References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt145",{id:"formSmash:upper:j_idt145",widgetVar:"widget_formSmash_upper_j_idt145",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt146_j_idt148",{id:"formSmash:upper:j_idt146:j_idt148",widgetVar:"widget_formSmash_upper_j_idt146_j_idt148",target:"formSmash:upper:j_idt146:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

One-dimensional theory of the quantum Hall systemPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2008 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Stockholm: Fysikum , 2008. , 70 p.
##### Keyword [en]

fractional quantum Hall effect, thin torus, spin chains, conformal field theory, strong correlations, non-abelian states
##### National Category

Condensed Matter Physics
##### Research subject

Theoretical Physics
##### Identifiers

URN: urn:nbn:se:su:diva-7545ISBN: 978-91-7155-627-1OAI: oai:DiVA.org:su-7545DiVA: diva2:198562
##### Public defence

2008-05-28, sal FB53, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 13:15 (English)
##### Opponent

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt375",{id:"formSmash:j_idt375",widgetVar:"widget_formSmash_j_idt375",multiple:true});
##### Supervisors

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt381",{id:"formSmash:j_idt381",widgetVar:"widget_formSmash_j_idt381",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt387",{id:"formSmash:j_idt387",widgetVar:"widget_formSmash_j_idt387",multiple:true});
Available from: 2008-05-01 Created: 2008-05-01 Last updated: 2010-02-23Bibliographically approved
##### List of papers

The quantum Hall (QH) system---cold electrons in two dimensions in a perpendicular magnetic field---is a striking example of a system where unexpected phenomena emerge at low energies. The low-energy physics of this system is effectively one-dimensional due to the magnetic field. We identify an exactly solvable limit of this interacting many-body problem, and provide strong evidence that its solutions are adiabatically connected to the observed QH states in a similar manner as the free electron gas is related to real interacting fermions in a metal according to Landau's Fermi liquid theory.

The solvable limit corresponds to the electron gas on a thin torus. Here the ground states are gapped periodic crystals and the fractionally charged excitations appear as domain walls between degenerate ground states. The fractal structure of the abelian Haldane-Halperin hierarchy is manifest for generic two-body interactions. By minimizing a local k+1-body interaction we obtain a representation of the non-abelian Read-Rezayi states, where the domain wall patterns encode the fusion rules of the underlying conformal field theory.

We provide extensive analytical and numerical evidence that the Laughlin/Jain states are continuously connected to the exact solutions. For more general hierarchical states we exploit the intriguing connection to conformal field theory and construct wave functions that coincide with the exact ones in the solvable limit. If correct, this construction implies the adiabatic continuation of the pertinent states. We provide some numerical support for this scenario at the recently observed fraction 4/11.

Non-QH phases are separated from the thin torus by a phase transition. At half-filling, this leads to a Luttinger liquid of neutral dipoles which provides an explicit microscopic example of how weakly interacting quasiparticles in a reduced (zero) magnetic field emerge at low energies. We argue that this is also smoothly connected to the bulk state.

1. Density Matrix Renormalization Group Study of a Lowest Landau Level Electron Gas on a Thin Cylinder$(function(){PrimeFaces.cw("OverlayPanel","overlay198553",{id:"formSmash:j_idt423:0:j_idt427",widgetVar:"overlay198553",target:"formSmash:j_idt423:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Half-Filled Lowest Landau Level on a Thin Torus$(function(){PrimeFaces.cw("OverlayPanel","overlay198554",{id:"formSmash:j_idt423:1:j_idt427",widgetVar:"overlay198554",target:"formSmash:j_idt423:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. 'One-dimensional' theory of the quantum Hall system$(function(){PrimeFaces.cw("OverlayPanel","overlay198555",{id:"formSmash:j_idt423:2:j_idt427",widgetVar:"overlay198555",target:"formSmash:j_idt423:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Pfaffian quantum Hall state made simple: Multiple vacua and domain walls on a thin torus$(function(){PrimeFaces.cw("OverlayPanel","overlay198556",{id:"formSmash:j_idt423:3:j_idt427",widgetVar:"overlay198556",target:"formSmash:j_idt423:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. Microscopic theory of the quantum Hall hierarchy$(function(){PrimeFaces.cw("OverlayPanel","overlay295416",{id:"formSmash:j_idt423:4:j_idt427",widgetVar:"overlay295416",target:"formSmash:j_idt423:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

6. Quantum Hall wave functions on the torus$(function(){PrimeFaces.cw("OverlayPanel","overlay295419",{id:"formSmash:j_idt423:5:j_idt427",widgetVar:"overlay295419",target:"formSmash:j_idt423:5:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

7. Quantum Hall system in Tao-Thouless limit$(function(){PrimeFaces.cw("OverlayPanel","overlay198559",{id:"formSmash:j_idt423:6:j_idt427",widgetVar:"overlay198559",target:"formSmash:j_idt423:6:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

8. Quantum Hall hierarchy wave functions: From conformal correlators to Tao-Thouless states$(function(){PrimeFaces.cw("OverlayPanel","overlay295421",{id:"formSmash:j_idt423:7:j_idt427",widgetVar:"overlay295421",target:"formSmash:j_idt423:7:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

9. Degeneracy of non-Abelian quantum Hall states on the torus: domain walls and conformal field theory$(function(){PrimeFaces.cw("OverlayPanel","overlay198561",{id:"formSmash:j_idt423:8:j_idt427",widgetVar:"overlay198561",target:"formSmash:j_idt423:8:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1080",{id:"formSmash:lower:j_idt1080",widgetVar:"widget_formSmash_lower_j_idt1080",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1081_j_idt1083",{id:"formSmash:lower:j_idt1081:j_idt1083",widgetVar:"widget_formSmash_lower_j_idt1081_j_idt1083",target:"formSmash:lower:j_idt1081:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});