@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 = {

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.

}, 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 {2498, title = {Hilbert-Space Fragmentation from Strict Confinement}, journal = {Phys. Rev. Lett.}, volume = {124}, year = {2020}, month = {5/22/2020}, abstract = {

We study one-dimensional spin-1/2 models in which strict confinement of Ising domain walls leads to the fragmentation of Hilbert space into exponentially many disconnected subspaces. Whereas most of the previous works emphasize dipole moment conservation as an essential ingredient for such fragmentation, we instead require two commuting U(1) conserved quantities associated with the total domain-wall number and the total magnetization. The latter arises naturally from the confinement of domain walls. Remarkably, while some connected components of the Hilbert space thermalize, others are integrable by Bethe ansatz. We further demonstrate how this Hilbert-space fragmentation pattern arises perturbatively in the confining limit of Z2 gauge theory coupled to fermionic matter, leading to a hierarchy of time scales for motion of the fermions. This model can be realized experimentally in two complementary settings.

}, doi = {https://doi.org/10.1103/PhysRevLett.124.207602}, url = {https://arxiv.org/abs/1912.04300}, author = {Zhi-Cheng Yang and Fangli Liu and Alexey V. Gorshkov and Thomas Iadecola} } @article {2720, title = {Localization and criticality in antiblockaded 2D Rydberg atom arrays}, year = {2020}, month = {12/7/2020}, abstract = {

Controllable Rydberg atom arrays have provided new insights into fundamental properties of quantum matter both in and out of equilibrium. In this work, we study the effect of experimentally relevant positional disorder on Rydberg atoms trapped in a 2D square lattice under anti-blockade (facilitation) conditions. We show that the facilitation conditions lead the connectivity graph of a particular subspace of the full Hilbert space to form a 2D Lieb lattice, which features a singular flat band. Remarkably, we find three distinct regimes as the disorder strength is varied: a critical regime, a delocalized but nonergodic regime, and a regime with a disorder-induced flat band. The critical regime\&$\#$39;s existence depends crucially upon the singular flat band in our model, and is absent in any 1D array or ladder system. We propose to use quench dynamics to probe the three different regimes experimentally.\ 

}, url = {https://arxiv.org/abs/2012.03946}, author = {Fangli Liu and Zhi-Cheng Yang and Przemyslaw Bienias and Thomas Iadecola and Alexey V. Gorshkov} } @article {2636, title = {Realizing and Probing Baryonic Excitations in Rydberg Atom Arrays}, year = {2020}, month = {7/14/2020}, abstract = {

We propose a realization of mesonic and baryonic quasiparticle excitations in Rydberg atom arrays with programmable interactions. Recent experiments have shown that such systems possess a Z3-ordered crystalline phase whose low-energy quasiparticles are defects in the crystalline order. By engineering a Z3-translational-symmetry breaking field on top of the Rydberg-blockaded Hamiltonian, we show that different types of defects experience confinement, and as a consequence form mesonic or baryonic quasiparticle excitations. We illustrate the formation of these quasiparticles by studying a quantum chiral clock model related to the Rydberg Hamiltonian. We then propose an experimental protocol involving out-of-equilibrium dynamics to directly probe the spectrum of the confined excitations. We show that the confined quasiparticle spectrum can limit quantum information spreading in this system. This proposal is readily applicable to current Rydberg experiments, and the method can be easily generalized to more complex confined excitations (e.g. {\textquoteleft}tetraquarks\&$\#$39;, {\textquoteleft}pentaquarks\&$\#$39;) in phases with Zq order for q\>3.\ 

}, url = {https://arxiv.org/abs/2007.07258}, author = {Fangli Liu and Seth Whitsitt and Przemyslaw Bienias and Rex Lundgren 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 = {

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.

}, 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} } @article {2465, title = {Momentum-space entanglement after a quench in one-dimensional disordered fermionic systems}, year = {2019}, month = {9/11/2019}, abstract = {

We numerically investigate the momentum-space entanglement entropy and entanglement spectrum of the random-dimer model and its generalizations, which circumvent Anderson localization, after a quench in the Hamiltonian parameters. The type of dynamics that occurs depends on whether or not the Fermi level of the initial state is near the energy of the delocalized states present in these models. If the Fermi level of the initial state is near the energy of the delocalized states, we observe an interesting slow logarithmic-like growth of the momentum-space entanglement entropy followed by an eventual saturation. Otherwise, the momentum-space entanglement entropy is found to rapidly saturate. We also find that the momentum-space entanglement spectrum reveals the presence of delocalized states in these models for long times after the quench and the many-body entanglement gap decays logarithmically in time when the Fermi level is near the energy of the delocalized states.

}, url = {https://arxiv.org/abs/1909.05140}, author = {Rex Lundgren and Fangli Liu and Pontus Laurell and Gregory A. Fiete} } @article {2487, title = {Real-time dynamics of string breaking in quantum spin chains}, year = {2019}, month = {2019/11/26}, abstract = {

String breaking is a central dynamical process in theories featuring confinement, where a string connecting two charges decays at the expense of the creation of new particle-antiparticle pairs. Here, we show that this process can also be observed in quantum Ising chains where domain walls get confined either by a symmetry-breaking field or by long-range interactions. We find that string breaking occurs, in general, as a two-stage process: First, the initial charges remain essentially static and stable. The connecting string, however, can become a dynamical object. We develop an effective description of this motion, which we find is strongly constrained. In the second stage, which can be severely delayed due to these dynamical constraints, the string finally breaks. We observe that the associated time scale can depend crucially on the initial separation between domain walls and can grow by orders of magnitude by changing the distance by just a few lattice sites. We discuss how our results generalize to one-dimensional confining gauge theories and how they can be made accessible in quantum simulator experiments such as Rydberg atoms or trapped ions.

}, url = {https://arxiv.org/abs/1911.11382}, author = {Roberto Verdel and Fangli Liu and Seth Whitsitt and Alexey V. Gorshkov and Markus Heyl} } @article {2211, title = {Asymmetric Particle Transport and Light-Cone Dynamics Induced by Anyonic Statistics}, journal = {Phys. Rev. Lett}, volume = {121}, year = {2018}, month = {2018/12/20}, abstract = {

We study the non-equilibrium dynamics of Abelian anyons in a one-dimensional system. We find that the interplay of anyonic statistics and interactions gives rise to spatially asymmetric particle transport together with a novel dynamical symmetry that depends on the anyonic statistical angle and the sign of interactions. Moreover, we show that anyonic statistics induces asymmetric spreading of quantum information, characterized by asymmetric light cones of out-of-time-ordered correlators. Such asymmetric dynamics is in sharp contrast with the dynamics of conventional fermions or bosons, where both the transport and information dynamics are spatially symmetric. We further discuss experiments with cold atoms where the predicted phenomena can be observed using state-of-the-art technologies. Our results pave the way toward experimentally probing anyonic statistics through non-equilibrium dynamics.

}, doi = {https://doi.org/10.1103/PhysRevLett.121.250404}, url = {https://arxiv.org/abs/1809.02614}, author = {Fangli Liu and James R. Garrison and Dong-Ling Deng and Zhe-Xuan Gong and Alexey V. Gorshkov} }