Exact holographic tensor networks for the Motzkin spin chain

Author:

Alexander Rafael N.12,Evenbly Glen3,Klich Israel4

Affiliation:

1. Centre for Quantum Computation and Communication Technology, School of Science, RMIT University, Melbourne, VIC 3000, Australia

2. Center for Quantum Information and Control, University of New Mexico, Albuquerque, NM 87131, USA

3. School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA

4. Department of Physics, University of Virginia, Charlottesville, Virginia 22903, USA

Abstract

The study of low-dimensional quantum systems has proven to be a particularly fertile field for discovering novel types of quantum matter. When studied numerically, low-energy states of low-dimensional quantum systems are often approximated via a tensor-network description. The tensor network's utility in studying short range correlated states in 1D have been thoroughly investigated, with numerous examples where the treatment is essentially exact. Yet, despite the large number of works investigating these networks and their relations to physical models, examples of exact correspondence between the ground state of a quantum critical system and an appropriate scale-invariant tensor network have eluded us so far. Here we show that the features of the quantum-critical Motzkin model can be faithfully captured by an analytic tensor network that exactly represents the ground state of the physical Hamiltonian. In particular, our network offers a two-dimensional representation of this state by a correspondence between walks and a type of tiling of a square lattice. We discuss connections to renormalization and holography.

Funder

National Science Foundation

Publisher

Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften

Subject

Physics and Astronomy (miscellaneous),Atomic and Molecular Physics, and Optics

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