Nonanalyticity of circuit complexity across topological phase transitions

Topological Aspects of Phase Transitions

In the past decade and a half, an alternative analysis of phase transitions, based in the topological behavior of system configuration spaces, has been introduced. This method offers a new understanding of many phase transitions, particularly those in finite systems, using topology and manifold behavior. While the broadest hypotheses offered by researchers have proven overly optimistic, the met...

Computational Complexity and Phase Transitions

Phase transitions in combinatorial problems have recently been shown [2] to be useful in locating “hard” instances of combinatorial problems. The connection between computational complexity and the existence of phase transitions has been addressed in Statistical Mechanics [2] and Artificial Intelligence [3], but not studied rigorously. We take a first step in this direction by investigating the...

Topological Phase Transitions in Multicomponent Superconductors.

We study the phase transition between a trivial and a time-reversal-invariant topological superconductor in a single-band system. By analyzing the interplay of symmetry, topology, and energetics, we show that for a generic normal state band structure, the phase transition occurs via extended intermediate phases in which even- and odd-parity pairing components coexist. For inversion-symmetric sy...

Topological transitions in Berry's phase interference effects.

Multifarious topological quantum phase transitions in two-dimensional topological superconductors

We study the two-dimensional topological superconductors of spinless fermions in a checkerboard-lattice Chern-insulator model. With the short-range p-wave superconducting pairing, multifarious topological quantum phase transitions have been found and several phases with high Chern numbers have been observed. We have established a rich phase diagram for these topological superconducting states. ...