arXiv subjects

Elias Starchl

Publications and source records attributed to Elias Starchl.

5 recordsLinked to original sources

arXiv2025

Absence of measurement- and unraveling-induced entanglement transitions in continuously monitored one-dimensional free fermions

Continuous monitoring of one-dimensional free fermionic systems can generate phenomena reminiscent of quantum criticality, such as logarithmic entanglement growth, algebraic correlations, and emergent conformal invariance, but in a nonequilibrium setting. However, whether these signatures reflect a genuine phase of nonequilibrium quantum matter or persist only over finite length scales is an active area of research. We address this question in a free fermionic chain subject to continuous monitoring of lattice-site occupations. An unraveling phase $\varphi$ interpolates between measurement schemes, corresponding to different stochastic unravelings of the same Lindblad master equation: For $\varphi = 0$, measurements disentangle lattice sites, while for $\varphi = \pi/2$ they act as unitary random noise, yielding volume-law steady-state entanglement. Using replica Keldysh field theory, we obtain a nonlinear sigma model describing the long-wavelength physics. This analysis shows that for $0 \leq \varphi < \pi/2$, entanglement ultimately obeys an area law, but only beyond the exponentially large scale $\ln(l_{\varphi,*}) \sim J/[\gamma \cos(\varphi)]$, where $J$ is the hopping amplitude and $\gamma$ the measurement rate. Resolving $l_{\varphi, *}$ in numerical simulations is difficult for $\gamma/J \to 0$ or $\varphi \to \pi/2$. However, the theory also predicts that critical-like behavior appears below a crossover scale that grows only algebraically in $J/\gamma$, making it numerically accessible. Our simulations confirm these predictions, establishing the absence of measurement- or unraveling-induced entanglement transitions in this model.

quant-ph↗

arXiv2025

Generalized Zeno effect and entanglement dynamics induced by fermion counting

We study a one-dimensional lattice system of free fermions subjected to a generalized measurement process: the system exchanges particles with its environment, but each fermion leaving or entering the system is counted. In contrast to the freezing of dynamics due to frequent measurements of lattice site occupation numbers, a high rate of fermion counts induces fast fluctuations in the state of the system. Still, through numerical simulations of quantum trajectories and an analytical approach based on replica Keldysh field theory, we find that instantaneous correlations and entanglement properties of free fermions subjected to fermion counting and local occupation measurements are strikingly similar. We explain this similarity through a generalized Zeno effect induced by fermion counting and a universal long-wavelength description in terms of a nonlinear sigma model. The physical requirements underlying this universal emergent behavior are conservation of the total number of particles in the system and its environment, and conservation of the purity of the state of the system by keeping a full record of all measurement outcomes. For both types of measurement processes, we present strong evidence against the existence of a critical phase with logarithmic entanglement and conformal invariance. Instead, we identify a finite critical range of length scales on which signatures of conformal invariance are observable. While area-law entanglement is established beyond a scale that is exponentially large in the measurement rate, the upper boundary of the critical range is only algebraically large and thus numerically accessible. Our finding that these properties do not rely on particle number conservation has far reaching implications for measurement-induced phenomena beyond noninteracting fermions, such as charge sharpening in random quantum circuits or generic interacting systems.

quant-ph↗

arXiv2024

Quantum quenches in driven-dissipative quadratic fermionic systems with parity-time symmetry

