arXiv subjects

M. Mierzejewski

Publications and source records attributed to M. Mierzejewski.

At least 19 recordsLinked to original sources

arXiv2026

Graph-Theoretic Detection of Hilbert Space Fragmentation

Hilbert-space fragmentation provides a mechanism for ergodicity breaking in quantum many-body systems even in the absence of disorder, leading to dynamically disconnected sectors and strong memory of initial conditions. However, identifying such structures is often challenging and typically relies on prior knowledge of conservation laws or model-specific analytical insight. Here we introduce an unbiased approach based on spectral graph theory and, within this framework, formulate the concept of nearly fragmented systems, in which perturbative processes couple otherwise fragmented sectors while preserving their dynamical imprint. By representing basis states as vertices and Hamiltonian matrix elements as edges, we map the connectivity structure of the many-body Hilbert space onto a graph and analyze it using tools such as the Laplacian spectrum, Fiedler vectors, and modularity. Exact fragmentation corresponds to disconnected graph components, while nearly fragmented systems manifest as weakly connected communities whose structure can still be resolved spectrally. Applying this framework to the one-dimensional $t$-$J$ model and its perturbations, we demonstrate that graph-theoretic diagnostics reliably identify both fragmented and nearly fragmented Hilbert-space structures and capture the hierarchy of dynamical time scales that governs the system's evolution. We further show that the method extends beyond kinetically constrained models by applying it directly to the Hubbard chain, where it reveals the emergence of nearly decoupled subspaces associated with doublon dynamics and spin configurations. Our results establish the spectral graph analysis as a general and scalable tool for diagnosing fragmentation and approximate dynamical constraints in complex quantum many-body systems.

cond-mat.str-el↗

arXiv2026

Local integrals of motion encoded in a few eigenstates

Many properties of a quantum system can be obtained from just a single eigenstate of its Hamiltonian. For example, a single eigenstate can be used to determine whether a system is integrable or chaotic and, in the latter case, to establish its thermal properties. Focusing on the XXZ model, we show that the local integrals of motion, which lie at the heart of integrability, can also be estimated from a small number of eigenstates. Moreover, as the system size increases, fewer eigenstates are required, so that in the thermodynamic limit, the integrals of motion can be obtained from a vanishingly small fraction of all eigenstates. Interestingly, this property does not extend to integrals of motion arising solely from Hilbert space fragmentation, as found in the folded XXZ model, where the majority of eigenstates has to be used. This represents one of the few fundamental differences known between integrability and Hilbert space fragmentation.

cond-mat.str-el↗

arXiv2025

Finding local integrals of motion in quantum lattice models in the thermodynamic limit

Local integrals of motion (LIOMs) play a key role in understanding the long-time properties of closed macroscopic systems. They were found for selected integrable systems via complex analytical calculations. The existence of LIOMs and their structure can also be studied via numerical methods, which, however, involve exact diagonalization of Hamiltonians, posing a bottleneck for such studies. We show that finding LIOMs in translationally invariant lattice models or unitary quantum circuits can be reduced to a problem for which one may numerically find an exact solution in the thermodynamic limit. We develop a simple algorithm and demonstrate its efficiency by calculating LIOMs and bounds on correlations (the Mazur bounds) for infinite integrable spin chains and unitary circuits. Finally, we demonstrate that this approach identifies slow modes in nearly integrable spin models and estimates their relaxation times.

cond-mat.str-el↗

arXiv2025

Magnon damping and mode softening in quantum double-exchange ferromagnets

We present a comprehensive analysis of the magnetic excitations and electronic properties of fully quantum double-exchange ferromagnets, i.e., systems where ferromagnetic ordering emerges from the competition between spin, charge, and orbital degrees of freedom, but without the canonical approximation of using classical localized spins. Specifically, we investigate spin excitations within the Kondo lattice-like model, as well as a two-orbital Hubbard Hamiltonian in proximity to the orbital-selective Mott phase. Computational analysis of the magnon dispersion, damping, and spectral weight within these models reveals unexpected phenomena, such as magnon mode softening and the anomalous decoherence of magnetic excitations as observed in earlier experimental efforts, but explained here without the use of the phononic degrees of freedom. We show that these effects are intrinsically linked to incoherent spectral features near the Fermi level, which arise due to the quantum nature of the local (on-site) triplets. This incoherent spectrum leads to a Stoner-like continuum on which spin excitations scatter, governing magnon lifetime and strongly influencing the dynamical spin structure factor. Our study explores the transition from coherent to incoherent magnon spectra by varying the electron density. Furthermore, we demonstrate that the magnitude of the localized spin mitigates decoherence by suppressing the incoherent spectral contributions near the Fermi level. We also discuss the effective $J_1$-$J_2$ spin Hamiltonian, which can accurately describe the large doping region characterized by the magnon-mode softening. Finally, we show that this behavior is also present in multiorbital models with partially filled orbitals, namely, in systems without localized spin moments, provided that the model is in a strong coupling regime.

