Boundary quantum critical phenomena with entanglement renormalization

Details Boundary quantum critical phenomena with entanglement renormalization Boundary quantum critical phenomena with entanglement renormalization

2009-12-09

arxiv.org/abs/0912.1642v2

Phys. Rev. B 82, 161107(R) (2010)

Physics

Condensed Matter

Strongly Correlated Electrons

8 pages, 12 figures, for a related work see arXiv:0912.2893

Scientific paper

10.1103/PhysRevB.82.161107

We extend the formalism of entanglement renormalization to the study of boundary critical phenomena. The multi-scale entanglement renormalization ansatz (MERA), in its scale invariant version, offers a very compact approximation to quantum critical ground states. Here we show that, by adding a boundary to the scale invariant MERA, an accurate approximation to the critical ground state of an infinite chain with a boundary is obtained, from which one can extract boundary scaling operators and their scaling dimensions. Our construction, valid for arbitrary critical systems, produces an effective chain with explicit separation of energy scales that relates to Wilson's RG formulation of the Kondo problem. We test the approach by studying the quantum critical Ising model with free and fixed boundary conditions.

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