Uhlmann fidelities from tensor networks
Abstract
Given two states ψ > and ϕ > of a quantum manybody system, one may use the overlap or fidelity <ψ ϕ > to quantify how similar they are. To further resolve the similarity of ψ > and ϕ > in space, one can consider their reduced density matrices ρ and σ on various regions of the system and compute the Uhlmann fidelity F (ρ ,σ ) =Tr√{ρ }σ √{ρ } . In this paper, we show how computing such subsystem fidelities can be done efficiently in many cases when the two states are represented as tensor networks. Formulated using Uhlmann's theorem, such subsystem fidelities appear as natural quantities to extract for certain subsystems of matrix product states and tree tensor networks, and evaluating them is algorithmically simple and computationally affordable. We demonstrate the usefulness of evaluating subsystem fidelities with three example applications: studying local quenches, comparing critical and noncritical states, and quantifying convergence in tensor network simulations.
 Publication:

Physical Review A
 Pub Date:
 October 2018
 DOI:
 10.1103/PhysRevA.98.042316
 arXiv:
 arXiv:1807.01640
 Bibcode:
 2018PhRvA..98d2316H
 Keywords:

 Quantum Physics;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 9+3 pages, many figures