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Roderich Moessner

Publications and source records attributed to Roderich Moessner.

At least 19 recordsLinked to original sources
arXiv2026

Random Matrix Spectra from Boltzmann-Weighted Lattice Ensembles

We introduce a random matrix framework for studying statistical-mechanical lattice systems through spectral observables. Equilibrium configurations sampled from a Boltzmann measure are mapped to matrix ensembles whose covariance structure is inherited from the spatial correlations of the underlying model. This construction maps real-space correlation functions to a momentum-space variance profile, providing a direct bridge between statistical-mechanical correlations and correlated random matrix ensembles. We derive this variance profile in finite-correlation-length and critical regimes, and compute spectral moments within a Wick-contraction expansion. A complementary self-consistent description of the bulk density is developed using the resolvent formalism. These analytical methods are benchmarked against Monte Carlo data for the two-dimensional Ising model and three-dimensional Edwards--Anderson spin glasses. In both cases, the spectra evolve from the semicircle law at high temperature to model-dependent critical forms reflecting the structure of correlations. The framework, therefore, provides a quantitative spectral route to probing collective behavior in ordered and disordered statistical systems, while also defining a class of physically motivated correlated random matrix ensembles.

cond-mat.dis-nn↗
arXiv2026

Constructing Large and Structured Decoherence-Free Subspaces in Hybrid Quantum Systems

We develop a framework to construct large decoherence-free subspaces with a nontrivial structure. The construction is based on hybrid quantum systems in which quantum matter is coupled to a dissipative bosonic mode. Dissipation imposes a global constraint on the matter by selecting the matter null states in the long-time limit. The decoherence-free subspaces spanned by matter null states can exhibit exotic quantum properties and emergent symmetries that do not characterize the full Liouvillian dynamics. We show how to construct many-body operators with physically interesting null states by employing representation theory of Lie algebras. This approach allows us to choose models based on their underlying algebraic structure. We consider explicitly the example of coupling a lossy optical cavity to the directed tunneling operator in one-dimension. In this case, the symmetries of the decoherence-free subspace originate in an $\mathfrak{sl}(2,\mathbb{C})$ algebra, leading to an exponentially large number of steady states. We characterize the null states for both fermionic and bosonic particles, employing analytical and numerical methods. The states exhibit several properties that underline their complex quantum nature: long-range kinetic correlations and volume-law entanglement. The nonreciprocal nature of the directed tunneling dynamics leads to the emergence in the many-body regime of a symmetry-constrained Liouvillian skin effect. The open light-matter system exhibits a strong symmetry stemming from spinless $η$-pairing algebras. We show how the nontrivial properties emerge in the dissipative dynamics from generic initial states, by performing the quantum evolution of the hybrid open system with time-dependent matrix product state. Our framework opens avenues for dissipatively engineering complex quantum correlations and harnessing nonreciprocity in a controlled manner.

cond-mat.quant-gas↗
arXiv2026

Reinforcement Learning to Harness Approximation Errors for Long-Time Quantum Simulation

Accurate digital quantum simulation at long times is limited by the accumulation of errors inherent to approximate simulation. Here we introduce RL-Trotter, a reinforcement-learning framework that treats unavoidable approximation errors as resources for error correction rather than merely imperfections to suppress. We show that low-dimensional information from conservation laws, such as the energy and energy variance, provides a sufficient learning signal to guide the agent, which learns to adapt a single scalar---the next Trotter step size---without access to the target wave function. By optimizing the entire long-time evolution rather than individual steps, RL-Trotter discovers self-correcting sequences in which later errors compensate for those accumulated earlier, increasing the accuracy of the long-time dynamics. The learned policies are intrinsically robust to measurement noise, substantially reducing measurement overhead. They also generalize to previously unseen, physically similar initial states and transfer from small, classically simulable systems to systems an order of magnitude larger. This enables a practical protocol based on classical pretraining followed by direct deployment or limited fine-tuning on quantum hardware. Our results establish a broader perspective for quantum algorithms: errors in approximate evolution can be orchestrated into resources for accurate and resource-efficient quantum dynamics.

