arXiv subjects

F David Wandler

Publications and source records attributed to F David Wandler.

3 recordsLinked to original sources

arXiv2024

Numerical fractional instantons in SU(2): center vortices, monopoles, and a sharp transition between them

We use a numerical cooling algorithm to study fractional instantons in $SU(2)$ pure Yang-Mills on $\mathbb{R}^2\times\mathbb{T}^2_*$, $\mathbb{R}^3\times S^1$, and $\mathbb{R}\times \mathbb{T}^2_* \times S^1$. We confirm that the fractional instantons are center vortices on $\mathbb{R}^2\times\mathbb{T}^2_*$ and monopoles on $\mathbb{R}^3\times S^1$, and we calculate several properties relevant to using these solutions for semiclassical calculations. On $\mathbb{R}\times \mathbb{T}^2_* \times S^1$, we interpolate between the large $\mathbb{T}^2_*$ limit and the large $S^1$ limit to study how the solutions interpolate between center vortices and monopoles. We find that they are separated by a sharp transition, with 't Hooft's constant field strength solutions living at the transition point. These results contrast but do not contradict recent results suggesting continuity between vortices and monopoles.

hep-lat↗

arXiv2023

Impact of gapped spin-orbit excitons on low energy pseudospin exchange interactions

The quest for exotic quantum magnetic ground states, including the Kitaev spin liquid and quantum spin-ices, has led to the discovery of several quantum materials where low energy pseudospin-$1/2$ doublets arise from the splitting of spin-orbit entangled multiplets with higher degeneracy. Such systems include $d$-orbital and $f$-orbital Mott insulators. When the gap between the low energy pseudospin-$1/2$ levels and the excited levels of the multiplet or `excitons' is not large, the effective low-energy exchange interactions between the low energy pseudospin-$1/2$ moments can acquire significant corrections from coupling to the excitons. We extract these corrections using higher order perturbation theory as well as an exact Schrieffer-Wolff transformation. Such corrections can impact the exchange matrix for the low energy pseudospin-$1/2$ levels by renormalizing the strength and the sign of Heisenberg exchange or Ising anisotropies, and potentially even inducing bond-anisotropic couplings such as Kitaev-$Γ$ exchange interactions. We discuss recent experiments on various cobaltate and osmate materials which hint at the ubiquity and importance of this physics.

cond-mat.str-el↗

arXiv2023

Gauge theory geography: charting a path between semiclassical islands

We study two semiclassical limits of $SU(2)$ Yang-Mills theory on a spatial torus with a 't Hooft twist: the ``femtouniverse,'' where all $\mathbb{T}^3$ directions are small, and deformed Yang-Mills theory on $\mathbb{T}^2 \times \mathbb{S}^1$, with small $\mathbb{S}^1$ and large or infinite $\mathbb{T}^2$. Carefully defining the symmetries, we show that the classical ground states, while different, have the same transformation properties under the 1-form center symmetry and parity. We argue that this is behind the identical multi-branch $θ$-dependent vacuum structure of these theories. We then calculate the one-loop potential for the $\mathbb{S}^1$-holonomy in the presence of twists on $\mathbb{T}^2$. We use it to study the quantum stability of the semiclassical ground states in gauge theories with massive or massless adjoint fermions on spatial $\mathbb{T}^2 \times \mathbb{S}^1$, with a twist in the $\mathbb{T}^2$. The results point towards some interesting features worthy of further study.

hep-th↗