36 research outputs found
A theory of minimal updates in holography
Consider two quantum critical Hamiltonians and on a
-dimensional lattice that only differ in some region . We study
the relation between holographic representations, obtained through real-space
renormalization, of their corresponding ground states and . We observe that, even
though and
disagree significantly both inside and outside region , they still
admit holographic descriptions that only differ inside the past causal cone
of region , where
is obtained by coarse-graining region .
We argue that this result follows from a notion of directed influence in the
renormalization group flow that is closely connected to the success of Wilson's
numerical renormalization group for impurity problems. At a practical level,
directed influence allows us to exploit translation invariance when describing
a homogeneous system with e.g. an impurity, in spite of the fact that the
Hamiltonian is no longer invariant under translations.Comment: main text: 5 pages, 4 figures, appendices: 7 pages, 7 figures.
Revised for greater clarit
Algorithms for entanglement renormalization: boundaries, impurities and interfaces
We propose algorithms, based on the multi-scale entanglement renormalization
ansatz, to obtain the ground state of quantum critical systems in the presence
of boundaries, impurities, or interfaces. By exploiting the theory of minimal
updates [G. Evenbly and G. Vidal, arXiv:1307.0831], the ground state is
completely characterized in terms of a number of variational parameters that is
independent of the system size, even though the presence of a boundary, an
impurity, or an interface explicitly breaks the translation invariance of the
host system. Similarly, computational costs do not scale with the system size,
allowing the thermodynamic limit to be studied directly and thus avoiding
finite size effects e.g. when extracting the universal properties of the
critical system.Comment: 29 pages, 29 figure
Scaling of entanglement entropy in the (branching) multi-scale entanglement renormalization ansatz
We investigate the scaling of entanglement entropy in both the multi-scale
entanglement renormalization ansatz (MERA) and in its generalization, the
branching MERA. We provide analytical upper bounds for this scaling, which take
the general form of a boundary law with various types of multiplicative
corrections, including power-law corrections all the way to a bulk law. For
several cases of interest, we also provide numerical results that indicate that
these upper bounds are saturated to leading order. In particular we establish
that, by a suitable choice of holographic tree, the branching MERA can
reproduce the logarithmic multiplicative correction of the boundary law
observed in Fermi liquids and spin-Bose metals in dimensions.Comment: 17 pages, 14 figure