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Bosonization and Scale Invariance on Quantum Wires
High Energy Physics - Theory · Submitted 8 Nov 2006
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Using the associated scattering matrices, we give a complete classification of the critical points on a star graph with any number of edges.
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The abstract, sentence by sentence
We develop a systematic approach to bosonization and vertex algebras on quantum wires of the form of star graphs. The related bosonic fields propagate freely in the bulk of the graph, but interact at its vertex. Our framework covers all possible interactions preserving unitarity. Special attention is devoted to the scale invariant interactions, which determine the critical properties of the system. Using the associated scattering matrices, we give a complete classification of the critical points on a star graph with any number of edges. Critical points where the system is not invariant under wire permutations are discovered. By means of an appropriate vertex algebra we perform the bosonization of fermions and solve the massless Thirring model. In this context we derive an explicit expression for the conductance and investigate its behavior at the critical points. A simple relation between the conductance and the Casimir energy density is pointed out.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We develop a systematic approach to bosonization and vertex algebras on quantum wires of the form of star graphs. | contribution 0.99 | 0.95 | 0.11 | asserted 1.00 |
| s1 | The related bosonic fields propagate freely in the bulk of the graph, but interact at its vertex. | background 0.56 | 0.30 | 0.05 | asserted 1.00 |
| s2 | Our framework covers all possible interactions preserving unitarity. | contribution 0.92 | 0.85 | 0.11 | asserted 1.00 |
| s3 | Special attention is devoted to the scale invariant interactions, which determine the critical properties of the system. | contribution 0.90 | 0.62 | 0.10 | asserted 0.98 |
| s4 | Using the associated scattering matrices, we give a complete classification of the critical points on a star graph with any number of edges. | result 0.61 | 0.95 | 0.33 | asserted 1.00 |
| s5 | Critical points where the system is not invariant under wire permutations are discovered. | result 0.99 | 0.93 | 0.12 | asserted 1.00 |
| s6 | By means of an appropriate vertex algebra we perform the bosonization of fermions and solve the massless Thirring model. | contribution 0.62 | 0.95 | 0.12 | asserted 1.00 |
| s7 | In this context we derive an explicit expression for the conductance and investigate its behavior at the critical points. | contribution 0.67 | 0.95 | 0.11 | asserted 1.00 |
| s8 | A simple relation between the conductance and the Casimir energy density is pointed out. | result 0.98 | 0.90 | 0.13 | asserted 0.99 |
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The paper
Original abstract
We develop a systematic approach to bosonization and vertex algebras on quantum wires of the form of star graphs. The related bosonic fields propagate freely in the bulk of the graph, but interact at its vertex. Our framework covers all possible interactions preserving unitarity. Special attention is devoted to the scale invariant interactions, which determine the critical properties of the system. Using the associated scattering matrices, we give a complete classification of the critical points on a star graph with any number of edges. Critical points where the system is not invariant under wire permutations are discovered. By means of an appropriate vertex algebra we perform the bosonization of fermions and solve the massless Thirring model. In this context we derive an explicit expression for the conductance and investigate its behavior at the critical points. A simple relation between the conductance and the Casimir energy density is pointed out.
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How the literature uses it
11 arXiv papers cite this in 51 sentences
Papers citing it · 39 sentences without a confident label
Builds on it 2 papers
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It is quite natural therefore to extend [ref] the bosonization procedure on the line to star graphs.
Quantum Field Theory on Star Graphs · Bosonization and vertex operators · 1.00
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We will show now that this strategy, which works [ref] nicely at criticality, can be extended to off-critical boundary conditions as well.
Off-critical Luttinger Junctions · Bulk theory and boundary conditions · 0.93
Uses its method or tool 1 paper
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In order to compute the conductance, we couple the Luttinger liquid on $Γ$ to a uniform classical electric field [ref] $E(t,i)=∂_t A_x(t,i)$, performing in ([ref]) the substitution [equation] This external field coupling deforms the bosonized version of the current according to [ref] [equation] The Hamiltonian encoding the interaction of $$ and $A_x$ is time dependent and reads [ref] [equation] We stress that now the system can exchange energy with the environment in two different ways.
Off-critical Luttinger Junctions · Off-critical conductance · 0.85
Compares with it 2 papers
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Non-linear effects are absent in the critical regime under consideration, which implies the conductance tensor [equation] We see that the NESS approach, adopted in this paper, confirms the result for $$, obtained previously for $=̨1$ by different methods, including renormalization group techniques [ref] , linear response theory [ref] and conformal field theory [ref] .
Luttinger Liquid in Non-equilibrium Steady State · Charge and heat transport · 0.98
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For example the discussion of multiple $(p,q)$ string junctions given in [ref] is very similar to the analysis of the junctions of quantum wires in [ref] .
String Junctions and Holographic Interfaces · Discussion · 0.96
Cites it as background 5 papers
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In order not to overload the text with heavy expressions, we will only present hereafter the result for scale invariant R-matrices as defined in [ref] , [ref] , [ref] .
Network Models: Action formulation · Bubble Diagram · 0.81
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A 2D QFT on a star graph background was developped in Refs. [ref] .], like a star or a rose with respectively $N$ leaves/petals of equal length/circumference $ℓ$.
Large Star/Rose Extra Dimension with Small Leaves/Petals · Introduction · 0.86
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The classification and the stability properties of these critical points have been extensively studied in the literature [ref] .
Off-critical Luttinger Junctions · Scattering matrix and solution of the model · 1.00
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