New frontiers in out-of-equilibrium quantum many-body dynamics

In chaotic many-body dynamics the relaxation of local correlation functions to equilibrium is generally understood through the framework of the Eigenstate Thermalization Hypothesis (ETH). An extension of ETH to out-of-time-order correlation functions has been recently proposed, based on the language of free probability, in which relaxation can be understood as operators becoming freely independent. In this talk I will discuss a minimal model in which this approach to free independence can be understood as a Markovian process. These results shed light on the appearance of two-step relaxation mechanisms and generalize the influence matrix approach to out-of-time-order correlation functions, and can be directly applied to more realistic models of many-body quantum dynamics.

Many kinds of correlation functions and information-theoretic quantities such as entanglement entropies exhibit striking universality in their late-time behavior across a wide range of chaotic quantum many-body systems. Understanding how such universal features emerge from vastly different microscopic dynamics remains a fundamental challenge. In this talk, I will demonstrate how this mechanism becomes manifest in a class of one-dimensional Brownian models with random, time-dependent Hamiltonians and diverse microscopic couplings. In these models, the averaged real-time Lorentzian evolution of these quantities can be mapped onto an imaginary-time Euclidean evolution governed by an effective Hamiltonian acting on multiple replicas of the system. The infinite-time saturation values of these quantities correspond to the ground states of the effective Hamiltonian, which are fully determined by the symmetries of the replicated evolution. The approach to saturation, including hydrodynamic regimes, can then be understood in terms of low-energy excitations above these ground states — which are again dictated by the symmetry algebra structure of the multi-replica system. For instance, diffusion in U(1)-conserving systems can be understood from spin-wave excitations atop a Heisenberg ferromagnet, while the entanglement membrane picture for Rényi entropies can be understood from domain-wall excitations on top of an Ising ferromagnet. I will further discuss generalizations to systems with both conventional and unconventional symmetries, the effects of measurements, and extensions to higher dimensions. Altogether, this provides a unifying framework for understanding the late-time universal behavior of correlation functions and entanglement entropies across a broad class of quantum many-body systems—with potential implications for non-random, time-independent systems as well.

I will describe a mixed quantum-classical framework, dubbed the Moving Born-Oppenheimer Approximation (MBOA), to describe the dynamics of slow degrees of freedom (DOFs) coupled to fast ones. As in the Born-Oppenheimer Approximation (BOA), the fast degrees of freedom adiabatically follow a state that depends on the slow ones. Unlike the BOA, this state depends on both the positions and the momenta of the slow DOFs. I will illustrate the physics captured by the MBOA in several model systems: a spin-1/2 particle and a spinful molecule moving in a spatially inhomogeneous magnetic field, and a gas of fast particles coupled to a piston. The MBOA reveals rich dynamics for the slow degree of freedom, including reflection, dynamical trapping, and mass renormalization. It also significantly modifies the state of the fast DOFs. For example, the spins in the molecule are entangled and squeezed, while the gas of fast particles develops gradients that are synchronized with the motion of the piston for a long time. The MBOA can be used to describe both classical and quantum systems and has potential applications in molecular dynamics, state preparation, and quantum sensing.

I will introduce a classical-quantum mapping for KCPs and use it to find their hydrodynamic properties (e.g. the diffusion coefficient). For some KCPs I will show that the gaussian approximation returns the exact diffusion coefficient, while for those KCPs where this is not true, I will show how to systematically compute corrections to the bare diffusion coefficient.

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It is shown that the stroboscopic time-evolution under a Floquet unitary, in any spatial dimension, and of any Hermitian operator, can be mapped to an operator Krylov space which is identical to that generated by the edge operator of the non-interacting Floquet transverse-field Ising model (TFIM) in one-spatial dimension, and with inhomogeneous Ising and transverse field couplings. The latter has four topological phases reflected by the absence (topologically trivial) or presence (topologically non-trivial) of edge modes at 0 and/or $\pi$ quasi-energies. It is shown that the Floquet dynamics share certain universal features characterized by how the Krylov parameters vary in the topological phase diagram of the Floquet TFIM with homogeneous couplings. Connections of our results with methods based on orthogonal polynomials on the unit circle are discussed. Several applications of the mapping are presented. This work has been done in collaboration with Dr. Hsiu-Chung Yeh.

