Publications

Free fermionic Gaussian, also known as matchgate, random circuits exhibit atypical behavior compared to generic interacting systems. They produce anomalously slow entanglement growth, characterized by diffusive scaling S(t)∼√t, and evolve into volume-law entangled states at late times, S∼N, which are highly unstable under measurements. Here, we investigate how doping such circuits with non-Gaussian resources (gates) restores entanglement structures of typical dynamics. We demonstrate that ballistic entanglement growth S(t)∼t is recovered after injecting an extensive total amount of non-Gaussian gates, which also restores Kardar-Parisi-Zhang fluctuations. When the evolution is perturbed with measurements, we uncover a measurement-induced phase transition between an area-law and a power-law entangled phase, S∼N^α, with α controlled by the doping. A genuine volume-law entangled phase is recovered only when non-Gaussian gates are injected at an extensive rate. Our findings bridge the dynamics of free and interacting fermionic systems, identifying non-Gaussianity as a key resource driving the emergence of nonintegrable behavior.

We investigate the critical behavior of the one-dimensional Ising model with long-range interactions using the functional renormalization group in the local potential approximation (LPA), and compare our findings with Dyson’s hierarchical model (DHM). While the DHM lacks translational invariance, it admits a field-theoretical description closely resembling the LPA, up to minor but nontrivial differences. After reviewing the real-space renormalization group approach to the DHM, we demonstrate a remarkable agreement in the critical exponent ν between the two methods across the entire range of power-law decays 1/2 < σ < 1. We further benchmark our results against Monte Carlo simulations and analytical expansions near the upper boundary of the nontrivial regime, 1

We study particle and energy transport in an open quantum system consisting of a three-harmonic oscillator chain coupled to thermal baths at different temperatures placed at the ends of the chain. We consider the exact dynamics of the open chain and its so-called local and global Markovian approximations. By comparing them, we show that, while all three yield a divergence-like continuity equation for the probability flow, the energy flow exhibits instead a distinct behavior. The exact dynamics and the local one preserve a standard divergence form for the energy transport, whereas the global open dynamics, due to the rotating wave approximation (RWA), introduces non-divergence sink/source terms. These terms also affect the continuity equation in the case of a master equation obtained through a time-coarse-graining method whereby RWA is avoided through a time-zoom parameter Δt. In such a scenario, sink and source contributions are always present for each Δt>0. While in the limit Δt→+∞ one recovers the global dissipative dynamics, sink and source terms instead vanish when Δt→0, restoring the divergence structure of the exact dynamics. Our results underscore how the choice of the dissipative Markovian approximation to an open system dynamics critically influences the energy transport descriptions, with implications for discriminating among them and thus, ultimately, for the correct modeling of the time-evolution of open quantum many-body systems.