Information geometric analysis of long range topological superconductors
arXiv:1904.04313 · doi:10.1088/1361-648X/ab3c70
Abstract
The Uhlmann connection is a mixed state generalisation of the Berry connection. The latter has a very important role in the study of topological phases at zero temperature. Closely related, the quantum fidelity is an information theoretical quantity which is a measure of distinguishability of quantum states. Moreover, it has been extensively used in the analysis of quantum phase transitions. In this work, we study topological phase transitions in 1D and 2D topological superconductors with long-range hopping and pairing amplitudes, using the fidelity and the quantity closely related to the Uhlmann connection. The drop in the fidelity and the departure of from zero signal the topological phase transitions in the models considered. The analysis of the ground state fidelity susceptibility and its associated critical exponents are also applied to the study of the aforementioned topological phase transitions.
arXiv comment10 pages, 5 figures; closer to published version
References in corpus (33)
- Unpaired Majorana fermions in quantum wires
- Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
- Entanglement in quantum critical phenomena
- Non-abelian statistics of half-quantum vortices in p-wave superconductors
- Scaling of Entanglement close to a Quantum Phase Transitions
- Ground state overlap and quantum phase transitions
- Decay of Loschmidt Echo Enhanced by Quantum Criticality
- Fidelity approach to quantum phase transitions
- Topological Superconductivity and Majorana Fermions in RKKY Systems
- Topological superconducting phase in helical Shiba chains
- Fermion zero modes on vortices in chiral superconductors
- Kitaev chains with long-range pairing
- Majorana zero modes in a quantum Ising chain with longer-ranged interactions
- Unconventional topological phase transitions in helical Shiba chains
- Exploring a proximity-coupled Co chain on Pb(110) as a possible Majorana platform
- Mapping the orbital structure of impurity bound states in a superconductor
- Topological Massive Dirac Edge Modes and Long-Range Superconducting Hamiltonians
- Probing the role of long-range interactions in the dynamics of a long-range Kitaev Chain
- Dynamical quantum phase transitions: Role of topological nodes in wavefunction overlaps
- Extended Kitaev chain with longer-range hopping and pairing
- Long-range topological insulators and weakened bulk-boundary correspondence
- Fidelity Between Partial States as Signature of Quantum Phase Transitions
- Topological Quantum Liquids with Long-Range Couplings
- Chiral Topological Superconductors Enhanced by Long-Range Interactions
- Macroscopic Distinguishability Between Quantum States Defining Different Phases of Matter: Fidelity and the Uhlmann Geometric Phase
- The Uhlmann connection in fermionic systems undergoing phase transitions
- Local entanglement and quantum phase transition in 1D transverse field Ising model
- Shiba chains of scalar impurities on unconventional superconductors
- Entanglement modes and topological phase transitions in superconductors
- Fidelity and Uhlmann connection analysis of topological phase transitions in two dimensions
- Fidelity spectrum and phase transitions of quantum systems
- Boltzmann-Gibbs states in topological quantum walks and associated many-body systems: Fidelity and Uhlmann parallel transport analysis of Phase Transitions
- Adiabatic continuity, wavefunction overlap and topological phase transitions
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- Topological quantum phase transitions and criticality in a longer-range Kitaev chain
- Interferometric geometry from symmetry-broken Uhlmann gauge group with applications to topological phase transitions
- Effects of Peierls phases in open linear chains
- Thermal Uhlmann phase in a locally driven two-spin system