Particles, Holes, and Solitons: A Matrix Product State Approach

Category: Scientific Highlights

Published in Physical Review Letters

ABSTRACT:

We introduce a variational method for calculating dispersion relations of translation invariant (1+1)-dimensional quantum field theories. The method is based on continuous matrix product states and can be implemented efficiently. We study the critical Lieb-Liniger model as a benchmark and excellent agreement with the exact solution is found. Additionally, we observe solitonic signatures of Lieb’s type II excitation. In addition, a nonintegrable model is introduced where a U(1)-symmetry breaking term is added to the Lieb-Liniger Hamiltonian. For this model we find evidence of a nontrivial bound-state excitation in the dispersion relation.

 

	Figure: Top: Dispersion relation of Ĥ′ with D=22 for γ≈26.4, μ=1, and u=1. Blue dots are the pairwise sum of all topological excitations. Red circles are trivial excitations and the right-hand inset shows the topological spectrum. Bottom: Convergence of the two lowest trivial eigenvalues and the lowest two-kink excitation energy as a function of D-1 at p=0.

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