Chaotic quantum systems at finite energy density are expected to act as their own heat baths, rapidly dephasing local quantum superpositions. We argue that in fact this dephasing is subexponential for chaotic dynamics with conservation laws in one spatial dimension: all local correlation functions decay as stretched exponentials or slower. The stretched exponential bound is saturated for operators that are orthogonal to all hydrodynamic modes. This anomalous decay is a quantum coherent effect, which lies beyond standard fluctuating hydrodynamics; it vanishes in the presence of extrinsic dephasing. Our arguments are general, subject principally to the assumption that there exist zero-entropy charge sectors (such as the particle vacuum) with no nontrivial dynamics: slow relaxation is due to the persistence of regions resembling these inert vacua, which we term "voids". In systems with energy conservation, this assumption is automatically satisfied because of the third law of thermodynamics.

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We demonstrate the existence of prethermal discrete time crystals whose sub-harmonic response is entirely localized to zero-dimensional corner modes. Within the exponentially long prethermal regime, we show that the robustness of these corner modes arises from two related, yet distinct mechanisms: the presence of a higher-order symmetry-protected topological phase in the effective Hamiltonian, or the emergence of a dynamical constraint that prevents the decay of the corner mode. While the first mechanism ensures the stability of the sub-harmonic response throughout the entirety of the prethermal regime, it is restricted to initial states in the ground state manifold of the effective Hamiltonian. By contrast, the second mechanism enables the observation of the prethermal time-crystalline order for arbitrary initial states, albeit with a time scale that is not only determined by the frequency of the drive, but also the relative energy scale across the system’s sublattices. We characterize these two mechanisms by simulating the dynamics of a periodically driven two-dimensional spin model, and discuss natural extensions of our model to all other dimensions.

The high degree of controllability in modern day quantum simulators has enabled the engineering of Floquet topological Bloch bands and even the realization of novel non-equilibrium states like the discrete time crystal, through the implementation of time-dependent driving. Such drives, though, have so far been largely limited to time-periodic (i.e., Floquet) modulations, and their time-quasiperiodic (i.e., multi-tone) generalizations. This leads to a natural question: what are more general classes of quantum drives, conceptually distinct from Floquet or time-quasiperiodic, which lead to interesting phase structure in dynamics? In this talk, I will present a general theoretical construction of quantum drives in which the position of a classical particle moving autonomously on a smooth connected manifold is used to steer a quantum Hamiltonian over time, thus leading to myriad time-dependent quantum Hamiltonians with properties dependent on the choice of underlying manifold and trajectory. Applying the construction we dub "geometric quantum driving" to a compact 2d hyperbolic Riemann surface, I will demonstrate a new class of drives called "hyperbolically driven quantum systems", and further show how in the adiabatic limit they are topologically classified by a quantized response that can be extracted through the dynamics of a simple local observable. We propose geometric quantum driving to be a general framework to chart the landscape of time-dependent quantum systems and investigate the universal phase structures they exhibit, as well as a useful tool to enhance the capabilities of modern day quantum simulators.

Flocks of animals represent a fascinating archetype of collective behavior in the macroscopic classical world, where the constituents, such as birds, concertedly perform motions and actions as if being one single entity. Here, we address the outstanding question of whether flocks can also form in the microscopic world at the quantum level. For that purpose, we introduce the concept of active quantum matter by formulating a class of models of active quantum particles on a one-dimensional lattice. We provide both analytical and large-scale numerical evidence that these systems can give rise to quantum flocks. A key finding is that these flocks, unlike classical ones, exhibit distinct quantum properties by developing strong quantum coherence over long distances. We propose that quantum flocks could be experimentally observed in Rydberg atom arrays. Our work paves the way towards realizing the intriguing collective behaviors of biological active particles in quantum matter systems. We expect that this opens up a path towards a yet totally unexplored class of nonequilibrium quantum many-body systems with unique properties.

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Ultracold atoms in optical lattices are one of the major platforms for experimental quantum simulations and many-body physics. In the past, most experiments focussed on the simplest lattice geometries, namely the primitive 1D lattice, the square lattice, and the cubic lattice. In this talk, we will look at experiments on non-equilibrium physics in other interesting 2D lattice geometries. These range from the triangular lattice, where geometric frustration can give rise to chiral superfluids, over the Kagome lattice, where it gives rise to a flat band, to optical quasicrystals, where the absence of periodicity gives rise to novel physics.

In this talk, I will discuss the interplay of hydrodynamic fluctuations and quantum measurements. I will introduce a general field theory framework to address this question, and show that it predicts a variety of new critical phases in monitored systems with global symmetries.

