The main question we address is how to probe the fractionalized excitations of a quantum spin liquid (QSL), for example, in the Kitaev honeycomb model. By analyzing the energy spectrum and entanglement entropy, for antiferromagnetic couplings and a field along either [111] or [001], we find a gapless QSL phase sandwiched between the non-Abelian Kitaev QSL and polarized phases. Increasing the field strength towards the polarized limit destroys this intermediate QSL phase, resulting in a considerable reduction in the number of frequency modes and the emergence of a beating pattern in the local dynamical correlations, possibly observable in pump-probe experiments.PACS numbers:

In their paper entitled “Quantum Enhancements and Biquandle Brackets”, Nelson, Orrison, and Rivera introduced biquandle brackets, which are customized skein invariants for biquandle-colored links. We prove herein that if a biquandle bracket [Formula: see text] is the pointwise product of the pair of functions [Formula: see text] with a function [Formula: see text], then [Formula: see text] is also a biquandle bracket if and only if [Formula: see text] is a biquandle 2-cocycle (up to a constant multiple). As an application, we show that a new invariant introduced by Yang factors in this way, which allows us to show that the new invariant is in fact equivalent to the Jones polynomial on knots. Additionally, we provide a few new results about the structure of biquandle brackets and their relationship with biquandle 2-cocycles.

The Biquandle Bracket is a generalization of the Jones Polynomial. In this paper, we outline a Khovanov Homology-style construction which generalizes Khovanov Homology and attempts to categorify the Biquandle Bracket. The Biquandle Bracket is not always recoverable from our construction, so this is not a true categorification. However, this deficiency leads to a new invariant: a canonical biquandle 2-cocycle associated to a biquandle bracket.