2021
DOI: 10.1007/s00023-021-01086-5
|View full text |Cite
|
Sign up to set email alerts
|

Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States

Abstract: 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 this work is a proof using the Bravyi–Hastings–Michalakis (BHM) strategy that under a condition of local topological quantum order (LTQO), the bulk gap is stable under perturbations that decay at long distances faster than a stretched exponential. Compared to previous work, we expand the class of frustration-free quantum spin mo… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1
1

Citation Types

3
41
0

Year Published

2021
2021
2024
2024

Publication Types

Select...
4
2
1

Relationship

2
5

Authors

Journals

citations
Cited by 24 publications
(44 citation statements)
references
References 98 publications
(228 reference statements)
3
41
0
Order By: Relevance
“…Both these maps depend on the choice of γ through their weight functions, w γ and W γ respectively, but we suppress this in the notation. Arguing as in [26, Section VI.E.1], see also [25,Section 4.3.2], we find that for all A ∈ A (3.17)…”
Section: 11supporting
confidence: 64%
See 3 more Smart Citations
“…Both these maps depend on the choice of γ through their weight functions, w γ and W γ respectively, but we suppress this in the notation. Arguing as in [26, Section VI.E.1], see also [25,Section 4.3.2], we find that for all A ∈ A (3.17)…”
Section: 11supporting
confidence: 64%
“…As explained in detail in [25,Section 8], if both the initial Hamiltonian and the perturbation (see below) have a local gauge symmetry, only observables A that commute with this symmetry need to satisfy (2.21). Other discrete symmetries can be treated similarly (see [25,Section 8]). Therefore, the stability results proved here (Theorems 2.7 and 2.8) will also hold for symmetry-protected topological phases.…”
Section: Resultsmentioning
confidence: 99%
See 2 more Smart Citations
“…The motivation of our analysis comes from recent studies of Hamiltonians of "topological insulators" appearing in the characterization of "topological phases", see e.g. [BN,BH,BHM,NSY2,NSY3]. However, the scope of our techniques is actually more general as shown in the present paper focused on boson systems.…”
Section: Introductionmentioning
confidence: 99%