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arXiv · 1910.11810

Existence of a Spectral Gap in the Affleck-Kennedy-Lieb-Tasaki Model on the Hexagonal Lattice

Marius Lemm·Anders W. Sandvik·Ling Wang
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Abstract

The $S=1$ Affleck-Kennedy-Lieb-Tasaki (AKLT) quantum spin chain was the first rigorous example of an isotropic spin system in the Haldane phase. The conjecture that the $S=3/2$ AKLT model on the hexagonal lattice is also in a gapped phase has remained open, despite being a fundamental problem of ongoing relevance to condensed-matter physics and quantum information theory. Here we confirm this conjecture by demonstrating the size-independent lower bound $Δ>0.006$ on the spectral gap of the hexagonal model with periodic boundary conditions in the thermodynamic limit. Our approach consists of two steps combining mathematical physics and high-precision computational physics. We first prove a mathematical finite-size criterion which gives an analytical, size-independent bound on the spectral gap if the gap of a particular cut-out subsystem of 36 spins exceeds a certain threshold value. Then we verify the finite-size criterion numerically by performing state-of-the-art DMRG calculations on the subsystem.

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Marius Lemm, Anders W. Sandvik, Ling Wang. 2020-05-02. Existence of a Spectral Gap in the Affleck-Kennedy-Lieb-Tasaki Model on the Hexagonal Lattice. https://doi.org/10.1103/physrevlett.124.177204

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