Analytical treatments of far-from-equilibrium quantum dynamics are few and far between. I will describe a promising candidate: the statistical Jacobi approximation (SJA). The SJA is a statistical description of the Jacobi diagonalization algorithm, which constructs eigenstates of a Hamiltonian through a sequence of two-level unitary rotations. Treating these rotations as random and uncorrelated, it is possible to derive flow equations describing the change in observable matrix elements in a basis which evolves from some pre-quench eigenbasis to a post-quench eigenbasis. The SJA allows us to propagate a minimal description of observables from the eigenstate thermalization hypothesis in the pre-quench Hamiltonian to a similar description in the post-quench Hamiltonian, and thus predict dynamical quantities. I will describe our recent analytic results predicting time-dependent fidelities and observable expectation values using the SJA technique, and broader progress on the development of SJA as a quantitative and predictive tool for quantum dynamics.

During the time evolution of many-body quantum systems entanglement grows rapidly, limiting exact simulations to small-scale systems and small timescales. Quantum information tends, however, to flow towards larger scales without returning to local scales, such that its detailed large-scale structure does not directly affect local observables. This allows for the removal of large-scale quantum information in a way that preserves all local observables and gives access to large-scale and large-time quantum dynamics. To this end, in [2] we proposed a novel approach that uses the information lattice [1,4] to organize quantum information into different scales, allowing us to define local information and information currents which we employ to systematically discard long- range quantum correlations in a controlled way. The resulting algorithm, which we refer to as local-information time evolution (LITE), is highly versatile and suitable for investigating large-scale many-body quantum dynamics in both closed and open systems with diverse hydrodynamic behaviors. In this talk, I will introduce the information lattice and present results obtained with LITE for energy and magnetization transport in various models [2,3]. Additionally, I will discuss how the information lattice can be employed to universally characterize many-body quantum states and compute their intrinsic correlation lengths [4]. Finally, I will show the features of the local information flow during quantum quench dynamics [5]. References: [1] T. Klein Kvorning, L. Herviou, and J. H. Bardarson, Time-evolution of local information: Thermalization dynamics of local observables, SciPost Phys. 13, 080 (2022). [2] C. Artiaco, C. Fleckenstein, D. Aceituno Chávez, T. Klein Kvorning, and J. H. Bardarson, Efficient Large- Scale Many-Body Quantum Dynamics via Local-Information Time Evolution, PRX Quantum 5 (2), 020352 (2024). [3] K. Harkins et al., Nanoscale engineering and dynamical stabilization of mesoscopic spin textures, Sci. Adv. 11 (13), eadn9021 (2025). [4] C. Artiaco, T. Klein Kvorning, D. Aceituno Chávez, L. Herviou, and J. H. Bardarson, Universal Characterization of Quantum Many-Body States through Local Information, Phys. Rev. Lett. 134, 190401 (2025). [5] N. P. Bauer, B. Trauzettel, T. Klein Kvorning, J. H. Bardarson, and C. Artiaco, Local Information Flow in Quantum Quench Dynamics, arXiv:2505:00537.

We demonstrate that slow growth of the number entropy following a quench from a local product state is consistent with many-body localization. To do this, we construct a novel random circuit -bit model with exponentially localized -bits and exponentially decaying interactions between them. We observe an ultraslow growth of the number entropy starting from a Néel state, saturating at a value that grows with system size. This suggests that the observation of such growth in microscopic models is not sufficient to rule out many-body localization.

Ultracold Fermi gases in optical lattices provide a highly controllable experimental platform for investigating strongly correlated quantum systems. When combined with quantum gas microscopy, which enables the manipulation and detection of atoms at the single-particle level, fermionic quantum simulators provide unique windows into the phase diagrams and dynamics of Fermi-Hubbard models. A central challenge is to extend the reach of such analog quantum simulators beyond the native Hubbard models they directly implement. Bridging this gap would enable their use in broader applications, such as material science and quantum chemistry. In this talk, I will discuss recently discovered connections between fermions in optical lattices and electronic structure problems in quantum chemistry [1]. We show that optical superlattices provide all the resources needed to implement state-of-the-art optimization algorithms from quantum chemistry. Ultracold fermions can thus encode molecular wavefunctions with very compact circuits due to their intrinsic fermionic symmetry and particle number conservation. I will discuss our scheme and provide some specific examples on how to prepare variational wavefunctions for small molecules. As a first experimental step towards the gate-based preparation of correlated states of fermionic atoms, we have recently demonstrated high-fidelity collisional gates in optical superlattices. The fidelity of these operations on motional degrees of fermions is en par with state-of-the-art gates in spin qubits. This approach opens a promising path toward gate-based preparation and readout of fermionic correlations in lattices. [F. Gkristis et al., PRX Quantum 6, 010318 (2025)]

