Abstract
We study the ground state of the low energy dense QCD with the assumption of chiral condensates of quarks. Under an external magnetic field, mesons could form soliton lattices via the chiral anomaly. For such scenarios, we present a unified description of pions and η meson with a U(2) field in the framework of the chiral perturbation theory. Our result shows the ground state is a mixture of the magnetized domain walls formed by neutral pion π0 and η meson when they coexist. The winding number of the ground state would alter according to the strength of the magnetic field. When the magnetic field is strong or the chemical potential is large, the proportion of the mixture is determined by the decay constants and the contributions to the anomalous action of π0 and η meson. The resulting configuration is either a mixed soliton lattice or a quasicrystal which could be dubbed a “chiral soliton quasicrystal”.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D.T. Son and M.A. Stephanov, Axial anomaly and magnetism of nuclear and quark matter, Phys. Rev. D 77 (2008) 014021 [arXiv:0710.1084] [INSPIRE].
M. Eto, K. Hashimoto and T. Hatsuda, Ferromagnetic neutron stars: axial anomaly, dense neutron matter, and pionic wall, Phys. Rev. D 88 (2013) 081701 [arXiv:1209.4814] [INSPIRE].
T. Brauner and N. Yamamoto, Chiral Soliton Lattice and Charged Pion Condensation in Strong Magnetic Fields, JHEP 04 (2017) 132 [arXiv:1609.05213] [INSPIRE].
T. Brauner, G. Filios and H. Kolešová, Chiral soliton lattice in QCD-like theories, JHEP 12 (2019) 029 [arXiv:1905.11409] [INSPIRE].
T. Brauner, H. Kolešová and N. Yamamoto, Chiral soliton lattice phase in warm QCD, Phys. Lett. B 823 (2021) 136767 [arXiv:2108.10044] [INSPIRE].
G.W. Evans and A. Schmitt, Chiral anomaly induces superconducting baryon crystal, JHEP 09 (2022) 192 [arXiv:2206.01227] [INSPIRE].
M.S. Grønli and T. Brauner, Competition of chiral soliton lattice and Abrikosov vortex lattice in QCD with isospin chemical potential, Eur. Phys. J. C 82 (2022) 354 [arXiv:2201.07065] [INSPIRE].
T. Brauner and S.V. Kadam, Anomalous low-temperature thermodynamics of QCD in strong magnetic fields, JHEP 11 (2017) 103 [arXiv:1706.04514] [INSPIRE].
T. Brauner and S. Kadam, Anomalous electrodynamics of neutral pion matter in strong magnetic fields, JHEP 03 (2017) 015 [arXiv:1701.06793] [INSPIRE].
T. Brauner and H. Kolešová, Chiral soliton lattice at next-to-leading order, arXiv:2302.06902 [INSPIRE].
X.-G. Huang, K. Nishimura and N. Yamamoto, Anomalous effects of dense matter under rotation, JHEP 02 (2018) 069 [arXiv:1711.02190] [INSPIRE].
K. Nishimura and N. Yamamoto, Topological term, QCD anomaly, and the η′ chiral soliton lattice in rotating baryonic matter, JHEP 07 (2020) 196 [arXiv:2003.13945] [INSPIRE].
M. Eto, K. Nishimura and M. Nitta, Phases of rotating baryonic matter: non-Abelian chiral soliton lattices, antiferro-isospin chains, and ferri/ferromagnetic magnetization, JHEP 08 (2022) 305 [arXiv:2112.01381] [INSPIRE].
H.-L. Chen, X.-G. Huang and J. Liao, QCD phase structure under rotation, Lect. Notes Phys. 987 (2021) 349 [arXiv:2108.00586] [INSPIRE].
M. Eto and M. Nitta, Quantum nucleation of topological solitons, JHEP 09 (2022) 077 [arXiv:2207.00211] [INSPIRE].
T. Higaki, K. Kamada and K. Nishimura, Formation of a chiral soliton lattice, Phys. Rev. D 106 (2022) 096022 [arXiv:2207.00212] [INSPIRE].
A. Yamada and N. Yamamoto, Floquet vacuum engineering: Laser-driven chiral soliton lattice in the QCD vacuum, Phys. Rev. D 104 (2021) 054041 [arXiv:2107.07074] [INSPIRE].
T. Brauner, G. Filios and H. Kolešová, Anomaly-Induced Inhomogeneous Phase in Quark Matter without the Sign Problem, Phys. Rev. Lett. 123 (2019) 012001 [arXiv:1902.07522] [INSPIRE].
D.T. Son and A.R. Zhitnitsky, Quantum anomalies in dense matter, Phys. Rev. D 70 (2004) 074018 [hep-ph/0405216] [INSPIRE].
S. Chen, K. Fukushima and Z. Qiu, Skyrmions in a magnetic field and π0 domain wall formation in dense nuclear matter, Phys. Rev. D 105 (2022) L011502 [arXiv:2104.11482] [INSPIRE].
S. Chen, K. Fukushima and Z. Qiu, Magnetic enhancement of baryon confinement modeled via a deformed Skyrmion, arXiv:2303.04692 [INSPIRE].
M. Kawaguchi, Y.-L. Ma and S. Matsuzaki, Chiral soliton lattice effect on baryonic matter from a skyrmion crystal model, Phys. Rev. C 100 (2019) 025207 [arXiv:1810.12880] [INSPIRE].
M. Eto, K. Nishimura and M. Nitta, How baryons appear in low-energy QCD: Domain-wall Skyrmion phase in strong magnetic fields, arXiv:2304.02940 [INSPIRE].
