Dual fermionic variables and renormalization group approach to junctions of strongly interacting quantum wires

Abstract

Making a combined use of bosonization and fermionization techniques, we build nonlocal transformations between dual fermion operators, describing junctions of strongly interacting spinful one-dimensional quantum wires. Our approach allows for trading strongly interacting (in the original coordinates) fermionic Hamiltonians for weakly interacting (in the dual coordinates) ones. It enables us to generalize to the strongly interacting regime the fermionic renormalization group approach to weakly interacting junctions. As a result, on one hand, we are able to pertinently complement the information about the phase diagram of the junction obtained within bosonization approach; on the other hand, we map out the full crossover of the conductance tensors between any two fixed points in the phase diagram connected by a renormalization group trajectory.

30 pages, 9 figures

References in corpus (20)

• Topological Kondo effect with Majorana fermions
• Impurity and correlation effects on transport in one-dimensional quantum wires
• Functional renormalization group for Luttinger liquids with impurities
• Quantum spins on star graphs and the Kondo model
• Junctions of three quantum wires for spin 1/2 electrons
• Renormalization-group analysis of the one-dimensional extended Hubbard model with a single impurity
• Correlation effects on resonant tunneling in one-dimensional quantum wires
• Non-Fermi liquid manifold in a Majorana device
• Tunneling spectroscopy of Majorana-Kondo devices
• Influence of the contacts on the conductance of interacting quantum wires
• Fermionic renormalization group methods for transport through inhomogeneous Luttinger liquids
• Screening Clouds and Majorana Fermions
• Enhanced Coherence of a Quantum Doublet Coupled to Tomonaga-Luttinger Liquid Leads
• Josephson current through a long quantum wire
• XXZ spin-1/2 representation of a finite-U Bose-Hubbard chain at half-integer filling
• Renormalization group study of transport through a superconducting junction of multiple one-dimensional quantum wires
• Constraints on conductances for Y-junction of quantum wires
• Interaction-induced Renormalization of Andreev Reflection
• The dc Josephson current in a long multi-channel quantum wire
• Temperature induced phase averaging in one-dimensional mesoscopic systems

Cited by in corpus (12)

• Lindblad equation approach to the optimal working point in nonequilibrium stationary states of an interacting electronic one-dimensional system: Application to the spinless Hubbard chain in the clean and in the weakly disordered limit
• Transfer matrix approach to the persistent current in hybrid normal-superconducting rings
• From four- to two-channel Kondo effect in junctions of XY spin chains
• Multi-particle scattering and breakdown of the Wiedemann-Franz law at a junction of N interacting quantum wires
• A fermionic approach to tunneling through junctions of multiple quantum wires
• From Kondo effect to weak-link regime in quantum spin-1/2 spin chains
• Real fermion modes, impurity entropy, and nontrivial fixed points in the phase diagram of junctions of interacting quantum wires and topological superconductors
• Kondo Length in Bosonic Lattices
• Quasi-one-dimensional ${}^4$He in nanopores
• Wetting critical behavior in the quantum Ising model within the framework of Lindblad dissipative dynamics
• Impurity entropy of junctions of multiple quantum wires
• Spin and thermal current scaling at a $Y$-junction of XX spin chains