quant-ph↗
arXiv2026

Gentle Floquet control of orbital Hall effect and orbital inverse Faraday effect

Floquet engineering controls material responses via a time-periodic electromagnetic drive. An important task in practice is to reduce the driving strengths required to implement Floquet protocols. We show that in systems with strong phase-space constraints, where the response is dominated by a small region of momentum space, the relative impact of a resonant Floquet drive is enhanced. We demonstrate this idea on the example of the orbital Hall effect, where equilibrium occupations restrict the interband coherence to a narrow momentum interval $\hbarΔk$. The ratio $eE_0/(Ω_0\hbarΔk)$, where $Ω_0$ is the frequency of the drive, is considerable even at modest field amplitudes $E_0$, leading to a large relative change in the orbital Hall conductivity. Due to the non-trivial orbital texture, the circularly polarized drive induces an inverse orbital Faraday effect by magnetizing the electrons. We show that the corresponding susceptibility is controlled by the interband quantum metric that determines the resonant Floquet hybridization.

cond-mat.mes-hall↗
arXiv2026

Long-Range Correlated Random Matrices

Motivated by the importance ascribed to correlations in random matrices used to model phenomena in various scientific disciplines, we report how algebraic correlations between matrix elements affect the eigenvalue statistics and spectral density of random matrices. These correlations, introduced through thresholded Gaussian fields on a square lattice, decay as a power law $\propto r^{-2H}$, with exponent $H>0$. As $H$ varies, both the eigenvalue distribution and excess kurtosis undergo qualitative changes. The spectral variance approaches $1/2$, while the moment of order $2n$ is finite only for $H>(n-1)/(2n)$. Long-wavelength scaling gives an algebraic density tail $|λ|^{-1-2/(1-2H)}$ for $0 1/2$ it is bounded and approaches the semicircle as $H\to\infty$. A self-consistent equation determines the limiting density from the binary covariance and fixes the excess kurtosis through the squared correlations along a row. Our results link real-space correlations to spectral regimes, distinguishing the roles of the long-distance exponent and the full covariance.

cond-mat.stat-mech↗
arXiv2026

Berry-Landau Fermi-liquid theory: transport in presence of quantum geometry

Landau Fermi-liquid theory characterizes interacting metals through quasiparticles and their residual interactions. It is a challenge to incorporate non-trivial quantum geometry -- as encoded by Berry phases and the quantum metric -- as a fundamental ingredient. We formulate a Berry-Landau Fermi-liquid theory for spinless fermions within an isolated band crossing the Fermi surface and derive the Landau functional through the Nozières--Luttinger construction. The instantaneous response to a perturbation of the Bloch waves generates both an anomalous Berry-connection potential in the action and an interaction-induced quantum-geometric contribution to the quasiparticle current. The conserved physical charge current is then obtained via the electromagnetic Ward identity as a combinati of this quantum-geometric current and the bare drift current. Therefore, the intrinsic anomalous Hall conductivity is fixed by the Berry-curvature integral of the dressed quasiparticle band while the Drude weight contains both conventional and quantum-geometric contributions. In the presence of Galilean symmetry, the Drude weight is protected against interaction renormalization. In the flat/narrow-band limit, transport is dominantly quantum-geometric and can be thermally enhanced. These results establish quasiparticle occupations, Landau interactions, and the quantum geometry carried by quasiparticles as the fundamental low-energy ingredients of a Berry-Landau Fermi liquid.

cond-mat.str-el↗
arXiv2026

Breakdown of Multipole Expansion in Emergent Electromagnetism

We find a striking departure from simple electrostatics in a family of two-dimensional lattice models whose effective description takes the form of an emergent electromagnetism: a high-order multipolar charge configuration can induce an electric field characteristic of a \textit{lower-}order multipole. Studying the archetypical hardcore dimer and U(1) spin-1/2 link models, we trace this to a breakdown of the superposition principle: for dense charge configurations, there can be a nonlinear suppression, or even enhancement, of the far field compared to the linear expectation. Our work establishes that microscopic lattice-scale constraints in models for emergent electromagnetism can change the far-field behaviour to differ from often utilized long-wavelength descriptions in standard effective continuum models.

