Quantum spins on star graphs and the Kondo model
arXiv:1210.7143 · doi:10.1016/j.nuclphysb.2013.03.001
Abstract
We study the XX model for quantum spins on the star graph with three legs (i.e., on a Y-junction). By performing a Jordan-Wigner transformation supplemented by the introduction of an auxiliary space we find a Kondo Hamiltonian of fermions, in the spin 1 representation of su(2), locally coupled with a magnetic impurity. In the continuum limit our model is shown to be equivalent to the 4-channel Kondo model coupling spin-1/2 fermions with a spin-1/2 impurity and exhibiting a non-Fermi liquid behavior. We also show that it is possible to find a XY model such that - after the Jordan-Wigner transformation - one obtains a quadratic fermionic Hamiltonian directly diagonalizable.
Accepted for publication in Nucl. Phys. B
References in corpus (40)
- Bosonization and Strongly Correlated Systems
- Bosonization for Beginners --- Refermionization for Experts
- Kirchhoff's Rule for Quantum Wires
- Topological Kondo effect with Majorana fermions
- Mapping local Hamiltonians of fermions to local Hamiltonians of spins
- Junctions of three quantum wires
- Junctions of three quantum wires and the dissipative Hofstadter model
- Inhomogeneous Systems with Unusual Critical Behaviour
- Negativity as the Entanglement Measure to Probe the Kondo Regime in the Spin-Chain Kondo Model
- Junction of several weakly interacting quantum wires: a renormalization group study
- Multi-Terminal Coulomb-Majorana Junction
- Entanglement probe of two-impurity Kondo physics in a spin chain
- Majorana-Klein hybridization in topological superconductor junctions
- Soliton solutions of nonlinear Schroedinger equation on simple networks
- Spectral Statistics for the Dirac Operator on Graphs
- Fast solitons on star graphs
- Bose-Einstein Condensation on inhomogeneous complex networks
- Bose-Einstein condensation in inhomogeneous Josephson arrays
- Bosonization and Scale Invariance on Quantum Wires
- Realization of 2-channel Kondo effect in a junction of three quantum Ising chains
- Solution of the Multichannel Coqblin-Schrieffer Impurity Model and Application to Multi-Level systems
- Dynamics of one-dimensional Bose liquids: Andreev-like reflection at Y-junctions and absence of the Aharonov-Bohm effect
- Toulouse limit for the overscreened four-channel Kondo problem
- Y-junction of superconducting Josephson chains
- Kondo Cloud Mediated Long Range Entanglement After Local Quench in a Spin Chain
- Finite-Size Bosonization of 2-Channel Kondo Model: a Bridge between Numerical Renormalization Group and Conformal Field Theory
- Nonequilibrium transport for crossed Luttinger liquids
- Frustration of decoherence in -shaped superconducting Josephson networks
- Quantum Impurity Problems in Condensed Matter Physics
- Modulation and correlations lengths in systems with competing interactions
- Topology Induced Spatial Bose-Einstein Condensation for Bosons on Star-Shaped Optical Networks
- Enhanced Coherence of a Quantum Doublet Coupled to Tomonaga-Luttinger Liquid Leads
- Even-odd parity effects in Majorana junctions
- Quantum Field Theory on Star Graphs
- Overscreened Single Channel Kondo Problem
- The generalized multi-channel Kondo model: Thermodynamics and fusion equations
- Direct computation of scattering matrices for general quantum graphs
- Inhomogeneous Superconductivity in Comb-Shaped Josephson Junction Networks
- Regular networks of Luttinger liquids
- Fermionization Transform for Certain Higher-Dimensional Quantum Spin Models
Cited by in corpus (43)
- Majorana-Klein hybridization in topological superconductor junctions
- Generic Dynamical Phase Transition in One-Dimensional Bulk-Driven Lattice Gases with Exclusion
- Conductance fingerprint of Majorana fermions in the topological Kondo effect
- Transport properties of the Coulomb-Majorana junction
- Bethe ansatz solution of the topological Kondo model
- Persistent current and zero-energy Majorana modes in a p-wave disordered superconducting ring
- Violation of the Wiedemann-Franz law in the Topological Kondo model
- Non-Fermi liquid manifold in a Majorana device
- Exact nonequilibrium transport in the topological Kondo effect
- Thermodynamics of the Topological Kondo Model
- Holographic optical traps for atom-based topological Kondo devices
- 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
- Emulating Majorana fermions and their braiding by Ising spin chains
- Topological Kondo effect in star junctions of Ising magnetic chains. Exact solution
- Energy flow and fluctuations in non-equilibrium conformal field theory on star graphs
- Jordan-Wigner transformations for tree structures
- Geometric Criterion for Solvability of Lattice Spin Systems
- Topological Kondo Device for distinguishing Quasi-Majorana and Majorana signatures
- Parafermionic generalization of the topological Kondo effect
- Realization of a two-channel Kondo model with Josephson junction networks
- Tunable Kondo screening length at a Y-junction of three inhomogenous spin chains
- Tunable spin/charge Kondo effect at a double superconducting island connected to two spinless quantum wires
- Josephson effect in Majorana box devices
- Junction of three off-critical quantum Ising chains and two-channel Kondo effect in a superconductor
- Dual fermionic variables and renormalization group approach to junctions of strongly interacting quantum wires
- Quantum spin circulator in Y junctions of Heisenberg chains
- Majorana boundary modes in Josephson junctions arrays with gapless bulk excitations
- From Kondo effect to weak-link regime in quantum spin-1/2 spin chains
- Traffic models and traffic-jam transition in quantum (+1)-level systems
- Transport across a system with three p-wave superconducting wires: effects of Majorana modes and interactions
- Kondo Length in Bosonic Lattices
- Star junctions and watermelons of pure or random quantum Ising chains : finite-size properties of the energy gap at criticality
- Universality and quantized response in bosonic nonfractionalized tunneling
- Spin-1/2 Ising-Heisenberg Cairo pentagonal model in the presence of an external magnetic field: Effect of Landé g-factors
- Nano-welding of quantum spin- chains at minimal dissipation
- Exactly solvable quantum impurity model with inverse-square interactions
- Fractonic criticality in Rydberg atom arrays
- The Ablowitz-Ladik system on a graph
- Analytical results for a coagulation/decoagulation model on an inhomogeneous lattice
- From Laplacian-to-Adjacency Matrix for Continuous Spins on Graphs
- Quantum impurity models from conformal field theory
- Spin and thermal current scaling at a -junction of XX spin chains