2013/07/31 by Glen Evenbly, Guifre Vidal, Guifré Vidal · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Combinatorics #Hamiltonian (control theory) #Invariant (physics) #Lattice (music) #Mathematical physics #Mathematics #Physics #Quantum Chromodynamics and Particle Interactions #Quantum many-body systems #Quantum mechanics #Renormalization #Renormalization group #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physrevb.91.205119
published as Phys. Rev. B 91, 205119 (2015) · main text: 5 pages, 4 figures, appendices: 7 pages, 7 figures. Revised for greater clarity
arxiv created 2015/04/24 · openalex publication_date 2015/05/20 · arxiv updated 2015/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Consider two quantum critical Hamiltonians H and \stackrel\ifmmode \else \~\fiH on a d-dimensional lattice that only differ in some region R. We study the relation between holographic representations, obtained through real-space renormalization, of their corresponding ground states |\ensuremathψ\ensuremath⟩ and |\stackrel\ifmmode \else \~\fi\ensuremathψ\ensuremath⟩. We observe that, even though |\ensuremathψ\ensuremath⟩ and |\stackrel\ifmmode \else \~\fi\ensuremathψ\ensuremath⟩ disagree significantly both inside and outside region R, they still admit holographic descriptions that only differ inside the past causal cone C(R) of region R, where C(R) is obtained by coarse-graining region R. 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.