cond-mat.stat-mech↗
arXiv2026

Transient and universal regimes in quantum reaction-transport kinetics

Quantum reaction-transport systems consist of coherently propagating particles that irreversibly react upon encounter. Their relaxation is commonly classified as reaction-limited or transport-limited, depending on the relative timescales of reaction and particle transport. We show that this expectation fails in low dimensions by studying the quantum binary annihilation, $A+A \to \emptyset$, where reaction processes acquire singular fluctuation corrections below the upper critical dimension $D_c=2$. Consequently, fluctuations dominate the asymptotic kinetics for $D<2$. In one dimension, they render mean-field relaxation transient and drive the system toward a transport-limited regime with $n\sim t^{-1/2}$, governed by a quantum-Zeno scale even for arbitrarily weak loss. At $D=2$, the kinetics acquires logarithmic corrections, whereas above two dimensions mean-field scaling is asymptotically restored. At and below the upper critical dimension, mean-field behavior can nevertheless persist over parametrically long crossover times before the asymptotic fluctuation-dominated regime emerges. We also show that the same fluctuations generate effective elastic collisions despite the absence of microscopic coherent interactions. In $D>1$, these collisions redistribute momentum populations and are parametrically faster than losses in the transport-limited regime, allowing the system to approach a quasi-stationary thermal state.

cond-mat.stat-mech↗
arXiv2026

Exact quantum spin liquids with topological order on maple-leaf and trellis lattices

We construct spin models with bond-dependent anisotropic interactions on the penta-coordinated maple-leaf and trellis lattices, which yield exact $\mathbb{Z}_2$ quantum spin liquids akin to the Kitaev honeycomb model. We characterize the resulting ground states by their flux sectors, Chern numbers, and topological excitations. Using replica exchange quantum Monte Carlo simulations, we find that the gauge fluxes are ordered at sufficiently low temperatures such that every unit triangle has $\pm π/2$-flux, where the sign is uniform across the system, and every unit hexagon (square) has $0$-flux ($π$-flux) within the parameter space of interest. We map out the topological phase diagram for each model, which reveals parameter regimes hosting $\mathbb{Z}_2$ and Ising topological orders, and we derive an analytical expression for the mass term of the Majorana fermions, the vanishing of which indicates a transition between these phases. We further establish the correspondence between individual vortices (i.e., flux excitations) and two species of anyons in the dimer limit, overcoming the obstacle faced by degenerate perturbation theory in treating odd-length elementary plaquettes. Interestingly, we find that two dimer limits of the maple-leaf model with distinct assignments of anyon species can be smoothly connected to each other in the vortex-free sector, but they are separated by fermion-gap-closing transitions in certain two-vortex sectors.

cond-mat.str-el↗
arXiv2026

Active quantum flocks

Flocks of animals represent a prominent 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 so far open 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 quantum flocks 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.

quant-ph↗
arXiv2026

Observation of far-from-equilibrium scaling in the transient dynamics of 2D quantum magnets

The transient regime of far-from-equilibrium quantum many-body dynamics lacks the established organizing principles that universality and scaling provide in equilibrium. It is least understood for two-dimensional short-range interacting systems, where mean-field arguments are not expected to hold, controlled theoretical descriptions are few, and fluctuations are strong. Here we investigate the quench dynamics of the transverse-field Ising model using programmable Rydberg-atom arrays realizing honeycomb, square, kagome, and triangular lattices. Starting from a fully magnetized state, we observe a pronounced softening of the dominant collective magnetization oscillation accompanied by a maximum in the damping rate, signaling a crossover between interaction- and field-dominated transient dynamics. Even though the microscopic lattice geometries are different, both the oscillation frequencies and the damping rates collapse onto common curves after being rescaled by the coordination-number-weighted interaction strength. Our findings show that a mean-field description effectively reproduces the magnetization oscillations. The importance of correlated quantum fluctuations is underlined by the failure of the discrete truncated Wigner approximation to predict the damping for strong interactions, while tree-tensor-network simulations reproduce the dynamics accurately. These results reveal a robust scaling regime governing the transient dynamics of short-range interacting two-dimensional quantum magnets. They reveal that the dominant transient dynamics is governed by a simple collective description despite the presence of strong quantum fluctuations --- an important insight in the quest to uncover organizing principles in far-from-equilibrium quantum matter.

