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Nuclear Physics A

The response of many-fermion system in the framework of spectral function and momentum distribution

Majid Modarres, Younes Younesizadeh

Published Mar 14, 2007• 8 citations
Publisher
DOI
10.1016/j.nuclphysa.2007.03.002

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Within the impulse approximation, the response of a many-body system at large momentum transfer can be directly related to ground state properties. Although the physics assumptions underlying impulse approximation are well defined, their implementation involves ambiguities that may cause significant differences in the calculated responses. We show that, while minimal use of the impulse approximation assumptions naturally leads to write the response in terms of the spectral function, the alternative definition in terms of the momentum distribution involves a more extended use of the same assumptions.
To calculate static response properties of a many-body system, local density approximation (LDA) can be safely applied. But, to obtain dynamical response functions, the applicability of LDA is limited bacause dynamics of the system needs to be considered as well. To examine this in the context of cold atoms, we consider a system of non-interacting spin4 fermions confined by a harmonic trapping potential. We have calculated a very important response function, the spectral intensity distribution function (SIDF), both exactly and using LDA at zero temperature and compared with each other for different dimensions, trap frequencies and momenta. The behaviour of the SIDF at a particular momentum can be explained by noting the behaviour of the density of states (DoS) of the free system (without trap) in that particular dimension. The agreement between exact and LDA SIDFs becomes better with increase in dimensions and number of particles.
We calculate the spectral function of a one-dimensional strongly interacting chain of fermions, where the response can be well understood in terms of spinon and holon excitations. Upon increasing the spin imbalance between the spin species, we observe the single-electron response of the fully polarised system to emanate from the holon peak while the spinon response vanishes. For experimental setups that probe one-dimensional properties, we propose this method as an additional generic tool to aid the identification of spectral structures, e.g. in ARPES measurements. We show that this applies even to trapped systems having cold atomic gas experiments in mind. Calculations of the spectral function in a magnetic field are presented in the full momentum range for the first time.