The evolution of entanglement entropy in quantum circuits composed of Haar-random gates and projective measurements shows versatile behavior, with connections to phase transitions and complexity theory. We reformulate the problem in terms of a classical Markov process for the dynamics of bipartition purities and establish a probabilistic cellular-automaton algorithm to compute entanglement entropy in monitored random circuits on arbitrary graphs. In one dimension, we further relate the evolution of the entropy to a simple classical spin model that naturally generalizes a two-dimensional lattice percolation problem. We also establish a Markov model for the evolution of the zeroth Rényi entropy and demonstrate that, in one dimension and in the limit of large local dimension, it coincides with the corresponding second-Rényi-entropy model. Finally, we extend the Markovian description to a more general setting that incorporates continuous-time dynamics, defined by stochastic Hamiltonians and weak local measurements continuously monitoring the system.

UR - https://arxiv.org/abs/2004.06736 ER - TY - JOUR T1 - A minimal model for fast scrambling Y1 - 2020 A1 - Ron Belyansky A1 - Przemyslaw Bienias A1 - Yaroslav A. Kharkov A1 - Alexey V. Gorshkov A1 - Brian Swingle AB -We study quantum information scrambling in spin models with both long-range all-to-all and short-range interactions. We argue that a simple global, spatially homogeneous interaction together with local chaotic dynamics is sufficient to give rise to fast scrambling, which describes the spread of quantum information over the entire system in a time that is logarithmic in the system size. This is illustrated in two exactly solvable models: (1) a random circuit with Haar random local unitaries and a global interaction and (2) a classical model of globally coupled non-linear oscillators. We use exact numerics to provide further evidence by studying the time evolution of an out-of-time-order correlator and entanglement entropy in spin chains of intermediate sizes. Our results can be verified with state-of-the-art quantum simulators.

UR - https://arxiv.org/abs/2005.05362 ER - TY - JOUR T1 - Quantum Lifshitz criticality in a frustrated two-dimensional XY model JF - Phys. Rev. B Y1 - 2020 A1 - Yaroslav A. Kharkov A1 - Jaan Oitmaa A1 - Oleg P. Sushkov AB -Antiferromagnetic quantum spin systems can exhibit a transition between collinear and spiral ground states,

driven by frustration. Classically this is a smooth crossover and the crossover point is termed a Lifshitz point.

Quantum fluctuations change the nature of the transition. In particular, it has been argued previously that in the two-dimensional (2D) case a spin liquid (SL) state is developed in the vicinity of the Lifshitz point, termed a Lifshitz SL. In the present work, using a field theory approach, we solve the Lifshitz quantum phase transition problem for the 2D frustrated XY model. Specifically, we show that, unlike the SU (2) symmetric Lifshitz case, in the XY model, the SL exists only at the critical point. At zero temperature we calculate nonuniversal critical exponents in the Néel and in the spin spiral state and relate these to properties of the SL. We also solve the transition problem at a finite temperature and discuss the role of topological excitations.