95 citations · 248 across the 19 of their papers we have counts for
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Local Topological Quantum Order and Spectral Gap Stability for the AKLT Models on the Hexagonal and Lieb Lattices
Thomas Jackson, Bruno Nachtergaele, Amanda Young
We prove that the ground state of the AKLT models on the hexagonal lattice and the Lieb lattice satisfy the local topological quantum order (LTQO) condition. This will be a consequ…
Recursive spectral relations and the charge versus neutral gap in fractional quantum Hall systems
Marius Lemm, Bruno Nachtergaele, Simone Warzel +1
We consider quantum lattice Hamiltonians and derive recursive spectral relations bridging successive particle number sectors. One relation gives conditions under which the charge g…
Quantum Spin Systems
Amanda Young
This work provides an overview of gapped quantum spin systems, including concepts, techniques, properties, and results. The basic framework and objects of interest for quantum spin…
On a bulk gap strategy for quantum lattice models
Amanda Young
Establishing the (non)existence of a spectral gap above the ground state in the thermodynamic limit is one of the fundamental steps for characterizing the topological phase of a qu…
A Nonvanishing Spectral Gap for AKLT Models on Generalized Decorated Graphs
Angelo Lucia, Amanda Young
We consider the spectral gap question for AKLT models defined on decorated versions of simple, connected graphs G. This class of decorated graphs, which are defined by replacing al…
Stability of the spectral gap and ground state indistinguishability for a decorated AKLT model
Angelo Lucia, Alvin Moon, Amanda Young
We use cluster expansions to establish local indistiguishability of the finite-volume ground states for the AKLT model on decorated hexagonal lattices with decoration parameter at…
The spectral gap of a fractional quantum Hall system on a thin torus
Simone Warzel, Amanda Young
We study a fractional quantum Hall system with maximal filling in the thin torus limit. The corresponding Hamiltonian is a truncated version of Haldane's pseudopotential…
A Bulk Spectral Gap in the Presence of Edge States for a Truncated Pseudopotential
Simone Warzel, Amanda Young
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 g…
Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems
Bruno Nachtergaele, Robert Sims, Amanda Young
We prove that uniformly small short-range perturbations do not close the bulk gap above the ground state of frustration-free quantum spin systems that satisfy a standard local topo…
Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States
Bruno Nachtergaele, Robert Sims, Amanda Young
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 resul…
Spectral Gaps and Incompressibility in a Fractional Quantum Hall System
Bruno Nachtergaele, Simone Warzel, Amanda Young
We study an effective Hamiltonian for the standard fractional quantum Hall system in the thin cylinder regime. We give a complete description of its ground state space in t…
A class of two-dimensional AKLT models with a gap
Houssam Abdul-Rahman, Marius Lemm, Angelo Lucia +2
The AKLT spin chain is the prototypical example of a frustration-free quantum spin system with a spectral gap above its ground state. Affleck, Kennedy, Lieb, and Tasaki also conjec…
Quasi-Locality Bounds for Quantum Lattice Systems. Part I. Lieb-Robinson Bounds, Quasi-Local Maps, and Spectral Flow Automorphisms
Bruno Nachtergaele, Robert Sims, Amanda Young
Lieb-Robinson bounds show that the speed of propagation of information under the Heisenberg dynamics in a wide class of non-relativistic quantum lattice systems is essentially boun…
Lieb-Robinson bounds, the spectral flow, and stability of the spectral gap for lattice fermion systems
Bruno Nachtergaele, Robert Sims, Amanda Young
We prove Lieb-Robinson bounds for a general class of lattice fermion systems. By making use of a suitable conditional expectation onto subalgebras of the CAR algebra, we can apply…
Spectral Gap and Edge Excitations of -dimensional PVBS models on half-spaces
Michael Bishop, Bruno Nachtergaele, Amanda Young
We analyze a class of quantum spin models defined on half-spaces in the -dimensional hypercubic lattice bounded by a hyperplane with inward unit normal vector …
Product Vacua and Boundary State Models in d Dimensions
Sven Bachmann, Eman Hamza, Bruno Nachtergaele +1
We introduce and analyze a class of quantum spin models defined on d-dimensional lattices Lambda subset of Z^d, which we call `Product Vacua with Boundary States' (PVBS). We charac…