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Bosonization and scale invariance on quantum wires

B. Bellazzini
(
- INFN, Pisa and
- Pisa, Scuola Normale Superiore
)
,
M. Mintchev
(
- INFN, Pisa and
- Pisa U.
)
,
P. Sorba
(
- Annecy, LAPTH
)

Nov, 2006

30 pages

Published in:

J.Phys.A 40 (2007) 2485-2508

e-Print:

hep-th/0611090 [hep-th]

DOI:

10.1088/1751-8113/40/10/017

Report number:

IFUP-TH-25-2006,
LAPTH-1166-06

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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.

Note:

LaTex 31+1 pages, 2 figures. Section 3.6 and two references added. To appear in J. Phys. A: Mathematical and Theoretical Report-no: IFUP-TH 25/2006, LAPTH-1166/06 Subj-class: High Energy Physics - Theory: Mesoscopic Systems and Quantum Hall Effect: Mathematical Physics

11.10.-z
73.63.Nm
11.10.Hi
11.25.Hf
field theory: scalar
duality
quantization
Hamiltonian formalism
bosonization
invariance: conformal

References(33)

Figures(0)

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M. Mintchev
(
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)
,
P. Sorba
(
- Annecy, LAPTH
)

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•
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•
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V. Caudrelier
(
- Annecy, LAPTH
)
,
M. Mintchev
(
- INFN, Pisa and
- Pisa U.
)
,
E. Ragoucy
(
- Annecy, LAPTH
)
,
P. Sorba
(
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)

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•
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•
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Mihail Mintchev
(
- INFN, Pisa and
- Pisa U.
)
,
Paul Sorba
(
- Annecy, LAPP
)

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Molecular Junctions by Joining Single-Walled Carbon Nanotubes

M. Terrones
(
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)
,
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(
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)
,
N. Grobert
(
- Sussex U.
)
,
J.-C. Charlier
(
- Louvain U. and
- Unlisted
)
,
H. Terrones
(
- IPICyT, San Luis Potosi
)

et al.

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Quantum Fields on Star Graphs

B. Bellazzini
(
- INFN, Pisa and
- Pisa, Scuola Normale Superiore
)
,
M. Mintchev
(
- INFN, Pisa and
- Pisa U.
)

- J.Phys.A 39 (2006) 11101-11118
•
e-Print:
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•
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