TY - JOUR

T1 - Self-consistent large-N analytical solutions of inhomogeneous condensates in quantum ℂP N − 1 model

AU - Nitta, Muneto

AU - Yoshii, Ryosuke

N1 - Funding Information:
The support of the Ministry of Education, Culture, Sports, Science (MEXT)-Supported Program for the Strategic Research Foundation at Private Universities ‘Topological Science’
Funding Information:
(Grant No. S1511006) is gratefully acknowledged. The work of M. N. is supported in part by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (KAKENHI Grant No. 16H03984) and by a Grant-in-Aid for Scientific Research on Innovative Areas “Topological Materials Science” (KAKENHI Grant No. 15H05855) from the MEXT of Japan.

PY - 2017/12/1

Y1 - 2017/12/1

N2 - We give, for the first time, self-consistent large-N analytical solutions of inhomogeneous condensates in the quantum ℂPN − 1 model in the large-N limit. We find a map from a set of gap equations of the ℂPN − 1 model to those of the Gross-Neveu (GN) model (or the gap equation and the Bogoliubov-de Gennes equation), which enables us to find the self-consistent solutions. We find that the Higgs field of the ℂPN − 1 model is given as a zero mode of solutions of the GN model, and consequently only topologically non-trivial solutions of the GN model yield nontrivial solutions of the ℂPN − 1 model. A stable single soliton is constructed from an anti-kink of the GN model and has a broken (Higgs) phase inside its core, in which ℂPN − 1 modes are localized, with a symmetric (confining) phase outside. We further find a stable periodic soliton lattice constructed from a real kink crystal in the GN model, while the Ablowitz-Kaup-Newell-Segur hierarchy yields multiple solitons at arbitrary separations.

AB - We give, for the first time, self-consistent large-N analytical solutions of inhomogeneous condensates in the quantum ℂPN − 1 model in the large-N limit. We find a map from a set of gap equations of the ℂPN − 1 model to those of the Gross-Neveu (GN) model (or the gap equation and the Bogoliubov-de Gennes equation), which enables us to find the self-consistent solutions. We find that the Higgs field of the ℂPN − 1 model is given as a zero mode of solutions of the GN model, and consequently only topologically non-trivial solutions of the GN model yield nontrivial solutions of the ℂPN − 1 model. A stable single soliton is constructed from an anti-kink of the GN model and has a broken (Higgs) phase inside its core, in which ℂPN − 1 modes are localized, with a symmetric (confining) phase outside. We further find a stable periodic soliton lattice constructed from a real kink crystal in the GN model, while the Ablowitz-Kaup-Newell-Segur hierarchy yields multiple solitons at arbitrary separations.

KW - 1/N Expansion

KW - Field Theories in Lower Dimensions

KW - Sigma Models

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U2 - 10.1007/JHEP12(2017)145

DO - 10.1007/JHEP12(2017)145

M3 - Article

AN - SCOPUS:85040060129

VL - 2017

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 12

M1 - 145

ER -