We study the quench dynamics of noninteracting fermionic quantum many-body systems that are subjected to Markovian drive and dissipation and are described by a quadratic Liouvillian which has parity-time (PT) symmetry. In recent work, we have shown that such systems relax locally to a maximum entropy ensemble that we have dubbed the PT-symmetric generalized Gibbs ensemble (PTGGE), in analogy to the generalized Gibbs ensemble that describes the steady state of isolated integrable quantum many-body systems after a quench. Here, using driven-dissipative versions of the Su-Schrieffer-Heeger (SSH) model and the Kitaev chain as paradigmatic model systems, we corroborate and substantially expand upon our previous results. In particular, we confirm the validity of a dissipative quasiparticle picture at finite dissipation by demonstrating light cone spreading of correlations and the linear growth and saturation to the PTGGE prediction of the quasiparticle-pair contribution to the subsystem entropy in the PT-symmetric phase. Further, we introduce the concept of directional pumping phases, which is related to the non-Hermitian topology of the Liouvillian and based upon qualitatively different dynamics of the dual string order parameter and the subsystem fermion parity in the SSH model and the Kitaev chain, respectively: Depending on the postquench parameters, there can be pumping of string order and fermion parity through both ends of a subsystem corresponding to a finite segment of the one-dimensional lattice, through only one end, or there can be no pumping at all. We show that transitions between dynamical pumping phases give rise to a new and independent type of dynamical critical behavior of the rates of directional pumping, which are determined by the soft modes of the PTGGE.

cond-mat.stat-mech↗

arXiv2022

Relaxation to a Parity-Time Symmetric Generalized Gibbs Ensemble after a Quantum Quench in a Driven-Dissipative Kitaev Chain

The construction of the generalized Gibbs ensemble, to which isolated integrable quantum many-body systems relax after a quantum quench, is based upon the principle of maximum entropy. In contrast, there are no universal and model-independent laws that govern the relaxation dynamics and stationary states of open quantum systems, which are subjected to Markovian drive and dissipation. Yet, as we show, relaxation of driven-dissipative systems after a quantum quench can, in fact, be determined by a maximum entropy ensemble, if the Liouvillian that generates the dynamics of the system has parity-time symmetry. Focusing on the specific example of a driven-dissipative Kitaev chain, we show that, similarly to isolated integrable systems, the approach to a parity-time symmetric generalized Gibbs ensemble becomes manifest in the relaxation of local observables and the dynamics of subsystem entropies. In contrast, the directional pumping of fermion parity, which is induced by nontrivial non-Hermitian topology of the Kitaev chain, represents a phenomenon that is unique to relaxation dynamics in driven-dissipative systems. Upon increasing the strength of dissipation, parity-time symmetry is broken at a finite critical value, which thus constitutes a sharp dynamical transition that delimits the applicability of the principle of maximum entropy. We show that these results, which we obtain for the specific example of the Kitaev chain, apply to broad classes of noninteracting fermionic models, and we discuss their generalization to a noninteracting bosonic model and an interacting spin chain.

cond-mat.stat-mech↗

arXiv2021

Unraveling the origin of higher success probabilities in quantum versus semi-classical annealing

Quantum annealing aims at finding optimal solutions to complex optimization problems using a suitable quantum many body Hamiltonian encoding the solution in its ground state. To find the solution one typically evolves the ground state of a soluble initial Hamiltonian adiabatically to the ground state of the designated final Hamiltonian. Here we explore whether and when a full quantum representation of the dynamics leads to higher probability to end up in the desired ground when compared to a classical mean field approximation. As simple, nontrivial example we target the ground state of interacting bosons trapped in a tight binding lattice with small local defect by turning on long range interactions. Already two atoms in four sites interacting via two cavity modes prove complex enough to exhibit significant differences between the full quantum model and a mean field approximation for the cavity fields mediating the interactions. We find a large parameter region of highly successful quantum annealing where the semi-classical approach largely fails. Here we see strong evidence for the importance of entanglement to end close to the optimal solution. The quantum model also reduces the minimal time for a high target occupation probability. In contrast to naive expectations that enlarging the Hilbert space is beneficial, different numerical cut-offs of the Hilbert space reveal an improved performance for lower cut-offs, i.e. an nonphysical reduced Hilbert space, for short simulation times. Hence a less faithful representation of the full quantum dynamics sometimes creates a higher numerical success probability in shorter time. However, a sufficiently high cut-off proves relevant to obtain near perfect fidelity for long simulations times in a single run. Overall our results exhibit a clear improvement based on a quantum model versus simulations based on a classical field approximation.

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