418 citations · 476 across the 8 of their papers we have counts for
14 papers · 1 filter
Lieb-Robinson Bounds and the Exponential Clustering Theorem
Bruno Nachtergaele, Robert Sims
We give a Lieb-Robinson bound for the group velocity of a large class of discrete quantum systems which can be used to prove that a non-vanishing spectral gap implies exponential c…
Quantum Spin Systems
Bruno Nachtergaele
This article is a short introduction to the general topic of quantum spin systems. After a brief sketch of the history of the subject, the standard mathematical framework for formu…
A Ferromagnetic Lieb-Mattis Theorem
Bruno Nachtergaele, Shannon Starr
We prove ferromagnetic ordering of energy levels for XXX Heisenberg chains of any spin and XXZ spin chains with all spins equal to 1/2. Ferromagnetic ordering means that the minimu…
Central limit theorems for the large-spin asymptotics of quantum spins
Tom Michoel, Bruno Nachtergaele
We use a generalized form of Dyson's spin wave formalism to prove several central limit theorems for the large-spin asymptotics of quantum spins in a coherent state.
The large-spin asymptotics of the ferromagnetic XXZ chain
Tom Michoel, Bruno Nachtergaele
We present new results and give a concise review of recent previous results on the asymptotics for large spin of the low-lying spectrum of the ferromagnetic XXZ Heisenberg chain wi…
Path integral representations for the spin-pinned quantum XXZ chain
Oscar Bolina, Pierluigi Contucci, Bruno Nachtergaele
Two discrete path integral formulations for the ground state of a spin-pinned quantum anisotropic XXZ Heisenberg chain are introduced. Their properties are discussed and two recurs…