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Construction by bosonization of a fermion-phonon model
KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik.ORCID-id: 0000-0003-0011-2937
2015 (Engelska)Ingår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 56, nr 9, artikel-id 091902Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
2015. Vol. 56, nr 9, artikel-id 091902
Nationell ämneskategori
Fysik
Identifikatorer
URN: urn:nbn:se:kth:diva-175654DOI: 10.1063/1.4930299ISI: 000362569200020Scopus ID: 2-s2.0-84941912006OAI: oai:DiVA.org:kth-175654DiVA, id: diva2:864027
Anmärkning

QC 20151023

Tillgänglig från: 2015-10-23 Skapad: 2015-10-19 Senast uppdaterad: 2018-11-20Bibliografiskt granskad
Ingår i avhandling
1. Interacting fermions and non-equilibrium properties of one-dimensional many-body systems
Öppna denna publikation i ny flik eller fönster >>Interacting fermions and non-equilibrium properties of one-dimensional many-body systems
2016 (Engelska)Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
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.

Ort, förlag, år, upplaga, sidor
Stockholm: KTH Royal Institute of Technology, 2016. s. 35
Serie
TRITA-FYS, ISSN 0280-316X ; 2016:59
Nationell ämneskategori
Fysik
Forskningsämne
Fysik
Identifikatorer
urn:nbn:se:kth:diva-193330 (URN)978-91-7729-089-6 (ISBN)
Presentation
2016-10-25, sal FB42, AlbaNova, Kungl. Tekniska högskolan, Stockholm, 15:00
Opponent
Handledare
Anmärkning

QC 20161003

Tillgänglig från: 2016-10-03 Skapad: 2016-09-30 Senast uppdaterad: 2016-10-06Bibliografiskt granskad
2. Non-equilibrium dynamics of exactly solvable quantum many-body systems
Öppna denna publikation i ny flik eller fönster >>Non-equilibrium dynamics of exactly solvable quantum many-body systems
2018 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
Abstract [en]

Recent experimental advances on ultracold atomic gases and trapped ions have made it possible to simulate exactly solvable quantum systems of interacting particles. In particular, the feasibility of making rapid changes, so-called quantum quenches, to such set-ups has allowed experimentalists to probe non-equilibrium phenomena in closed interacting quantum systems. This, in turn, has spurred a considerable theoretical interest in quantum many-body systems out of equilibrium.

In this thesis, we study non-equilibrium properties of quantum many-body systems in the framework of exactly solvable quantum field theory in one spatial dimension. Specific systems include interacting fermions described by the Luttinger model and effective descriptions of spin chains using conformal field theory (CFT). Special emphasis is placed on heat and charge transport, studied from the point of view of quench dynamics, and, in particular, the effects of breaking conformal symmetries on transport properties. Examples include the Luttinger model with non-local interactions, breaking Lorentz and scale invariance, and inhomogeneous CFT, which generalizes standard CFT in that the usual propagation velocity v is replaced by a function v(x) that depends smoothly on the position x, breaking translation invariance.

The quench dynamics studied here is for quantum quenches between, in general, different smooth inhomogeneous systems. An example of this is the so-called smooth-profile protocol, in which the initial state is defined by, e.g., smooth inhomogeneous profiles of inverse temperature and chemical potential, and the time evolution is governed by a homogeneous Hamiltonian. Using this protocol, we compute exact analytical results for the full time evolution of the systems mentioned above. In particular, we derive finite-time results that are universal in the sense that the same relations between the non-equilibrium dynamics and the initial profiles hold for any unitary CFT. These results also make clear that heat and charge transport in standard CFT are purely ballistic.

Finally, we propose and study an inhomogeneous CFT model with v(x) given by a random function. We argue that this model naturally emerges as an effective description of one-dimensional quantum many-body systems with certain static random impurities. Using tools from wave propagation in random media, we show that such impurities lead to normal and anomalous diffusive contributions to heat transport on top of the ballistic one known from standard CFT.

Ort, förlag, år, upplaga, sidor
Stockholm, Sweden: KTH Royal Institute of Technology, 2018. s. 94
Serie
TRITA-SCI-FOU ; 2018:49
Nationell ämneskategori
Fysik
Forskningsämne
Fysik
Identifikatorer
urn:nbn:se:kth:diva-239155 (URN)978-91-7873-032-2 (ISBN)
Disputation
2018-12-14, FD5, AlbaNova University Center, KTH Royal Institute of Technology, Stockholm, 10:00
Opponent
Handledare
Anmärkning

QC 20181119

Tillgänglig från: 2018-11-19 Skapad: 2018-11-16 Senast uppdaterad: 2018-11-21Bibliografiskt granskad

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Moosavi, Per

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