Speaker
Description
Topological phases of matter, such as those realized in the Kitaev chain, are of great interest due to their robustness and potential applications in quantum computing. The Kitaev chain, a one-dimensional superconducting model, hosts Majorana edge modes in its topological phase.
This project investigates how electron-electron interactions impact the chain’s topological properties using the Density Matrix Renormalization Group (DMRG) method, which is particularly well-suited for studying strongly correlated one-dimensional systems.
We simulated a 10-site Kitaev chain, first in the non-interacting case, and then with an on-site Coulomb interaction:
$U = \sum^{N=10}_{i} n_i n_{i+1}$
For U=0, correlations decay exponentially, signaling the presence of topological edge states. Introducing U≠0 suppressed this behavior, indicating a transition to a trivial phase. The superconducting parameter Δ was key in inducing correlations, while the interaction U suppressed them.
Entanglement entropy, computed from the single-particle correlation matrix, exhibited a peak within the range 2 < μ/t < 2, consistent with the topological regime. Outside this range, entropy dropped sharply.
These results demonstrate how interactions can destabilize topological order, offering insights into designing more realistic quantum systems.
