Critical properties of homogeneous binary trees

TL;DR

This paper investigates homogeneous binary-tree tensor states, revealing their power-law correlations, connection to specific Hamiltonians, and large ground state degeneracy, advancing understanding of complex many-body quantum states.

Contribution

It introduces a class of states with binary-tree tensor structure, linking them to ground states of local Hamiltonians with limited-range couplings and analyzing their spectral properties.

Findings

States exhibit power-law two-body correlations

Ground states correspond to Hamiltonians with up to third-neighbor couplings

Ground space is exponentially large

Abstract

Many-body states whose wave-function admits a representation in terms of a uniform binary-tree tensor decomposition are shown to obey to power-law two-body correlations functions. Any such state can be associated with the ground state of a translational invariant Hamiltonian which, depending on the dimension of the systems sites, involve at most couplings between third-neighboring sites. A detailed analysis of their spectra shows that they admit an exponentially large ground space.