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Jackson R. Fliss
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We study the extent to which knot and link states (that is, states in 3d Chern-Simons theory prepared by path integration on knot and link complements) can or cannot be described by stabilizer states. States which are not classical mixtures of stabilizer states are known as magic states and play a key role in quantum resource theory. By implementing a particular magic monotone known as the mana we quantify the magic of knot and link states. In particular, for $SU(2)_k$ Chern-Simons theory we show that knot and link states are generically magical. For link states, we further investigate the mana associated to correlations between separate boundaries which characterizes the states long-range magic. Our numerical results suggest that the magic of a majority of link states is entirely long-range. We make these statements sharper for torus links.
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We study interacting critical UV regime of the long-range $O(N)$ vector model with quartic coupling. Analyzing CFT data within the scope of $epsilon$- and $1/N$-expansion, we collect evidence for the equivalence of this model and the critical IR limit of the cubic model coupled to a generalized free field $O(N)$ vector multiplet.
We study the quasiparticle excitation and quench dynamics of the one-dimensional transverse-field Ising model with power-law ($1/r^{alpha}$) interactions. We find that long-range interactions give rise to a confining potential, which couples pairs of domain walls (kinks) into bound quasiparticles, analogous to mesonic bound states in high-energy physics. We show that these quasiparticles have signatures in the dynamics of order parameters following a global quench and the Fourier spectrum of these order parameters can be expolited as a direct probe of the masses of the confined quasiparticles. We introduce a two-kink model to qualitatively explain the phenomenon of long-range-interaction induced confinement, and to quantitatively predict the masses of the bound quasiparticles. Furthermore, we illustrate that these quasiparticle states can lead to slow thermalization of one-point observables for certain initial states. Our work is readily applicable to current trapped-ion experiments.
Long-range interacting many-body systems exhibit a number of peculiar and intriguing properties. One of those is the scaling of relaxation times with the number $N$ of particles in a system. In this paper I give a survey of results on long-range quantum spin models that illustrate this scaling behaviour, and provide indications for its common occurrence by making use of Lieb-Robinson bounds. I argue that these findings may help in understanding the extraordinarily short equilibration timescales predicted by typicality techniques.
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