TY - JOUR
T1 - Dimension changing phase transitions in instanton crystals
AU - Kaplunovsky, Vadim
AU - Sonnenschein, Jacob
PY - 2014/4
Y1 - 2014/4
N2 - We investigate lattices of instantons and the dimension-changing transitions between them. Our ultimate goal is the 3D → 4D transition, which is holographically dual to the phase transition between the baryonic and the quarkyonic phases of cold nuclear matter. However, in this paper (just as in [1]) we focus on lower dimensions - the 1D lattice of instantons in a harmonic potential V ∝M22x22+M 32x22,+M4 2x42 and the zigzag-shaped lattice as a first stage of the 1D → 2D transition. We prove that in the low- and moderate-density regimes, interactions between the instantons are dominated by two-body forces. This drastically simplifies finding the ground state of the instantons' orientations, so we made a numeric scan of the whole orientation space instead of assuming any particular ansatz. We find that depending on the M 2 /M 3 /M 4 ratios, the ground state of instanton orientations can follow a wide variety of patterns. For the straight 1D lattices, we found orientations periodically running over elements of a ℤ2, Klein, prismatic, or dihedral subgroup of the (2)ℤ2, as well as irrational but link-periodic patterns. For the zigzag-shaped lattices, we detected 4 distinct orientation phases - the anti-ferromagnet, another abelian phase, and two non-abelian phases. Allowing the zigzag amplitude to vary as a function of increasing compression force, we obtained the phase diagrams for the straight and zigzag-shaped lattices in the (force, M 3 /M 4), (chemical potential, M 3 /M 4), and (density, M 3 /M 4) planes. Some of the transitions between these phases are second-order while others are first-order. Our techniques can be applied to other types of non-abelian crystals.
AB - We investigate lattices of instantons and the dimension-changing transitions between them. Our ultimate goal is the 3D → 4D transition, which is holographically dual to the phase transition between the baryonic and the quarkyonic phases of cold nuclear matter. However, in this paper (just as in [1]) we focus on lower dimensions - the 1D lattice of instantons in a harmonic potential V ∝M22x22+M 32x22,+M4 2x42 and the zigzag-shaped lattice as a first stage of the 1D → 2D transition. We prove that in the low- and moderate-density regimes, interactions between the instantons are dominated by two-body forces. This drastically simplifies finding the ground state of the instantons' orientations, so we made a numeric scan of the whole orientation space instead of assuming any particular ansatz. We find that depending on the M 2 /M 3 /M 4 ratios, the ground state of instanton orientations can follow a wide variety of patterns. For the straight 1D lattices, we found orientations periodically running over elements of a ℤ2, Klein, prismatic, or dihedral subgroup of the (2)ℤ2, as well as irrational but link-periodic patterns. For the zigzag-shaped lattices, we detected 4 distinct orientation phases - the anti-ferromagnet, another abelian phase, and two non-abelian phases. Allowing the zigzag amplitude to vary as a function of increasing compression force, we obtained the phase diagrams for the straight and zigzag-shaped lattices in the (force, M 3 /M 4), (chemical potential, M 3 /M 4), and (density, M 3 /M 4) planes. Some of the transitions between these phases are second-order while others are first-order. Our techniques can be applied to other types of non-abelian crystals.
KW - AdS-CFT Correspondence
KW - Holography and condensed matter physics (AdS/CMT)
KW - Phase Diagram of QCD
UR - http://www.scopus.com/inward/record.url?scp=84898939344&partnerID=8YFLogxK
U2 - 10.1007/JHEP04(2014)022
DO - 10.1007/JHEP04(2014)022
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AN - SCOPUS:84898939344
SN - 1126-6708
VL - 2014
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 4
M1 - 22
ER -