Edge Theories in Projected Entangled Pair State Models

Category: Scientific Highlights

Published in Physical Review Letters

ABSTRACT:

We analyze the low energy excitations of spin lattice systems in two dimensions at zero temperature within the framework of projected entangled pair state models. Perturbations in the bulk give rise to physical excitations located at the edge. We identify the corresponding degrees of freedom, give a procedure to derive the edge Hamiltonian, and illustrate that it can exhibit a rich phase diagram. For topological models, the edge Hamiltonian is constrained by the topological order in the bulk, which gives rise to one-dimensional edge models with unconventional properties; for instance, a topologically ordered bulk can protect a ferromagnetic Ising chain at the edge against spontaneous symmetry breaking.

Figure: Edge Hamiltonian for the perturbed AKLT model, Eq. (1). (a) Phase diagram as a function of anisotropy g=J and field h=J, for J > 0. Three phases are observed: a fully polarized ferromagnetic (FM) phase (with magnetization mz ¼ 1 2), an antiferromagnetic (AFM) phase (mz ¼ 0), and an XY Luttinger liquid phase. The shading shows mz for the ground state of the full edge Hamiltonian H for Nv ¼ 14; the solid lines give phase boundaries determined analytically using fully polarized and mean-field AFM Ansätze, both for H and Hamiltonians Hk where the sum in (2) and (3) is restricted to l < k. (b) Correlation functions CxxðlÞ ¼ hSxi Sxi þli and CzzðlÞ ¼ hSzi Szi þli for the three phases, computed at the points marked × in (a). DMRG calculations for Hk show that in the XY phase, Cxx decays algebraically.

Yang S., Lehman L., Poilblanc D., Van Acoleyen K., Verstraete F., Cirac J.I., Schuch N. (2014), Edge Theories in Projected Entangled Pair State Models, Phys. Rev. Lett. 112, 036402. DOI:10.1103/PhysRevLett.112.036402, pdf

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