Partition function of the Kitaev quantum double model
Physical Review B American Physical Society 113:16 (2026) 165106
Abstract:
We compute the degeneracy of energy levels in the Kitaev quantum double model for any discrete group $G$ on any planar graph forming the skeleton of a closed orientable surface of arbitrary genus. The derivation is based on the fusion rules of the properly identified vertex and plaquette excitations, which are selected among the anyons, i.e., the simple objects of the Drinfeld center $\mathcal{Z}(\mathrm{Vec}_G)$. These degeneracies are given in terms of the quantum dimensions of the anyons and allow one to obtain the exact finite-temperature partition function of the model, valid for any finite-size system.
Phase separation in a mixture of proliferating and motile active matter
Physical Review Research American Physical Society (APS) 8:2 (2026) l022012
Abstract:
Proliferation and motility are ubiquitous drivers of activity in biological systems. Here, we study a dense binary mixture of motile and proliferating particles with exclusively repulsive interactions, where homeostasis in the proliferating subpopulation is maintained by pressure-induced removal. Using numerical simulations, we show that phase separation emerges naturally in this system at high density and weak enough self-propulsion. We map the full two-component system to an effective single-component active Brownian particle model that recapitulates this behavior. This allows us to identify the emergent effects of the proliferating matrix on motile particles that interact to produce phase separation: enhanced diffusion, renormalized self-propulsion, reduced persistence, and an effective attraction between motile particles. Our results establish a specific type of phase transition based on these emergent effects and pave a way to reinterpret the physics of dense cellular populations, such as bacterial colonies or tumors, as systems of mixed active matter.
Phases of itinerant anyons in Laughlin's quantum Hall states on a lattice
preprint, arXiv:2603.22389
Abstract:
We study phases of itinerant anyons when hole-doping Laughlin-like states in fractional Chern insulators (FCIs). In light of the recent observation of time-reversal-broken superconductivity near FCIs in van der Waals materials, a theoetical understanding of doped fractional quantum Hall states on a lattice has been developed by Shi and Senthil [Phys. Rev. X 15, 031069], reviving old ideas about "anyon superconductivity". We test these ideas analytically within an effective parton mean-field theory and numerically with variational Monte Carlo, pointing out that the predicted state depends on whether the Laughlin order at ν=1/m is described by a U(1), or an SU(m) Chern-Simons field, the latter implying a symmetry between the m parton species. Our results demonstrate that the interplay between band Berry curvature and effective anyon dispersion has crucial implications for which anyonic phase is realized. In the expermentally relevant scenario of hole-doping the ν=1/3 fermionic FCI, our results uncover a mechanism for the formation of an anyon superconducting state of half-integer central charge in the case when the energetically cheapest excitations are the fundamental 1/3 charge anyons, bypassing the need for these anyons to pair into charge-2/3 composites, which has generally been assumed in similar anyon superconductivity constructions.
Phases of itinerant anyons in Laughlin's quantum Hall states on a lattice
(2026)
Paired Parton Trial States for the Superfluid-Fractional Chern Insulator Transition
(2026)