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Universal Resonances in a Spinful Luttinger Liquid

Yichen Hu, C. L. Kane

APSMar 1, 20150 citations

Representation of the Luttinger Liquid with Single Point-like Impurity as a Field Theory for the Phase of Scattering

V. V. Afonin

A new approach describing Luttinger Liquid with point-like impurity as field theory for the phase of scattering is developed. It based on a matching of the electron wave functions at impurity position point. As a result of the approach, an expression for non-local action has been taken. The non-locality of the theory leads to convergence of the observed values in an ultraviolet region. It allows studying conductance of the channel up to electron-electron interaction strength of the order of unit. Expansion of the non-local action in small frequency powers makes possible to develop a new approach to the renormalization group analysis of the problem. This method differs from the "poor man's"\ approach widely used in solid-state physics. We have shown, in the Luttinger Liquid "poor man's"\ approach breaks already in two-loop approximation. We analyse the reason of this discrepancy. The qualitative description of the phenomenon is discussed in detail.A new approach describing Luttinger Liquid with point-like impurity as field theory for the phase of scattering is developed. It based on a matching of the electron wave functions at impurity position point. As a result of the approach, an expression for non-local action has been taken. The non-locality of the theory leads to convergence of the observed values in an ultraviolet region. It allows studying conductance of the channel up to electron-electron interaction strength of the order of unit. Expansion of the non-local action in small frequency powers makes possible to develop a new approach to the renormalization group analysis of the problem. This method differs from the "poor man's"\ approach widely used in solid-state physics. We have shown, in the Luttinger Liquid "poor man's"\ approach breaks already in two-loop approximation. We analyse the reason of this discrepancy. The qualitative description of the phenomenon is discussed in detail.

arXiv:2511.00876Nov 2, 20250 citations

Luttinger liquid with one impurity: Equivalent field theory and duality

V. V. Afonin, Victor Yu. Petrov

We derive by functional integral method one-dimensional theory equivalent to Luttinger liquid with one impurity. It is shown that the single quantity has to be calculated for the formulation the effective field theory is the electron density jump at the impurity. We show that duality which relates models with electron-electron attraction and repulsion, and simultaneous exchange of transition and reflection coefficients, is an exact property of the theory.

Journal of Experimental and Theoretical Physics LettersJul 1, 20135 citations

Theory of Nonlinear Luttinger Liquids

L. I. Glazman

Bulletin of the American Physical SocietyMar 16, 20100 citations

Universality of One-Dimensional Fermi Systems, II. The Luttinger Liquid Structure

G. Benfatto, P. Falco, V. Mastropietro

arXiv:1303.3684Communications in Mathematical PhysicsMar 25, 201416 citations

Ground state fidelity of Luttinger liquids: a wavefunctional approach

John Ove Fjærestad

We use a wavefunctional approach to calculate the fidelity of ground states in the Luttinger liquid universality class of one-dimensional gapless quantum many-body systems. The ground state wavefunctionals are discussed using both the Schrödinger (functional differential equation) formulation and a path integral formulation. The fidelity between Luttinger liquids with Luttinger parameters K and K ′ is found to decay exponentially with system size, and to obey the symmetry F ( K , K ′) = F (1/ K ,1/ K ′) as a consequence of a duality in the bosonization description of Luttinger liquids.We use a wavefunctional approach to calculate the fidelity of ground states in the Luttinger liquid universality class of one-dimensional gapless quantum many-body systems. The ground state wavefunctionals are discussed using both the Schrödinger (functional differential equation) formulation and a path integral formulation. The fidelity between Luttinger liquids with Luttinger parameters K and K ′ is found to decay exponentially with system size, and to obey the symmetry F ( K , K ′) = F (1/ K ,1/ K ′) as a consequence of a duality in the bosonization description of Luttinger liquids.

arXiv:0712.3439Journal of Statistical Mechanics Theory and ExperimentJul 10, 200833 citations

Luttinger Liquid with One Impurity: Duality, Universality and Qualitative Description of the Phenomenon

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Luttinger Liquid with One Impurity: Duality, Universality and Qualitative Description of the Phenomenon

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