cond-mat.quant-gas↗
arXiv2026

Validation and calibration of quantum hardware through the many-body quantum Mpemba effect

We introduce a validation process that harnesses engineered many-body relaxation to control and calibrate quantum hardware. On two independently developed neutral-atom processors, we realize the many-body quantum Mpemba effect in an open system for the first time. Initial-state engineering creates fast and slow relaxation pathways: the fast pathway opens access to unreachable mixed-state physics before hardware noise obscures the target dynamics, whereas the slow pathway amplifies hidden imperfections in preparation and control. Computational-basis measurements directly and independently benchmark dynamical reliability, revealing each processor's actual operating window as a many-body simulator. The processors are thus judged by the very dynamics they are built to reproduce. Complementary responses disentangle control errors and drive an adaptive, time-resolved scheme that supplies hardware developers directly actionable corrections, enhancing faithful reproduction of the target dynamics. These results establish many-body relaxation as a transferable validation and calibration tool for programmable quantum processors.

quant-ph↗
arXiv2026

Fractal deconfinement and confinement in Sierpinski ice

We study the six-vertex model on the Sierpinski gasket, a four-coordinated hierarchical fractal with Hausdorff dimension $d_f=\log_23$. Given the importance of dimensionality for the long-wavelength behavior of such models, we specifically consider correlations and confinement as a function of the vertex weights, with the equal-weight point corresponding to the ice model. We calculate the partition function and correlators recursively to obtain a rich phase diagram hosting many different regimes. While the ice model shows entropic charge confinement, a particular four-vertex limit exhibits fractal deconfinement, with the string joining the deconfined charges itself a statistical fractal with fractal dimension $d_l=\log_2(5/2)\approx 1.3$. Finally, we propose a setup as an artificial spin ice to enable experimental study of the rich phenomenology of Sierpinski ice and its generalisations.

cond-mat.stat-mech↗
arXiv2026

Many-body cages: disorder-free glassiness from flat bands in Fock space, and many-body Rabi oscillations

We introduce many-body caging as a novel mechanism for nonthermal behaviour in quantum matter. We define many-body cages as eigenstates that, through quantum interference, become localised on a subgraph of the many-body state graph. These many-body cages can lead to the formation of flat bands in the many-body spectrum at characteristic, system-independent energies. These flat bands can realize a novel type of glassy eigenspectrum order in the absence of disorder, which we quantify by a band-overlap order parameter with an intricate, possibly fractal, distribution over the many-body state graph. We further show that these many-body cages exhibit distinctive signatures in experimentally accessible quantities, such as through a nonvanishing long-time memory of the initial condition, and many-body Rabi oscillations set by the characteristic flat band energies. While our predictions in principle apply to any constrained quantum system, we demonstrate them here for 2D lattice gauge theories and models relevant for current experiments in Rydberg atoms. We expect that these many-body cages offer a promising route to realize nonequilibrium quantum states with novel properties.

