Circuit complexity across a topological phase transition
Fangli Liu, Seth Whitsitt, Jonathan B. Curtis, Rex Lundgren, Paraj Titum, Zhi-Cheng Yang, James R. Garrison, Alexey V. Gorshkov
Abstract
topological phase transitions. Moreover, we show that the locality property of the real-space optimal Hamiltonian connecting two different ground states depends crucially on whether the two states belong to the same or different phases. This provides a concrete example of classifying different gapped phases using Nielsen's circuit complexity. We further generalize our results to a Kitaev chain with long-range pairing, and we discuss generalizations to higher dimensions. Our result opens up an avenue for using circuit complexity as a tool to understand quantum many-body systems.
Topics & Concepts
Phase transitionTopology (electrical circuits)Transition (genetics)Phase (matter)PhysicsCondensed matter physicsMathematicsChemistryQuantum mechanicsCombinatoricsGeneBiochemistryTopological Materials and PhenomenaGraphene research and applicationsQuantum and electron transport phenomena