🍩 Database of Original & NonTheoretical Uses of Topology
(found 4 matches in 0.001275s)


Homological Analysis of MultiQubit Entanglement (2018)
Alessandra di Pierro, Stefano Mancini, Laleh Memarzadeh, Riccardo MengoniAbstract
We propose the usage of persistent homologies to characterize multipartite entanglement. On a multiqubit data set we introduce metriclike measures defined in terms of bipartite entanglement and then we derive barcodes. We show that, depending on the distance, they are able to produce different classifications. In one case, it is possible to obtain the standard separability classes. In the other case, a new classification of entangled states of three and four qubits is provided. 
Crystallographic Interacting Topological Phases and Equvariant Cohomology: To Assume or Not to Assume (2020)
Daniel Sheinbaum, Omar AntolĂn CamarenaAbstract
For symmorphic crystalline interacting gapped systems we derive a classification under adiabatic evolution. This classification is complete for nondegenerate ground states. For the degenerate case we discuss some invariants given by equivariant characteristic classes. We do not assume an emergent relativistic field theory nor that phases form a topological spectrum. We also do not assume shortrange entanglement nor the existence of quasiparticles as is done in SPT and SET classifications respectively. Using a slightly generalized Bloch decomposition and Grassmanians made out of ground state spaces, we show that the \$P\$equivariant cohomology of a \$d\$dimensional torus gives rise to different interacting phases. We compare our results to bosonic symmorphic crystallographic SPT phases and to noninteracting fermionic crystallographic phases in class A. Finally we discuss the relation of our assumptions to those made for crystallographic SPT and SET phases. 
Topological Persistence Machine of Phase Transitions (2020)
Quoc Hoan Tran, Mark Chen, Yoshihiko HasegawaAbstract
The study of phase transitions from experimental data becomes challenging, especially when little prior knowledge of the system is available. Topological data analysis is an emerging framework for characterizing the shape of data and has recently achieved success in detecting structural transitions in material science such as glassliquid transition. However, data obtained from physical states may not have explicit shapes as structural materials. We propose a general framework called topological persistence machine to construct the shape of data from correlations in states; hence decipher phase transitions via the qualitative changes of the shape. Our framework enables an effective and unified approach in phase transition analysis. We demonstrate the impact in highly precise detection of BerezinskiiKosterlitzThouless phase transitions in the classical XY model, and quantum phase transition in the transverse Ising model and BoseHubbard model. Intriguingly, these phase transitions have proven to be notoriously difficult in traditional methods but can be characterized in our framework without requiring prior knowledge about phases. Our approach is thus expected applicable and brings a remarkable perspective for exploring phases of experimental physical systems.