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Abstract
The natural excitations of an interacting onedimensional system at low energy are hydrodynamic modes of Luttinger liquid, protected by the Lorentz invariance of the linear dispersion. We show that beyond low energies, where quadratic dispersion reduces the symmetry to Galilean, the main character of the manybody excitations changes into a hierarchy: calculations of dynamic correlation functions for fermions (without spin) show that the spectral weights of the excitations are proportional to powers of $\mathcal{R}^{2}/L^{2}$, where $\mathcal{R}$ is a lengthscale related to interactions and $L$ is the system length. Thus only small numbers of excitations carry the principal spectral power in representative regions on the energymomentum planes. We have analysed the spectral function in detail and have shown that the firstlevel (strongest) excitations form a mode with parabolic dispersion, like that of a renormalised single particle. The secondlevel excitations produce a singular powerlaw line shape to the firstlevel mode and multiple powerlaws at the spectral edge. We have illustrated crossover to Luttinger liquid at low energy by calculating the local density of state through all energy scales: from linear to nonlinear, and to above the chemical potential energies. In order to test this model, we have carried out experiments to measure momentumresolved tunnelling of electrons (fermions with spin) from/to a wire formed within a GaAs heterostructure. We observe wellresolved spincharge separation at low energy with appreciable interaction strength and only a parabolic dispersion of the firstlevel mode at higher energies. We find structure resembling the secondlevel excitations, which dies away rapidly at high momentum in line with the theoretical predictions here.
Original language  English 

Article number  075147 
Number of pages  21 
Journal  Physical Review B 
Volume  93 
Issue number  7 
DOIs  
Publication status  Published  24 Feb 2016 
Bibliographical note
23 pages, 10 figures, 2 tablesKeywords
 condmat.strel
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Dive into the research topics of 'Nature of the manybody excitations in a quantum wire: theory and experiment'. Together they form a unique fingerprint.Projects
 1 Finished

Beyond Luttinger LiquidsSpinCharge Separation at High Excitation Energies
Schofield, A.
Engineering & Physical Science Research Council
31/10/12 → 29/04/15
Project: Research Councils