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Hierarchy of modes in an interacting one-dimensional system
O Tsyplyatyev1, A J Schofield1, Y Jin2
1School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom.
Physical Review Letters
|May 30, 2015
Summary
We theoretically and experimentally discovered a hierarchy of interacting fermion excitations in one dimension. This hierarchy, separated by interaction and system length scales, reveals distinct spectral weight patterns.
Area of Science:
- Condensed Matter Physics
- Quantum Mechanics
- Low-Dimensional Systems
Background:
- Interacting fermions in one dimension exhibit complex quantum phenomena.
- Understanding spectral properties is crucial for characterizing these systems.
- High-energy excitations in such systems remain an active area of research.
Purpose of the Study:
- To theoretically predict and experimentally observe a hierarchy of spectral weights in interacting one-dimensional fermions.
- To characterize the dispersion relations and line shapes of these excitations.
- To investigate the role of spin-charge separation in the observed phenomena.
Main Methods:
- Theoretical diagonalization of a spinless fermion model.
- Analysis of spectral weight hierarchy based on interaction (R) and system (L) length scales.
- Experimental measurement of momentum-resolved tunneling in a GaAs heterostructure wire.
- Observation of electron (fermions with spin) tunneling dynamics.
Main Results:
- A theoretical hierarchy of spectral weights for excitations, separated by powers of R²/L².
- Identification of first-level excitations with parabolic dispersion, akin to renormalized single particles.
- Experimental observation of parabolic dispersion for first-level modes.
- Evidence for second-level excitations manifesting as singular power-law line shapes and spectral edge features.
- Observation of spin-charge separation at low energies in the experimental system.
Conclusions:
- The study confirms a predicted hierarchy of interacting fermion excitations in one dimension.
- Experimental data supports the theoretical model, including parabolic dispersion and evidence of higher-level excitations.
- The findings provide insights into the complex spectral properties of strongly interacting one-dimensional quantum systems.
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