Thermal DMRG for highly frustrated quantum spin chains: a user perspective

Thermal DMRG is investigated with emphasis of employability in molecular magnetism studies. To this end magnetic observables at finite temperature are evaluated for two one-dimensional quantum spin systems: a Heisenberg chain with nearest-neighbor antiferromagnetic interaction and a frustrated sawtooth (delta) chain. It is found that thermal DMRG indeed accurately approximates magnetic observables for the chain as well as for the sawtooth chain, but in the latter case only for sufficiently high temperatures. We speculate that the reason is due to the peculiar structure of the low-energy spectrum of the sawtooth chain induced by frustration.Comment: 18 pages, 5 figure

Mean Curvature, Singularities and Time Functions in Cosmology

In this contribution, we study spacetimes of cosmological interest, withoutmaking any symmetry assumptions. We prove a rigid Hawking singularity theoremfor positive cosmological constant, which sharpens known results. Inparticular, it implies that any spacetime with $\operatorname{Ric} \geq -ng$ intimelike directions and containing a compact Cauchy hypersurface with meancurvature $H \geq n$ is timelike incomplete. We also study the properties ofcosmological time and volume functions, addressing questions such as: When dothey satisfy the regularity condition? When are the level sets Cauchyhypersurfaces? What can one say about the mean curvature of the level sets?This naturally leads to consideration of Hawking type singularity theorems forCauchy surfaces satisfying mean curvature inequalities in a certain weak sense

Mean Curvature, Singularities and Time Functions in Cosmology

In this contribution, we study spacetimes of cosmological interest, without making any symmetry assumptions. We prove a rigid Hawking singularity theorem for positive cosmological constant, which sharpens known results. In particular, it implies that any spacetime with $\operatorname{Ric} \geq -ng$ in timelike directions and containing a compact Cauchy hypersurface with mean curvature $H \geq n$ is timelike incomplete. We also study the properties of cosmological time and volume functions, addressing questions such as: When do they satisfy the regularity condition? When are the level sets Cauchy hypersurfaces? What can one say about the mean curvature of the level sets? This naturally leads to consideration of Hawking type singularity theorems for Cauchy surfaces satisfying mean curvature inequalities in a certain weak sense.Comment: 15 pages, 2 figure