12 citations · 20 across the 8 of their papers we have counts for
7 papers · 1 filter
Existence of a Spectral Gap in the Affleck-Kennedy-Lieb-Tasaki Model on the Hexagonal Lattice
Marius Lemm, Anders W. Sandvik, Ling Wang
The 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 AKL…
On the finite-size Lyapunov exponent for the Schroedinger operator with skew-shift potential
Paul Michael Kielstra, Marius Lemm
It is known that a one-dimensional quantum particle is localized when subjected to an arbitrarily weak random potential. It is conjectured that localization also occurs for an arbi…
A central limit theorem for integrals of random waves
Matthew de Courcy-Ireland, Marius Lemm
We derive a central limit theorem for the mean-square of random waves in the high-frequency limit over shrinking sets. Our proof applies to any compact Riemannian manifold of arbit…
A remark on a surprising result by Bourgain in homogenization
Mitia Duerinckx, Antoine Gloria, Marius Lemm
In a recent work, Bourgain gave a fine description of the expectation of solutions of discrete linear elliptic equations on with random coefficients in a perturbative…
Gaplessness is not generic for translation-invariant spin chains
Marius Lemm
The existence of a spectral gap above the ground state has far-reaching consequences for the low-energy physics of a quantum many-body system. A recent work of Movassagh [R. Movass…
Finite-size criteria for spectral gaps in -dimensional quantum spin systems
Marius Lemm
We generalize the existing finite-size criteria for spectral gaps of frustration-free spin systems to dimensions. We obtain a local gap threshold of , independen…