From one-dimensional charge conserving superconductors to the gapless Haldane phase
| Autor: | Patrick Azaria, Erez Berg, Anna Keselman |
|---|---|
| Přispěvatelé: | Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC), Laboratoire de Physique Théorique de la Matière Condensée ( LPTMC ), Université Pierre et Marie Curie - Paris 6 ( UPMC ) -Centre National de la Recherche Scientifique ( CNRS ) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Bosonization
Phase transition FOS: Physical sciences 02 engineering and technology 01 natural sciences Superconductivity (cond-mat.supr-con) Condensed Matter - Strongly Correlated Electrons Gapless playback Superfluidity and superconductivity Quantum mechanics 0103 physical sciences Mesoscale and Nanoscale Physics (cond-mat.mes-hall) [ PHYS.PHYS.PHYS-GEN-PH ] Physics [physics]/Physics [physics]/General Physics [physics.gen-ph] 010306 general physics Phase diagram Physics Charge conservation Condensed Matter - Mesoscale and Nanoscale Physics Strongly Correlated Electrons (cond-mat.str-el) Density matrix renormalization group Condensed Matter - Superconductivity Fermion Renormalization group 021001 nanoscience & nanotechnology [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph] Condensed Matter::Strongly Correlated Electrons 0210 nano-technology |
| Zdroj: | Physical Review B Physical Review B, American Physical Society, 2018, 98 (21), pp.214501. ⟨10.1103/PhysRevB.98.214501⟩ Phys.Rev.B Phys.Rev.B, 2018, 98 (21), pp.214501. ⟨10.1103/PhysRevB.98.214501⟩ |
| ISSN: | 0550-3213 2469-9950 2469-9969 |
| DOI: | 10.1103/PhysRevB.98.214501⟩ |
| Popis: | International audience; We develop a framework to analyze the topological properties of one-dimensional systems with charge conservation and tendency towards topological superconducting order. In particular, we consider models with N flavors of fermions and (Z2)N symmetry, associated with the conservation of the fermionic parity of each flavor. For N=1, and with no other symmetry other than charge conservation, we recover the result that there is no distinct topological phase with exponentially localized zero modes. For N>1, however, we show that the ends of the system can host low-energy, exponentially-localized modes. To illustrate these ideas, we focus on lattice models with SON symmetric interactions and study the phase transition between the trivial and the topological gapless phases using bosonization and a weak-coupling renormalization group analysis. As a concrete example, we study in detail the case of N=3. In this case, the topologically nontrivial superconducting phase corresponds to a gapless analog of the Haldane phase in spin-1 chains. In this phase, although the bulk hosts gapless modes, corresponding to composite fermionic excitations with an enlarged Fermi surface, the ends host spin-1/2 degrees of freedom which are exponentially localized and protected by the spin gap in the bulk. We obtain the full phase diagram of the model using density matrix renormalization group calculations. Within this model, we identify the self-dual line studied by Andrei and Destri [Nucl. Phys. B 231, 445 (1984)NUPBBO0550-321310.1016/0550-3213(84)90514-5] as a first-order transition line between the gapless Haldane phase and a trivial gapless phase. This allows us to identify the propagating spin-1/2 kinks in the Andrei-Destri model as the topological end modes at the domain walls between the two phases. |
| Databáze: | OpenAIRE |
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