



@article {2364,
	title = {Circuit Complexity across a Topological Phase Transition},
	journal = {Physical Review Research },
	volume = {2},
	year = {2020},
	month = {03/16/2020},
	pages = {013323},
	abstract = {<p>We use Nielsen\&$\#$39;s approach to quantify the circuit complexity in the one-dimensional Kitaev model. In equilibrium, we find that the circuit complexity of ground states exhibits a divergent derivative at the critical point, signaling the presence of a topological phase transition. Out of equilibrium, we study the complexity dynamics after a sudden quench, and find that the steady-state complexity exhibits nonanalytical behavior when quenched across critical points. We generalize our results to the long-range interacting case, and demonstrate that the circuit complexity correctly predicts the critical point between regions with different semi-integer topological numbers. Our results establish a connection between circuit complexity and quantum phase transitions both in and out of equilibrium, and can be easily generalized to topological phase transitions in higher dimensions. Our study opens a new avenue to using circuit complexity as a novel quantity to understand many-body systems.</p>},
	doi = {https://doi.org/10.1103/PhysRevResearch.2.013323},
	url = {https://arxiv.org/abs/1902.10720},
	author = {Fangli Liu and Rex Lundgren and Paraj Titum and James R. Garrison and Alexey V. Gorshkov}
}
@article {2264,
	title = {Confined Dynamics in Long-Range Interacting Quantum Spin Chains},
	journal = {Phys. Rev. Lett.},
	volume = {122 },
	year = {2019},
	month = {04/17/2019},
	abstract = {<p>We study the quasiparticle excitation and quench dynamics of the one-dimensional transverse-field Ising model with power-law (1/rα) 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 bound states have dramatic consequences for the non-equilibrium dynamics following a global quantum quench, such as suppressed spreading of quantum information and oscillations of order parameters. The masses of these bound states can be read out from the Fourier spectrum of these oscillating order parameters. We then use a two-kink model to qualitatively explain the phenomenon of long-range-interaction-induced confinement. The masses of the bound states predicted by this model are in good quantitative agreement with exact diagonalization results. Moreover, we illustrate that these bound states lead to weak thermalization of local observables for initial states with energy near the bottom of the many-body energy spectrum. Our work is readily applicable to current trapped-ion experiments.</p>},
	doi = {https://doi.org/10.1103/PhysRevLett.122.150601},
	url = {https://arxiv.org/abs/1810.02365},
	author = {Fangli Liu and Rex Lundgren and Paraj Titum and Guido Pagano and Jiehang Zhang and Christopher Monroe and Alexey V. Gorshkov}
}