Out-of-equilibrium phases in many-body systems constitute a new paradigm in quantum matter—they exhibit dynamical properties that may otherwise be forbidden by equilibrium thermodynamics. Among these non-equilibrium phases are periodically driven (Floquet) systems, which are generally difficult to simulate classically due to their high entanglement. Using an array of superconducting qubits, we realize a Floquet topologically ordered state, image the characteristic dynamics of its chiral edge modes, and characterize its emergent anyonic excitations. By devising an interferometric algorithm, we introduce and measure a bulk topological invariant to probe the dynamical transmutation of anyons for system sizes up to 58 qubits. Our work demonstrates that quantum processors can provide key insights into the largely unexplored landscape of highly entangled non-equilibrium phases of matter.

Rydberg atoms in tweezer arrays are a promising platform for quantum simulation, with scaling limits that have yet to be reached. Unlike laser-accessible Rydberg states which have radiative lifetimes on the order of 100 µs, circular Rydberg states - characterized by their maximum angular momentum - can live up to tens of milliseconds in a cryogenic environment. This extended lifetime could provide access to dynamics beyond the reach of conventional Rydberg states. To study these long-time dynamics, circular atoms need to be trapped. The nearly free Rydberg electron experiences a ponderomotive potential from the trapping light, which is repulsive. Blue-detuned traps with specialized geometries can trap these states but require high laser power and therefore limit scalability. An alternative approach is to use alkaline-earth-like species and to exploit the polarizability of the ionic core to trap the Rydberg atom. We have developed a cryogenic (4 K) experimental setup capable of trapping strontium atoms in an optical tweezer array and exciting them to circular Rydberg states. Once the Rydberg atoms are trapped, we will demonstrate that the broad transition of the ionic core enables direct imaging of the Rydberg states, without the need to transfer the atoms back to the ground state. In addition, the electrostatic interaction between the Rydberg electron and the ionic core induces a shift in the ion’s energy levels that depends on the Rydberg state. By resolving this shift, it becomes possible to implement local manipulations and non-destructive measurements of the Rydberg state.

We identify many-body caging, the many-body counterpart of flat bands, as a general mechanism for non-equilibrium phenomena such as a novel type of glassy eigenspectrum order and many-body Rabi oscillations in the time domain. We focus on constrained systems of great current interest in the context of Rydberg atoms and synthetic or emergent gauge theories. We find that their state graphs host motifs which produce flat bands in the many-body spectrum at a particular set of universal energies. Basis states in Fock space exhibit Edwards-Anderson type order {\it in the absence of quenched disorder}, with an intricate, possibly fractal, distribution over Fock space, which is reflected in a distinctive structure of a non-vanishing post-quench long-time Loschmidt echo, an experimentally accessible quantity. In general, phenomena familiar from single-particle flat bands manifest themselves in characteristic many-body incarnations, such as a reentrant `Anderson' delocalisation, offering a rich ensemble of experimental signatures in the abovementioned quantum simulators. The variety of single-particle flat band types suggests an analogous typology--and concomitant phenomenological richness to be explored--of their many-body counterparts.

We introduce a synthetic Mach-Zehnder interferometer for digitized quantum computing devices to probe fractional exchange statistics of anyonic excitations that appear in quantum spin liquids. Employing an IonQ quantum computer, we apply this scheme to the toric ladder, a quasi-one-dimensional reduction of the toric code. We observe interference patterns resulting from the movement of `electric' excitations in the presence and absence of `magnetic' ones. Using this framework, we propose a method to define a many-body quantum coherence length scale, which effectively mirrors the problem of a quantum particle on a ring, with or without flux through it. We propose using the maximum length of the ring for which the presence or absence of flux can be clearly discerned, as a simple measure of the many-body quantum coherence grade (Q-grade) in a given quantum hardware. We demonstrate how this approach can be implemented on gate-based quantum platforms to estimate and compare the quantum coherence of current devices, such as those from Google, IBM, IonQ, IQM, and Quantinuum that we considered here. This work aims to contribute to the creation of a live Web interface where the latest developments and advancements can be demonstrated, and progress in quantum coherence resources tracked over time. Establishing such a standardized quantum test would enable monitoring the growth of quantum coherence in gate-based quantum platforms, in a spirit similar to Moore's law.

