Some aspects of Affleck–Kennedy–Lieb–Tasaki models: Tensor network, physical properties, spectral gap, deformation, and quantum computation
Abstract Affleck, Kennedy, Lieb, and Tasaki constructed a spin-1 model that is isotropic in
spins and possesses a provable finite gap above the ground state more than three decades …
spins and possesses a provable finite gap above the ground state more than three decades …
Demonstrating the Affleck-Kennedy-Lieb-Tasaki spectral gap on 2D degree-3 lattices
We report results on solving a long outstanding problem—whether the two-dimensional spin-
3/2 antiferromagnetic valence-bond model of Affleck, Kennedy, Lieb, and Tasaki (AKLT) …
3/2 antiferromagnetic valence-bond model of Affleck, Kennedy, Lieb, and Tasaki (AKLT) …
Existence of a spectral gap in the Affleck-Kennedy-Lieb-Tasaki model on the hexagonal lattice
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 …
example of an isotropic spin system in the Haldane phase. The conjecture that the S= 3/2 …
Quasi-locality bounds for quantum lattice systems. Part II. Perturbations of frustration-free spin models with gapped ground states
We study the stability with respect to a broad class of perturbations of gapped ground-state
phases of quantum spin systems defined by frustration-free Hamiltonians. The core result of …
phases of quantum spin systems defined by frustration-free Hamiltonians. The core result of …
Efficient verification of Affleck-Kennedy-Lieb-Tasaki states
T Chen, Y Li, H Zhu - Physical Review A, 2023 - APS
Affleck-Kennedy-Lieb-Tasaki (AKLT) states are an important class of many-body quantum
states that are useful in quantum information processing, including measurement-based …
states that are useful in quantum information processing, including measurement-based …
Finite-size criteria for spectral gaps in D-dimensional quantum spin systems
M Lemm - Analytic trends in mathematical physics, 2020 - books.google.com
We generalize the existing finite-size criteria for spectral gaps of frustration-free spin systems
to D> 2 dimensions. We obtain a local gap threshold of scaling persists n3, for independent …
to D> 2 dimensions. We obtain a local gap threshold of scaling persists n3, for independent …
Random translation-invariant Hamiltonians and their spectral gaps
I Jauslin, M Lemm - Quantum, 2022 - quantum-journal.org
We consider random translation-invariant frustration-free quantum spin Hamiltonians on
$\mathbb Z^ D $ in which the nearest-neighbor interaction in every direction is randomly …
$\mathbb Z^ D $ in which the nearest-neighbor interaction in every direction is randomly …
AKLT models on decorated square lattices are gapped
The nonzero spectral gap of the original two-dimensional Affleck-Kennedy-Lieb-Tasaki
(AKLT) models has remained unproven for more than three decades. Recently, Abdul …
(AKLT) models has remained unproven for more than three decades. Recently, Abdul …
Entanglement subvolume law for 2D frustration-free spin systems
Let H be a frustration-free Hamiltonian describing a 2D grid of qudits with local interactions,
a unique ground state, and local spectral gap lower bounded by a positive constant. For any …
a unique ground state, and local spectral gap lower bounded by a positive constant. For any …
A bulk spectral gap in the presence of edge states for a truncated pseudopotential
We study the low-energy properties of a truncated Haldane pseudopotential with maximal
half filling, which describes a strongly correlated system of spinless bosons in a cylinder …
half filling, which describes a strongly correlated system of spinless bosons in a cylinder …