Recursive contact tracing in Reed–Frost epidemic models
Physical Biology IOP Publishing 18:6 (2021) 065001
How smooth is quantum complexity?
Journal of High Energy Phyics Springer Nature 2021:10 (2021) 230
Abstract:
The “quantum complexity” of a unitary operator measures the difficulty of its construction from a set of elementary quantum gates. While the notion of quantum complexity was first introduced as a quantum generalization of the classical computational complexity, it has since been argued to hold a fundamental significance in its own right, as a physical quantity analogous to the thermodynamic entropy. In this paper, we present a unified perspective on various notions of quantum complexity, viewed as functions on the space of unitary operators. One striking feature of these functions is that they can exhibit non-smooth and even fractal behaviour. We use ideas from Diophantine approximation theory and sub-Riemannian geometry to rigorously quantify this lack of smoothness. Implications for the physical meaning of quantum complexity are discussed.Theory of competing excitonic orders in insulating WTe_2 monolayers
Physical Review B: Condensed Matter and Materials Physics American Physical Society 104 (2021) 125133
Abstract:
We develop a theory of the excitonic phase recently proposed as the zero-field insulating state observed near charge neutrality in monolayer WTe$_2$. Using a Hartree-Fock approximation, we numerically identify two distinct gapped excitonic phases: a spin density wave state for weak but non-zero interaction strength $U_0$, and spin spiral order at larger $U_0$, separated by a narrow window of trivial insulator. We introduce a simplified model capturing essential features of the WTe$_2$ band structure, in which the two phases may be viewed as distinct valley ferromagnetic orders. We link the competition between the two phases to the orbital structure of the electronic wavefunctions at the Fermi surface and hence its proximity to the underlying gapped Dirac point in WTe$_2$. We briefly discuss collective modes of the two excitonic states, and comment on implications for experiments.One-Dimensional Luttinger Liquids in a Two-Dimensional Moiré Lattice
(2021)
Quantum oscillations in the Zeroth Landau level: serpentine Landau fan and the chiral anomaly
Physical Review Letters American Physical Society 127 (2021) 116602