TY - JOUR

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

AU - Nitta, Muneto

AU - Yoshii, Ryosuke

N1 - Publisher Copyright:
Copyright © 2017, The Authors. All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2017/7/11

Y1 - 2017/7/11

N2 - We give, for the first time, self-consistent large-N analytical solutions of inhomogeneous condensates in the quantum CPN-1model in the large-N limit. We find a map from a set of gap equations of the CPN-1model 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-1model is given as a zero mode of solutions of the GN model, and consequently only topologically nontrivial solutions of the GN model yield nontrivial solutions of the CPN-1model. A stable single soliton is constructed from an antikink of the GN model and has a broken (Higgs) phase inside its core, in which CPN-1modes 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-1model in the large-N limit. We find a map from a set of gap equations of the CPN-1model 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-1model is given as a zero mode of solutions of the GN model, and consequently only topologically nontrivial solutions of the GN model yield nontrivial solutions of the CPN-1model. A stable single soliton is constructed from an antikink of the GN model and has a broken (Higgs) phase inside its core, in which CPN-1modes 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.

UR - http://www.scopus.com/inward/record.url?scp=85094311043&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85094311043&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85094311043

JO - Mathematical Social Sciences

JF - Mathematical Social Sciences

SN - 0165-4896

ER -