Perturbative approach to an exactly solved problem: Kitaev honeycomb model

Vidal J, Schmidt KP, Dusuel S (2008)

Publication Status: Published

Publication Type: Journal article

Publication year: 2008

Journal

Physical Review B American Physical Society

Publisher: AMER PHYSICAL SOC

Book Volume: 78

Journal Issue: 24

DOI: 10.1103/PhysRevB.78.245121

Abstract

We analyze the gapped phase of the Kitaev honeycomb model perturbatively in the isolated-dimer limit. Our analysis is based on the continuous unitary transformations method, which allows one to compute the spectrum as well as matrix elements of operators between eigenstates at high order. The starting point of our study consists of an exact mapping of the original honeycomb spin system onto a square-lattice model involving an effective spin and a hard-core boson. We then derive the low-energy effective Hamiltonian up to order 10 which is found to describe an interacting-anyon system, contrary to the order 4 result which predicts a free theory. These results give the ground-state energy in any vortex sector and thus also the vortex gap, which is relevant for experiments. Furthermore, we show that the elementary excitations are emerging free fermions composed of a hard-core boson with an attached spin- and phase-operator string. We also focus on observables and compute, in particular, the spin-spin correlation functions. We show that they admit a multiplaquette expansion that we derive up to order 6. Finally, we study the creation and manipulation of anyons with local operators, show that they also create fermions, and discuss the relevance of our findings for experiments in optical lattices.

Authors with CRIS profile

Kai Phillip Schmidt Professur für Theoretische Physik

Involved external institutions

University of Paris 6 - Pierre et Marie Curie / Université Paris VI Pierre et Marie Curie (UPMC)

France (FR) Lycée Saint-Louis

France (FR)

How to cite

APA:

Vidal, J., Schmidt, K.P., & Dusuel, S. (2008). Perturbative approach to an exactly solved problem: Kitaev honeycomb model. Physical Review B, 78(24). https://doi.org/10.1103/PhysRevB.78.245121

MLA:

Vidal, Julien, Kai Phillip Schmidt, and Sebastien Dusuel. "Perturbative approach to an exactly solved problem: Kitaev honeycomb model." Physical Review B 78.24 (2008).

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