Existence of a Spectral Gap in the Affleck-Kennedy-Lieb-Tasaki Model on the Hexagonal Lattice.
Existence of a Spectral Gap in the Affleck-Kennedy-Lieb-Tasaki Model on the Hexagonal Lattice.
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DOI：
10.1103/physrevlett.124.177204
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发表时间：
2019-10
影响因子：
8.6
通讯作者：
M. Lemm;A. Sandvik;Ling Wang
中科院分区：
文献类型：
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作者：
M. Lemm;A. Sandvik;Ling Wang
S=1 Affleck-Kennedy-Lieb-Tasaki （AKLT）量子自旋链是Haldane相中各向同性自旋系统的第一个严格例子。六边形晶格上的S=3/2 AKLT模型也处于间隙相的猜想仍然是开放的，尽管这是一个与凝聚态物理和量子信息理论持续相关的基本问题。在热力学极限下，我们证明了具有周期边界条件的六边形模型的谱隙的尺寸无关的下界Δ>0.006，从而证实了这一猜想。我们的方法由数学物理和高精度计算物理相结合的两个步骤组成。我们首先证明了一个数学上的有限尺寸准则，该准则给出了当特定的36个自旋的切断子系统的谱隙超过一定的阈值时，谱隙的解析性的、与尺寸无关的界。然后，我们通过在子系统上执行最先进的DMRG计算，在数值上验证了有限尺寸标准。
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.