Decay of fermionic quasiparticles in one-dimensional quantum liquids.
The low-energy properties of one-dimensional quantum liquids are commonly described in terms of the Tomonaga-Luttinger liquid theory, in which the elementary excitations are free bosons. To this approximation, the theory can be alternatively recast in terms of free fermions. In both approaches, small perturbations give rise to finite lifetimes of excitations. We evaluate the decay rate of fermionic excitations and show that it scales as the eighth power of energy, in contrast to the much faster decay of bosonic excitations. Our results can be tested experimentally by measuring the broadening of power-law features in the density structure factor or spectral functions.
Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA.
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Matveev
Condensed Matter Theory Laboratory, RIKEN, Wako, Saitama 351-0198, Japan and RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan.
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Furusaki