cond-mat.quant-gas↗
arXiv2026

Fractional diffusion without disorder in two dimensions

We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale the path of a single defect exhibits anomalously long retractions, amounting to dynamical caging in a continuous-time random-walk framework, culminating in an effective fractional diffusion equation. Mapping to a height field yields an effective random walk subject to an emergent (entropic) logarithmic potential, whose strength is tunable, related to the exponent of algebraic ground-state correlations. The defect's path, viewed as non-equilibrium growth process, yields a frontier of fractal dimension of $5/4$, the value for a loop-erased random walk, rather than $4/3$ for simple and self-avoiding random walks. Such frustration/constraint-induced subdiffusion is expected to be relevant to platforms such as artificial spin ice and quantum simulators aiming to realize discrete link models and emergent gauge theories.

cond-mat.mes-hall↗
arXiv2026

Directed Polymer Transfer Matrices as a Unified Generator of Distinct One-Point Fluctuation Laws

We numerically revisit the transfer-matrix formulation of directed polymers in random media and show that a common finite-dimensional framework organizes the canonical one-point fluctuation laws in $(1+1)$ dimensions. For a fixed realization of the bulk disorder, full-space partition functions are obtained from the same time-ordered product $W(t)$ through endpoint contractions or a Brownian-weighted initial vector, while the half-space construction modifies only the transfer rule at the absorbing boundary. These choices yield distributions consistent with the standard KPZ subclasses: Tracy--Widom GUE for point-to-point geometry, Tracy--Widom GOE for point-to-line geometry, Tracy--Widom GSE for half-space point-to-point geometry, and Baik--Rains for the stationary line-to-point construction. In all four cases, the free-energy fluctuations grow as $t^{1/3}$, and the low-order cumulants approach the corresponding universal benchmarks. The matrix-product formulation also provides access to intrinsic spectral observables. For the leading eigenvalue $λ_1(t)$, the fluctuations of $\lnλ_1(t)$ exhibit an intermediate $t^{1/3}$ regime, while the standardized distribution remains distinct from the canonical benchmark laws over the studied time range.

cond-mat.soft↗
arXiv2026

Hydrodynamic Memory and Long-Time Tails in Clean Frustrated Magnets

In a simple, clean but constrained magnet, we identify a self-interacting random walk with memory. For the motion of a single monopole -- a fractionalized quasiparticle in spin ice -- this produces a subtle and unusually slow relaxation toward diffusive motion. This is manifested as an algebraic long-time tail in the velocity autocorrelation function, decaying as $t^{-3/2}$. At finite monopole density, the interactions between the trails of different monopoles introduce an additional timescale, corresponding to the disruption of a monopole's memory by other monopoles, and leading to an exponential cutoff of the long-time tail. Our results identify clean frustrated magnets as microscopic platforms for studying self-interacting stochastic processes, hydrodynamic memory, and the emergence of non-Markovian quasiparticle transport from local Markovian dynamics.

cond-mat.str-el↗
arXiv2026

Universal Dynamic Scaling of 2D Quantum Ising Transition on the Fuzzy Sphere

We revisit the problem of \textit{real-time} quantum dynamics of the paradigmatic two dimensional transverse-field Ising model using the recently developed fuzzy sphere regularization scheme. By linearly ramping the transverse field from the paramagnetic phase to criticality, we study the finite-time scaling behavior of the squared order parameter $\langle m_z^2 \rangle$, the excitation energy density $Q$, and the two-point correlation function of $m_z$. We establish numerically that, at intermediate quench rate, $\langle m_z^2 \rangle$ follows the conventional Kibble-Zurek prediction set by the critical exponents of the $3$D Ising universality class, and the correlation function exhibits the expected exponential decay whose correlation length can be used to estimate the non-universal scaling coefficient in the freeze-out time/length. In contrast, the excitation energy density $Q$ does not reach the same scaling regime at available system sizes due to large effective finite-size gap from symmetry-enforced level sparsity in the energy spectrum. At slow quench rates the universal quasi-adiabatic scaling for both $\langle m_z^2 \rangle$ and $Q$ is recovered. Since the fuzzy sphere construction can realize not only the Ising conformal field theory (CFT), but a broad family of $(2+1)d$ CFTs, our results establish a route to the real-time critical dynamics of strongly coupled CFTs that are otherwise computationally challenging to study.

cond-mat.str-el↗