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arXiv 2201.11101cond-mat.str-elmath-phmath.MPmath.NTphysics.comp-phquant-ph
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长程相互作用系统的精确连续统表示与非常规超导体中涌现的奇异相

Exact Continuum Representation of Long-range Interacting Systems and Emerging Exotic Phases in Unconventional Superconductors

Andreas A. Buchheit, Torsten Keßler, Peter K. Schuhmacher, Benedikt Fauseweh

AI总结:

本研究提出长程相互作用晶格的精确连续统表示方法,基于爱泼斯坦ζ函数描述晶格贡献,推导广义BCS能隙方程发现二维超导体奇异相,并证实长程相互作用可微调希格斯模式稳定性。

摘要:

连续统极限是多体系统研究中的有力工具,但在存在长程相互作用时,其有效性往往并不明确。在本研究中,我们严格解决了这一问题,提出了长程相互作用晶格的一种精确表示方法,将模型拆分为描述其连续对应体的项(即积分贡献),以及完全解析微观结构的项(即晶格贡献)。对于任意系统维度、任意晶格、任意幂律相互作用,以及线性、非线性和多原子晶格,我们证明晶格贡献可通过基于黎曼ζ函数的多维推广——即爱泼斯坦ζ函数(Epstein zeta function)——的微分算子来描述。我们在傅里叶空间中运用该表示方法,解决了长程相互作用非常规超导体这一重要问题。我们推导了广义的巴丁-库珀-施里弗(Bardeen–Cooper–Schrieffer)能隙方程,并在具有拓扑相变的二维超导体中发现了涌现的奇异相。最后,我们利用非平衡希格斯(Higgs)谱学分析了长程相互作用对凝聚体集体激发的影响。研究表明,这些相互作用可用于微调希格斯模式的稳定性,其范围从振荡振幅的指数衰减到完全稳定。

英文摘要:

Continuum limits are a powerful tool in the study of many-body systems, yet their validity is often unclear when long-range interactions are present. In this work, we rigorously address this issue and put forth an exact representation of long-range interacting lattices that separates the model into a term describing its continuous analog, the integral contribution, and a term that fully resolves the microstructure, the lattice contribution. For any system dimension, any lattice, any power-law interaction, and for linear, nonlinear, and multi-atomic lattices, we show that the lattice contribution can be described by a differential operator based on the multidimensional generalization of the Riemann zeta function, namely the Epstein zeta function. We employ our representation in Fourier space to solve the important problem of long-range interacting unconventional superconductors. We derive a generalized Bardeen--Cooper--Schrieffer gap equation and find emerging exotic phases in two-dimensional superconductors with topological phase transitions. Finally, we utilize non-equilibrium Higgs spectroscopy to analyze the impact of long-range interactions on the collective excitations of the condensate. We show that the interactions can be used to fine-tune the Higgs mode's stability, ranging from exponential decay of the oscillation amplitude up to complete stabilization.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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