Open Access
Nuclear Physics B, volume 897, pages 405-420
Particle-hole duality, integrability, and Russian doll BCS model
Bork L. V.
1
,
Pogosov Walter V.
2, 3
Publication type: Journal Article
Publication date: 2015-08-01
Nuclear and High Energy Physics
Abstract
We address a generalized Richardson model (Russian doll BCS model), which is characterized by the breaking of time-reversal symmetry. This model is known to be exactly solvable and integrable. We point out that the Russian doll BCS model, on the level of Hamiltonian, is also particle–hole symmetric. This implies that the same state can be expressed both in the particle and hole representations with two different sets of Bethe roots. We then derive exact relations between Bethe roots in the two representations, which can hardly be obtained staying on the level of Bethe equations. In a quasi-classical limit, similar identities for usual Richardson model, known from literature, are recovered from our results. We also show that these relations for Richardson roots take a remarkably simple form at half-filling and for a symmetric with respect to the middle of the interaction band distribution of one-body energy levels, since, in this special case, the rapidities in the particle and hole representations up to the translation satisfy the same system of equations.
Citations by journals
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1
2
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Journal of Physics A: Mathematical and Theoretical
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Journal of Physics A: Mathematical and Theoretical
2 publications, 66.67%
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Nuclear Physics B
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Nuclear Physics B
1 publication, 33.33%
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1
2
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Citations by publishers
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1
2
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IOP Publishing
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IOP Publishing
2 publications, 66.67%
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Elsevier
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Elsevier
1 publication, 33.33%
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1
2
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Bork L., Pogosov W. V. Particle-hole duality, integrability, and Russian doll BCS model // Nuclear Physics B. 2015. Vol. 897. pp. 405-420.
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Bork L., Pogosov W. V. Particle-hole duality, integrability, and Russian doll BCS model // Nuclear Physics B. 2015. Vol. 897. pp. 405-420.
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TY - JOUR
DO - 10.1016/j.nuclphysb.2015.05.031
UR - https://doi.org/10.1016%2Fj.nuclphysb.2015.05.031
TI - Particle-hole duality, integrability, and Russian doll BCS model
T2 - Nuclear Physics B
AU - Bork, L. V.
AU - Pogosov, Walter V.
PY - 2015
DA - 2015/08/01 00:00:00
PB - Elsevier
SP - 405-420
VL - 897
SN - 0550-3213
ER -
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@article{2015_Bork,
author = {L. V. Bork and Walter V. Pogosov},
title = {Particle-hole duality, integrability, and Russian doll BCS model},
journal = {Nuclear Physics B},
year = {2015},
volume = {897},
publisher = {Elsevier},
month = {aug},
url = {https://doi.org/10.1016%2Fj.nuclphysb.2015.05.031},
pages = {405--420},
doi = {10.1016/j.nuclphysb.2015.05.031}
}
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