Abstract
The continuous multiscale entanglement renormalization ansatz (cMERA) [J. Haegeman et al., Phys. Rev. Lett. 110, 100402 (2013)] gives a variational wave functional for ground states of quantum field-theoretic Hamiltonians. A cMERA is defined as the result of applying to a reference unentangled state a unitary evolution generated by a quasilocal operator, the entangler. This makes the extension of the formalism to the case where boundaries and defects are present nontrivial. Here we show how this generalization works, using the ($1+1$)-dimensional free boson cMERA as a proof-of-principle example, and restricting ourselves to conformal boundaries and defects. In our prescription, the presence of a boundary or defect induces a modification of the entangler localized only to its vicinity, in analogy with the so-called principle of minimal updates for the lattice tensor network MERA.
Highlights
The continuous multiscale entanglement renormalization ansatz [J
A continuous multiscale entanglement renormalization ansatz (cMERA) is defined as the result of applying to a reference unentangled state a unitary evolution generated by a quasilocal operator, the entangler
In this paper we have introduced cMERA approximations for the ground states of boundary CFT (BCFT) and defect CFT (DCFT), reconciling the quasilocality of the entangler with the sharpness of boundaries and defects, and further expanding the application domain of the ansatz
Summary
The cMERA contruction generates a one-parameter family | (s) of ansatz wave functionals, which can be used to approximate the ground state of a given QFT [38]. They are defined by means of a unitary evolution applied to a reference state | : s. The cMERA approximation for | is given by specifying the three elements in its construction, namely, | , L, 1Even though generally it need not be the case, in the free bosonic cMERAs we work with here, the initial state does depend on the entangling length scale −1, which justifies the notation |. The ultraviolet divergences from Cφφ (x), Cππ (x) are replaced by an onsite delta term such as the one in Eq (2) [42]
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