Rydberg simulators, superconducting qubit arrays and other quantum simulation platforms are increasingly able to simulate isolated quantum many-body dynamics in two spatial dimensions, and explore uncharted territory for theory. Recent experiments studied order parameter dynamics in both slow ramps and (fast) quenches involving phase transitions, thereby placing the physics of quantum coarsening in the experimental realm. We present a simple theory accounting for two central observations in one of these recent experiments [T. Manovitz et al., Nature 638, 86 (2025)]: an apparent speeding up of the coarsening process as the phase transition is approached; and persistent oscillations of the order parameter after quenches within the ordered phase. Our theory, based on the Hamiltonian structure of the equations of motion in the classical limit of the quantum model, finds a speeding up already deep within the ordered phase, with subsequent slowing down as the domain wall tension vanishes upon approaching the critical line. Further, the oscillations are captured within a mean-field treatment of the order parameter field. For quenches within the ordered phase, small spatially-varying fluctuations in the initial mean-field lead to a remarkable long-time effect, wherein the system dynamically destroys its long-range order and has to coarsen to re-establish it. We term this phenomenon symmetry re-breaking, as the resulting late-time magnetization can have a sign opposite to the initial magnetization.

Neutral atoms trapped in optical lattices are a versatile platform to study many-body physics in and out of equilibrium. The relaxation behavior of isolated quantum systems taken out of equilibrium is among the most intriguing problems in many-body physics. Quantum systems out of equilibrium typically relax to thermal equilibrium states by scrambling local information and building up entanglement entropy. In this talk, I will present our recent experiments on probing an exception to this expected thermalization behavior in two-dimensional tilted Hubbard models with strong kinetic constraints. Combining local initial-state control with site-resolved measurements in our quantum-gas microscope, we find a strong dependence of the relaxation dynamics on the specific initial state - a hallmark of the shattering of the underlying Hilbert space in disconnected fragments. Leveraging the control over individual atoms, we furthermore inject mobile excitations into an otherwise immobile state and track their dynamics. We find subdimensional dynamics, which is a feature characteristic of fractonic excitations. Our results pave the way for in-depth studies of microscopic transport phenomena in constrained systems.

In recent decades, one of the central goals of condensed matter physics has been the classification and characterization of quantum phases of matter at zero temperature. This has led to the discovery of many exotic phases, notable those exhibiting topological order, characterized by long-range quantum entanglement and a ground state degeneracy that depends on the underlying topology. Much less is known about the situation at finite, non-zero temperatures; for example no examples of finite temperature topological order exist in spatial dimensions below 4. In this talk, I will discuss a series of results relevant to the problem of quantum phases at nonzero temperatures. First, I will discuss a theorem that provides a "dynamical" perspective on finite temperature phases, relating them to open system dynamics. As an application of this perspective, I will discuss a family of spatially non-local models that exhibit a new kind of "topological quantum spin glass", combining quantum topological order, with features of classical mean-field spin glasses. Finally, I will discuss a model that realizes quantum topological order in 3 spatial dimensions for the first time.

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In this talk I will first discuss how one can define chaos both in quantum and classical systems using quantum geometric tensor or equivalently fidelity. In this way chaos can be understood either through irregular dynamics of observables or through instabilities of time averaged probability distributions/quantum states to infinitesimal perturbations. Then I will focus on emergence of chaos/ergodicity/mixing from slightly perturbed integrable models. I will argue there are at least three distinct universality classes : critical, confined , and deconfined. Critical chaos emerges in, for example, disordered models close to localization transition or in low dimensional classical systems with mixed phase space. It is characterized by slow power-law relaxation. Confined chaos is the most common scenario occurring in local interacting models. It is characterized by fast relaxation of angle variables and much slower relaxation of actions, which can be described perturbatively by standard kinetic approaches. Finally, deconfined chaos can occur in perturbed superintegrable models with highly inhomogeneous phase space. It is characterized by the fastest possible non-perturbative decay rate, which scales as the absolute value of the integrability breaking coupling. In this scenario there is no separation between relaxation of action and angle variables. An example of a system where deconfined chaos is realized is the central spin XX-model at zero energy. Other likely candidate for the deconfined chaos is the SYK model.

