Hidden symmetries, the Bianchi classification and geodesics of the quantum geometric ground-state manifolds
Diego Liska, Vladimir Gritsev
SciPost Phys. 10, 020 (2021) · published 28 January 2021
- doi: 10.21468/SciPostPhys.10.1.020
We study the Killing vectors of the quantum ground-state manifold of a parameter-dependent Hamiltonian. We find that the manifold may have symmetries that are not visible at the level of the Hamiltonian and that different quantum phases of matter exhibit different symmetries. We propose a Bianchi-based classification of the various ground-state manifolds using the Lie algebra of the Killing vector fields. Moreover, we explain how to exploit these symmetries to find geodesics and explore their behaviour when crossing critical lines. We briefly discuss the relation between geodesics, energy fluctuations and adiabatic preparation protocols. Our primary example is the anisotropic transverse-field Ising model. We also analyze the Ising limit and find analytic solutions to the geodesic equations for both cases.
Cited by 2
Sels et al., Dynamical obstruction to localization in a disordered spin chain
Phys. Rev. E 104, 054105 (2021) [Crossref]
Liska et al., The Loschmidt Index
SciPost Phys. 10, 100 (2021) [Crossref]
Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Diego Liska,
- 1 2 Vladimir Gritsev
- 1 Institute of Physics, University of Amsterdam [IoP, UvA]
- 2 Международный центр квантовой оптики и квантовых технологий / Russian Quantum Center