Momentum-dependent power law measured in an interacting quantum wire beyond the Luttinger limit
Abstract

Power laws in physics have until now always been associated with a scale invariance originating from the absence of a length scale. Recently, an emergent invariance even in the presence of a length scale has been predicted by the newly-developed nonlinear-Luttinger-liquid theory for a one-dimensional (1D) quantum fluid at finite energy and momentum, at which the particle’s wavelength provides the length scale. We present experimental evidence for this new type of power law in the spectral function of interacting electrons in a quantum wire using a transport-spectroscopy technique. The observed momentum dependence of the power law in the high-energy region matches the theoretical predictions, supporting not only the 1D theory of interacting particles beyond the linear regime but also the existence of a new type of universality that emerges at finite energy and momentum.

Authors:
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Publication Date:
NSF-PAR ID:
10153424
Journal Name:
Nature Communications
Volume:
10
Issue:
1
ISSN:
2041-1723
Publisher:
Nature Publishing Group
5. We consider the well-known Lieb-Liniger (LL) model for \begin{document}$N$\end{document} bosons interacting pairwise on the line via the \begin{document}$\delta$\end{document} potential in the mean-field scaling regime. Assuming suitable asymptotic factorization of the initial wave functions and convergence of the microscopic energy per particle, we show that the time-dependent reduced density matrices of the system converge in trace norm to the pure states given by the solution to the one-dimensional cubic nonlinear Schrödinger equation (NLS) with an explict rate of convergence. In contrast to previous work [3] relying on the formalism of second quantization and coherent states and without an explicit rate, our proof is based on the counting method of Pickl [65,66,67] and Knowles and Pickl [44]. To overcome difficulties stemming from the singularity of the \begin{document}$\delta$\end{document} potential, we introduce a new short-range approximation argument that exploits the Hölder continuity of the \begin{document}$N$\end{document}-body wave function in a single particle variable. By further exploiting the \begin{document}$L^2$\end{document}-subcritical well-posedness theory for the 1D cubic NLS, we can prove mean-field convergence when the limiting solution to the NLS has finitemore »