Time-dependent drives hold the promise of realizing non-equilibrium many-body phenomena that are absent in undriven systems. Yet, drive-induced heating normally destabilizes the systems, which can be parametrically suppressed in the high-frequency regime by using periodic (Floquet) drives. It remains largely unknown to what extent highly controllable quantum simulators can suppress heating in non-periodically driven systems. Using the 78-qubit superconducting quantum processor, Chuang-tzu 2.0, we report the experimental observation of long-lived prethermal phases in many-body systems with tunable heating rates, driven by structured random protocols, characterized by n-multipolar temporal correlations. By measuring both the particle imbalance and subsystem entanglement entropy, we monitor the entire heating process over 1,000 driving cycles and observe the existence of the prethermal plateau. The prethermal lifetime is ‘doubly tunable’: one way by driving frequency, the other by multipolar order; it grows algebraically with the frequency with the universal scaling exponent 2n+1. Using quantum state tomography on different subsystems, we demonstrate a non-uniform spatial entanglement distribution and observe a crossover from area-law to volume-law entanglement scaling. With 78 qubits and 137 couplers in a 2D configuration, the entire far-from-equilibrium heating dynamics are beyond the reach of simulation using tensor-network numerical techniques. Our work highlights superconducting quantum processors as a powerful platform for exploring universal scaling laws and non-equilibrium phases of matter in driven systems in regimes where classical simulation faces formidable challenges. Reference: arXiv: 2503.21553.

We study the canonical Aubry-Andre (aka Harper/Hofstadter) model at criticality. We show that for generic irrational incommensuration the RG flow is chaotic and without stable fixed points. Remarkably, we show that universal properties nevertheless emerge, and are characterised by the statistically robust features of this chaotic flow. This manifests as a novel t ~ r^( \zeta \log \log r) length time scaling for a universal value of \zeta. Previously reported power law scaling for particular values of the incommensuration ratio are shown to correspond to the unstable periodic orbits of this flow. These special orbits avoid regions of parameter space which generically dominate the scaling. We argue that this RG flow is generic for non interacting models in any incommensurate potential (or flux), and that chaotic RG should be expected as a feature of more general incommensurate models.

State preparation is crucial for the simulation of quantum systems. In this talk, I will discuss recent advances in sampling Gibbs states through Lindbladian time evolution. I will highlight key challenges in implementing these techniques on quantum hardware and explore potential solutions. Finally, I will examine connections to driven dissipative time-dynamics, enabling implementation on near-term quantum devices.

Recent experiments on artificial quantum systems have motivated researchers to study universal phenomena in dissipative quantum many-body systems under measurement. In the first part of my talk, I will discuss spectral transitions occurring in monitored quantum many-body systems [1,2]. We numerically study the Lyapunov spectrum that characterizes quantum dynamics under weak measurement and show that the gapless-gapped spectral transition occurs [1] at the critical measurement strength for measurement-induced entanglement transition [3]. While the correspondence between spectral and entanglement transitions looks analogous to ground-state transitions for isolated quantum systems, distinct system-size scalings appear in gapless phases, which is attributed to a non-local structure of the effective Hamiltonian. Moreover, we demonstrate that the Lyapunov analysis is also crucial to understand measurement-induced topological phases since it enables us to discuss edge modes, topological invariant, and the bulk-edge correspondence in such systems [2]. In the second part, I will talk about how measurement and many-body effect lead to universality of quantum jump statistics in continuously monitored quantum systems, which are free from the post-selection problem [4]. Studying a subsystem fluctuation of quantum jumps of hardcore bosons under local particle measurement, we find a nontrivial crossover from Poissonian to super-Poissonian statistics. That is, while the fluctuations exhibit the standard volume law $\propto L$ for sufficiently weak measurement strength, anomalous yet universal scaling law $\propto L^2.7$ appears for strong measurement strength. This drastically affects the precision of estimating the rate of quantum jumps: for strong (weak) measurement, the estimation uncertainty is enhanced (suppressed) as the system size increases. [1] K. Mochizuki and R. Hamazaki, Physical Review Letters 134 (1), 010410 (2025). [2] H. Oshima, K. Mochizuki, R. Hamazaki, and Y. Fuji, Physical Review Letters 134 (24), 240401 (2025). [3] Y. Li, X. Chen, and M. P. A. Fisher, Phys. Rev. B 98, 205136 (2018); B. Skinner, J. Ruhman, and A. Nahum, Phys. Rev. X 9, 031009 (2019); A. Chan, R. M. Nandkishore, M. Pretko, and G. Smith, Phys. Rev. B 99, 224307 (2019). [4] K. Yamamoto and R. Hamazaki, arXiv:2503.02418 (2025).