Conical surfaces, with a δ function of Gaussian curvature at the apex, are perhaps the simplest example of
geometric frustration. We study two-dimensional liquid crystals with p-fold rotational symmetry (p-atics) on
the surfaces of cones. For free boundary conditions at the base, we find both the ground state(s) and a discrete
ladder of metastable states as a function of both the cone angle and the liquid crystal symmetry p. We find that
these states are characterized by a set of fractional defect charges at the apex and that the ground states are in
general frustrated due to effects of parallel transport along the azimuthal direction of the cone. We check our
predictions for the ground-state energies numerically for a set of commensurate cone angles (corresponding to a
set of commensurate Gaussian curvatures concentrated at the cone apex), whose surfaces can be polygonized as
a perfect triangular or squaremesh, and find excellent agreement with our theoretical predictions.
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This content will become publicly available on June 1, 2025
Interferometric geometric phases of PT -symmetric quantum mechanics
We present a generalization of the geometric phase to pure and thermal states in $\mathcal{PT}$-symmetric quantum mechanics (PTQM) based on the approach of the interferometric geometric phase (IGP). The formalism first introduces the parallel-transport conditions of quantum states and reveals two geometric phases, $\theta^1$ and $\theta^2$, for pure states in PTQM according to the states under parallel-transport. Due to the non-Hermitian Hamiltonian in PTQM, $\theta^1$ is complex and $\theta^2$ is its real part. The imaginary part of $\theta^1$ plays an important role when we generalize the IGP to thermal states in PTQM. The generalized IGP modifies the thermal distribution of a thermal state, thereby introducing effective temperatures. \textcolor{red}{At certain critical points, the generalized IGP may exhibit discrete jumps at finite temperatures, signaling a geometric phase transition. We illustrate the IGP of PTQM through two examples and compare their differences}.
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- Award ID(s):
- 2310656
- NSF-PAR ID:
- 10517996
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review B
- Volume:
- 109
- Issue:
- 24
- ISSN:
- 2469-9950
- Page Range / eLocation ID:
- 245411
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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