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arXiv · 0812.1046

Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit

Adilet Imambekov·Leonid I. Glazman
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Abstract

We consider zero temperature behavior of dynamic response functions of 1D systems near edges of support in momentum-energy plane $(k, ω).$ The description of the singularities of dynamic response functions near an edge $ε(k)$ is given by the effective Hamiltonian of a mobile impurity moving in a Luttinger liquid. For Galilean-invariant systems, we relate the parameters of such an effective Hamiltonian to the properties of the function $ε(k).$ This allows us to express the exponents which characterize singular response functions of spinless bosonic or fermionic liquids in terms of $ε(k)$ and Luttinger liquid parameters for any $k.$ For an antiferromagnetic Heisenberg spin-1/2 chain in a zero magnetic field, SU(2) invariance fixes the exponents from purely phenomenological considerations.

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Adilet Imambekov, Leonid I. Glazman. 2009-03-27. Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit. https://doi.org/10.1103/physrevlett.102.126405

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