Homogeneous binary trees as ground states of quantum critical Hamiltonians

2009/12/31 by Pietro Silvi, P. Silvi, Vittorio Giovannetti +8 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #cond-mat.stat-mech #quant-ph

paper · pdf · doi:10.1103/physreva.81.062335

published as Phys. Rev. A 81, 062335 (2010) · 6 pages, 2 figures

openalex publication_date 2010/06/24 · arxiv created 2010/09/10 · arxiv updated 2010/09/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Many-body states whose wave functions admit a representation in terms of a uniform binary-tree tensor decomposition are shown to obey power-law two-body correlation functions. Any such state can be associated with the ground state of a translationally invariant Hamiltonian which, depending on the dimension of the systems sites, involves at most couplings between third-neighboring sites. Under general conditions it is shown that they describe unfrustrated systems which admit an exponentially large degeneracy of the ground state.

Citations

• Simulation of time evolution with multiscale entanglement renormalization ansatz
• Area laws for the entanglement entropy - a review
• Matrix product representations for all valence bond states
• Matrix product states represent ground states faithfully
• String-net condensation: A physical mechanism for topological phases
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• The generalized Lyapunov theorem and its application to quantum channels

Cited by

• Tensor Networks: a quantum-information perspective on numerical renormalization groups