M. Nitta, Correspondence between Skyrmions in 2+1 and 3+1 Dimensions, Phys. Rev. D 87 (2013) 025013 [arXiv:1210.2233] [INSPIRE].
M. Nitta, Relations among topological solitons, Phys. Rev. D 105 (2022) 105006 [arXiv:2202.03929] [INSPIRE].
C. Ross and M. Nitta, Domain-wall skyrmions in chiral magnets, Phys. Rev. B 107 (2023) 024422 [arXiv:2205.11417] [INSPIRE].
M.G. Alford, K. Rajagopal and F. Wilczek, QCD at finite baryon density: Nucleon droplets and color superconductivity, Phys. Lett. B 422 (1998) 247 [hep-ph/9711395] [INSPIRE].
R. Rapp, T. Schäfer, E.V. Shuryak and M. Velkovsky, Diquark Bose condensates in high density matter and instantons, Phys. Rev. Lett. 81 (1998) 53 [hep-ph/9711396] [INSPIRE].
M.G. Alford, K. Rajagopal and F. Wilczek, Color flavor locking and chiral symmetry breaking in high density QCD, Nucl. Phys. B 537 (1999) 443 [hep-ph/9804403] [INSPIRE].
S. Aoki and M. Creutz, Pion Masses in Two-Flavor QCD with η Condensation, Phys. Rev. Lett. 112 (2014) 141603 [arXiv:1402.1837] [INSPIRE].
M. Nitta, Non-Abelian Sine-Gordon Solitons, Nucl. Phys. B 895 (2015) 288 [arXiv:1412.8276] [INSPIRE].
M. Eto and M. Nitta, Non-Abelian Sine-Gordon Solitons: Correspondence between SU(N) Skyrmions and ℂPN−1 Lumps, Phys. Rev. D 91 (2015) 085044 [arXiv:1501.07038] [INSPIRE].
E. Nakano and T. Tatsumi, Chiral symmetry and density wave in quark matter, Phys. Rev. D 71 (2005) 114006 [hep-ph/0411350] [INSPIRE].
D. Nickel, How many phases meet at the chiral critical point?, Phys. Rev. Lett. 103 (2009) 072301 [arXiv:0902.1778] [INSPIRE].
G. Basar, G.V. Dunne and M. Thies, Inhomogeneous Condensates in the Thermodynamics of the Chiral NJL2 model, Phys. Rev. D 79 (2009) 105012 [arXiv:0903.1868] [INSPIRE].
M. Buballa and S. Carignano, Inhomogeneous chiral condensates, Prog. Part. Nucl. Phys. 81 (2015) 39 [arXiv:1406.1367] [INSPIRE].
Y. Hidaka, K. Kamikado, T. Kanazawa and T. Noumi, Phonons, pions and quasi-long-range order in spatially modulated chiral condensates, Phys. Rev. D 92 (2015) 034003 [arXiv:1505.00848] [INSPIRE].
R. Casalbuoni and G. Nardulli, Inhomogeneous superconductivity in condensed matter and QCD, Rev. Mod. Phys. 76 (2004) 263 [hep-ph/0305069] [INSPIRE].
R. Anglani et al., Crystalline color superconductors, Rev. Mod. Phys. 86 (2014) 509 [arXiv:1302.4264] [INSPIRE].
P. Steinhardt, The Second Kind of Impossible: The Extraordinary Quest for a New Form of Matter, Simon & Schuster (2019).
T. Janssen, Aperiodic crystals: A contradictio in terminis?, Phys. Rept. 168 (1988) 55.
D. DiVincenzo and P. Steinhardt, Quasicrystals: The State of the Art, Series on directions in condensed matter physics, World Scientific (1999).
C. Janot, Quasicrystals: A Primer, Monographs on the physics and chemistry of materials, Clarendon Press (1997).
T. Janssen et al., Aperiodic crystals: from modulated phases to quasicrystals, Vol. 20, Oxford University Press (2007).
Z. Stadnik, Physical Properties of Quasicrystals, Springer Series in Solid-State Sciences, Springer Berlin Heidelberg (2012).
T. Fan, Mathematical Theory of Elasticity of Quasicrystals and Its Applications, Springer Series in Materials Science, Springer Singapore (2016).
J. Scott and N. Clark, Incommensurate Crystals, Liquid Crystals, and Quasi-Crystals, Nato Science Series B, Springer US (2012).
M. Jaric, M. Jaric, P. Bak and D. Gratias, Introduction to Quasicrystals, Advances in Veterinary Medicine, Academic Press (1988).
M. Baggioli and M. Landry, Effective Field Theory for Quasicrystals and Phasons Dynamics, SciPost Phys. 9 (2020) 062 [arXiv:2008.05339] [INSPIRE].
P. Surówka, Dual gauge theory formulation of planar quasicrystal elasticity and fractons, Phys. Rev. B 103 (2021) L201119 [arXiv:2101.12234] [INSPIRE].
Acknowledgments
We thank Thomas Brauner for useful comments. This work is supported in part by JSPS KAKENHI [Grants No. JP22H01221], and the WPI program “Sustainability with Knotted Chiral Meta Matter (SKCM2)” at Hiroshima University. Z.Q was supported by JSPS KAKENHI, Grant-in-Aid for Scientific Research No. JP20J20974 (PD).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2304.05089
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Qiu, Z., Nitta, M. Quasicrystals in QCD. J. High Energ. Phys. 2023, 170 (2023). https://doi.org/10.1007/JHEP05(2023)170
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2023)170