Quantum systems evolving unitarily and subject to quantum measurements exhibit various types of nonequilibrium phase transitions, arising from the competition between unitary evolution and measurements. Dissipative phase transitions in steady states of timeindependent Liouvillians and measurement induced phase transitions at the level of quantum trajectories are two primary examples of such transitions. Investigating a manybody spin system subject to periodic resetting measurements, we argue that manybody dissipative Floquet dynamics provides a natural framework to analyze both types of transitions. We show that a dissipative phase transition between a ferromagnetic ordered phase and a paramagnetic disordered phase emerges for longrange systems as a function of measurement probabilities. A measurement induced transition of the entanglement entropy between volume law scaling and subvolume law scaling is also present, and is distinct from the ordering transition. The two phases correspond to an errorcorrecting and a quantumZeno regimes, respectively. The ferromagnetic phase is lost for short range interactions, while the volume law phase of the entanglement is enhanced. An analysis of multifractal properties of wave function in Hilbert space provides a common perspective on both types of transitions in the system. Our findings are immediately relevant to trapped ion experiments, for which we detail a blueprint proposal based on currently available platforms.
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Classical algorithms, correlation decay, and complex zeros of partition functions of quantum manybody systems
We present a quasipolynomial time classical algorithm that estimates the partition function of quantum manybody systems at temperatures above the thermal phase transition point. It is known that in the worst case, the same problem is NPhard below this point. Together with our work, this shows that the transition in the phase of a quantum system is also accompanied by a transition in the hardness of approximation. We also show that in a system of n particles above the phase transition point, the correlation between two observables whose distance is at least Ω(logn) decays exponentially. We can improve the factor of logn to a constant when the Hamiltonian has commuting terms or is on a 1D chain. The key to our results is a characterization of the phase transition and the critical behavior of the system in terms of the complex zeros of the partition function. Our work extends a seminal work of Dobrushin and Shlosman on the equivalence between the decay of correlations and the analyticity of the free energy in classical spin models. On the algorithmic side, our result extends the scope of a recent approach due to Barvinok for solving classical counting problems to quantum manybody systems.
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 NSFPAR ID:
 10216638
 Date Published:
 Journal Name:
 STOC 2020: Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing
 Page Range / eLocation ID:
 378 to 386
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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