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arXiv:2306.09893 · Physical review. B./Physical review. B

Density and current statistics in boundary-driven monitored fermionic chains

Xhek Turkeshi, Lorenzo Piroli, Marco Schirò

Published Apr 23, 2024• 21 citations
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Abstract

We consider a one-dimensional system of noninteracting fermions featuring both boundary driving and continuous monitoring of the bulk particle density. Due to the measurements, the expectation values of the local density and current operators are random variables whose average behavior is described by a well-studied Lindblad master equation. By means of exact numerical computations, we go beyond the averaged dynamics and study their full probability distribution functions, focusing on the late-time stationary regime. We find that contrary to the averaged values, the spatial profiles of the median density and current are nontrivial, exhibiting qualitative differences as a function of the monitoring strength. At weak monitoring, the medians are close to the means, displaying diffusive spatial profiles. At strong monitoring, we find that the median density and current develop a domain-wall and single-peak profile, respectively, which are suggestive of a Zeno-like localization in typical quantum trajectories. While we are not able to identify a sharp phase transition as a function of the monitoring rate, our work highlights the usefulness of characterizing typical behavior beyond the averaged values in the context of monitored many-body quantum dynamics.

DOI
10.1103/physrevb.109.144306

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We consider a one-dimensional system of noninteracting fermions featuring both boundary driving and continuous monitoring of the bulk particle density. Due to the measurements, the expectation values of the local density and current operators are random variables whose average behavior is described by a well-studied Lindblad master equation. By means of exact numerical computations, we go beyond the averaged dynamics and study their full probability distribution functions, focusing on the late-time stationary regime. We find that contrary to the averaged values, the spatial profiles of the median density and current are nontrivial, exhibiting qualitative differences as a function of the monitoring strength. At weak monitoring, the medians are close to the means, displaying diffusive spatial profiles. At strong monitoring, we find that the median density and current develop a domain-wall and single-peak profile, respectively, which are suggestive of a Zeno-like localization in typical quantum trajectories. While we are not able to identify a sharp phase transition as a function of the monitoring rate, our work highlights the usefulness of characterizing typical behavior beyond the averaged values in the context of monitored many-body quantum dynamics.
We investigate entanglement dynamics in continuously monitored open quantum systems featuring current-carrying nonequilibrium states. We focus on a prototypical one-dimensional model of boundary-driven noninteracting fermions with monitoring of the local density, whose average Lindblad dynamics features a well-studied ballistic to diffusive crossover in transport. Here we analyze the dynamics of the fermionic negativity, mutual information, and purity along different quantum trajectories. We show that monitoring this boundary-driven system enhances its entanglement negativity at long times, which otherwise decays to zero in the absence of measurements. This result is in contrast with the case of unitary evolution where monitoring suppresses entanglement production. For small values of $\ensuremath{\gamma}$, the stationary-state negativity shows a logarithmic scaling with system size, transitioning to an area-law scaling as $\ensuremath{\gamma}$ is increased beyond a critical value. Similar critical behavior is found in the mutual information, while the late-time purity shows no apparent signature of a transition, being O(1)O(1)O(1) for all values of $\ensuremath{\gamma}$. Our work unveils the double role of weak monitoring in current-driven open quantum systems, simultaneously damping transport and enhancing entanglement.
We consider a class of either fermionic or bosonic noninteracting open quantum chains driven by dissipative interactions at the boundaries and study the interplay of coherent transport and dissipative processes, such as bulk dephasing and diffusion. Starting from the microscopic formulation, we show that the dynamics on large scales can be described in terms of fluctuating hydrodynamics. This is an important simplification as it allows us to apply the methods of macroscopic fluctuation theory to compute the large deviation (LD) statistics of time-integrated currents. In particular, this permits us to show that fermionic open chains display a third-order dynamical phase transition in LD functions. We show that this transition is manifested in a singular change in the structure of trajectories: while typical trajectories are diffusive, rare trajectories associated with atypical currents are ballistic and hyperuniform in their spatial structure. We confirm these results by numerically simulating ensembles of rare trajectories via the cloning method, and by exact numerical diagonalization of the microscopic quantum generator.
Boundary-driven quantum spin chains are paradigmatic nonequilibrium systems featuring the presence of particle currents. In general, it may not be possible to distinguish an incoherent type of particle transport from a truly quantum coherent one through monitoring the mean current, as both ballistic as well as diffusive regimes occur in either setting. Here, we show that genuine coherent features become manifest in large fluctuations which allow a discrimination between incoherent and coherent quantum transport: in the former case, realizations that are characterized by atypically large boundary activity are associated with larger than typical currents, i.e., an enhanced number of events at the boundaries goes together with a large current. Conversely, in the coherent case the Zeno effect leads to the suppression of current in trajectories with large activity at the boundary. We analyze how these different dynamical regimes are reflected in the structure of rare fluctuations. We show moreover that realizations supporting a large current are generated via weak long-range correlations within the spin chain, typically associated with hyperuniformity. We further observe critical time-coexistence behaviors with intermittent currents in rare fluctuations of the strongly interacting XXZ chain for completely asymmetric drivings.
We study a model of noninteracting spinless fermions coupled to local dephasing and boundary drive and described within a Lindblad master equation. The model features an interplay between infinite temperature thermalization due to bulk dephasing and a nonequilibrium stationary state due to the boundary drive and dissipation. We revisit the linear and nonlinear transport properties of the model, featuring a crossover from ballistic to diffusive scaling, and compute the spectral and occupation properties encoded in the single-particle Green's functions, that we compute exactly using the Lindblad equations of motion in spite of the interacting nature of the dephasing term. We show that the distribution function in the bulk of the system becomes frequency independent and flat, consistent with infinite temperature thermalization, while near the boundaries it retains strong nonequilibrium features that reflect the continuous injection and depletion of particles due to driving and dissipation.
We study transport dynamics of free fermions subject to the external monitoring of a conserved charge over an extensive region. Focusing on bipartition protocols, we consider monitoring the total particle number over half of the system, and study the profiles of local charges and currents at hydrodynamic scales. While the Lindbladian describing the averaged dynamics is non-local, we show that the profiles can be understood in terms of localized impurities. We present a general framework based on the generalized hydrodynamics (GHD) picture, allowing for a hybrid numerical-analytic solution of the quench dynamics at hydrodynamic scales. We illustrate our approach for domain-wall initial states, showing that monitoring leads to discontinuities in the profiles that become more pronounced as the rate increases and that lead to the absence of transport in the Zeno limit of infinite monitoring rates. Our GHD framework could be naturally extended to interacting systems, paving the way for a systematic study of transport of integrable models subject to extensive-charge measurements.
We study a general one-dimensional spinless fermionic system subject to a localized source, sink, and bulk dephasing. Within the Lindblad framework, we compute the time evolution of the density profile and spatial correlation functions. We find that the presence of bulk dephasing suppresses certain coherent quantum features, such as the Friedel oscillations, and it alters the transport dynamics to exhibit two distinct dynamical regimes instead of three as observed in the absence of dephasing. This effect can be understood as the destruction of ballistic motion caused by the dephasing noise. Under strong dephasing, the density profile becomes similar to the one expected for a classical diffusive regime. We also investigate the system in the presence of both a localized source and sink, placed at a distance of ΔΔΔ. Interestingly, quantum coherence generates secondary density peaks at integer multiples of the source-sink separation ΔΔΔ, which are systematically washed out as bulk dephasing drives the system toward the classical diffusive limit.