似，固定粒子数的波函数在零能量处编码了一个单电子谱函数，该函数从边缘开始呈指数衰减，其局域化长度与平均场值一致。仅基于粒子数投影基态的结构，我们构建了MZM算符的固定粒子数推广形式。它们可用于计算边缘隧穿电导；然而值得注意的是，零偏压电导的值与平均场情况相同，被量化为$2e^2/h$。我们还计算了粒子数投影波函数的拓扑纠缠熵，发现它包含一个“鲁棒”的$\log(2)$成分，以及对平均场结果的对数修正，该修正取决于用于计算它的精确分割方式。纠缠熵中对数项的存在表明，在基态之上没有能隙；当引入粒子数的涨落时，该修正平滑地消失。