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Construction by bosonization of a fermion-phonon model
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
KTH, School of Engineering Sciences (SCI), Theoretical Physics.ORCID iD: 0000-0003-0011-2937
2015 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 56, no 9, 091902Article in journal (Refereed) Published
Abstract [en]

We discuss an extension of the (massless) Thirring model describing interacting fermions in one dimension which are coupled to phonons and where all interactions are local. This fermion-phonon model can be solved exactly by bosonization.We present a construction and solution of this model which is mathematically rigorous by treating it as a continuum limit of a Luttinger-phonon model. A self-contained account of the mathematical results underlying bosonization is included, together with complete proofs.

Place, publisher, year, edition, pages
2015. Vol. 56, no 9, 091902
National Category
Physical Sciences
URN: urn:nbn:se:kth:diva-175654DOI: 10.1063/1.4930299ISI: 000362569200020ScopusID: 2-s2.0-84941912006OAI: diva2:864027

QC 20151023

Available from: 2015-10-23 Created: 2015-10-19 Last updated: 2016-09-30Bibliographically approved
In thesis
1. Interacting fermions and non-equilibrium properties of one-dimensional many-body systems
Open this publication in new window or tab >>Interacting fermions and non-equilibrium properties of one-dimensional many-body systems
2016 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Recent experimental progress on ultracold atomic gases have opened up the possibility to simulate many-body systems out of equilibrium. We consider such a system described by the Luttinger model, which is a model of interacting fermions in one spatial dimension.

It is well known that the Luttinger model is exactly solvable using bosonization. This also remains true for certain extensions of the model, e.g., where, in addition, the fermions are coupled to phonons. We give a self-contained account of bosonization, together with complete proofs, and show how this can be used to solve the Luttinger model and the above fermion-phonon model rigorously.

The main focus is on non-equilibrium properties of the Luttinger model. We use the exact solution of the Luttinger model, with non-local interactions, to study the evolution starting from a non-uniform initial state with a position-dependent chemical potential. The system is shown to reach a current-carrying final steady state, in which the universal value of the electrical conductance, known from near-to-equilibrium settings, is recovered. We also study the effects of suddenly changing the interactions and show that the final state has memory of the initial state, which is, e.g., manifested by non- equilibrium exponents in its fermion two-point correlation functions.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2016. 35 p.
TRITA-FYS, ISSN 0280-316X ; 2016:59
National Category
Physical Sciences
Research subject
urn:nbn:se:kth:diva-193330 (URN)978-91-7729-089-6 (ISBN)
2016-10-25, sal FB42, AlbaNova, Kungl. Tekniska högskolan, Stockholm, 15:00

QC 20161003

Available from: 2016-10-03 Created: 2016-09-30 Last updated: 2016-10-06Bibliographically approved

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