cond-mat.str-el↗

arXiv2025

Thouless approach in transport in integrable and perturbed easy-axis Heisenberg chains

We study transport in spin chains employing the Thouless approach based on the level sensitivity to the boundary conditions, $R$. Although spin transport in the integrable easy-axis XXZ model is diffusive, corresponding $R$ is much closer to ballistic chains than to chaotic diffusive systems. In the case of the grand canonical ensemble, this observation can be rigorously justified, while in the case of the canonical ensemble it can be demonstrated by numerical calculations. Integrability breaking perturbation (IBP) strongly reduces $R$ which reveals a pronounced minimum at the crossover from anomalous diffusive to normal dissipative transport. This minimum coincides with the onset of the universality of the random matrix theory. Results for various IBP suggest a discontinuous jump of the spin conductivity in the thermodynamic limit, and moreover that its value is proportional to the strength of the IBP.

cond-mat.str-el↗

arXiv2024

Evidence for valence-bond pairing in a one-dimensional two-orbital system

Valence bond (VB) states as the formation mechanism of Cooper pairs, eventually leading to high-temperature superconductivity, remain a controversial topic. Although various VB-like states find variational relevance in the description of specific spin models and quantum spin liquids, in the realm of many-body fermionic Hamiltonians, the evidence for such states as ground states wave functions remains elusive, challenging the valence-bond pairing mechanism. Here, we present evidence of a VB ground state with pairing tendencies, particularly at finite doping. We achieved this for the generic two-orbital Hubbard model in low dimension, where the VB states can be associated with the presence of the topological order manifested by edge states.

cond-mat.str-el↗

arXiv2023

Long-living prethermalization in nearly integrable spin ladders

Relaxation rates in nearly integrable systems usually increase quadratically with the strength of the perturbation that breaks integrability. We show that the relaxation rates can be significantly smaller in systems that are integrable along two intersecting lines in the parameter space. In the vicinity of the intersection point, the relaxation rates of certain observables increase with the fourth power of the distance from this point, whereas for other observables one observes standard quadratic dependence on the perturbation. As a result, one obtains exceedingly long-living prethermalization but with a reduced number of the nearly conserved operators. We show also that such a scenario can be realized in spin ladders.

cond-mat.str-el↗

arXiv2023

Emergent dipole moment conservation and subdiffusion in tilted chains

We study the transport dynamics of an interacting tilted (Stark) chain. We show that the crossover between diffusive and subdiffusive dynamics is governed by $F\sqrt{L}$, where $F$ is the strength of the field, and $L$ is the wave-length of the excitation. While the subdiffusive dynamics persist for large fields, the corresponding transport coefficient is exponentially suppressed with $F$ so that the finite-time dynamics appear almost frozen. We explain the crossover scale between the diffusive and subdiffusive transport by bounding the dynamics of the dipole moment for arbitrary initial state. We also prove its emergent conservation at infinite temperature. Consequently, the studied chain is one of the simplest experimentally realizable models for which numerical data are consistent with the hydrodynamics of fractons.

cond-mat.str-el↗

arXiv2023

Strongly disordered Anderson insulator chains with generic two-body interaction

The random-field spin-1/2 XXZ chains, and the corresponding Anderson insulators of spinless fermions with density-density interaction, have been intensively studied in the context of many-body localization. However, we recently argued [B. Krajewski et al., Phys. Rev. Lett. 129, 260601(2022)] that the two-body density-density interaction in these models is not generic since only a small fraction of this interaction represents a true local perturbation to the Anderson insulator. Here we study ergodicity of strongly disordered Anderson insulator chains choosing other forms of the two-body interaction for which the strength of the true perturbation is of the same order of magnitude as the bare two-body interaction. Focusing on the strong interaction regime, numerical results for the level statistics and the eigenstate thermalization hypothesis are consistent with emergence of ergodicity at arbitrary strong disorder.

cond-mat.stat-mech↗

arXiv2023

Optical manipulation of bipolarons in a system with nonlinear electron-phonon coupling

We investigate full quantum mechanical evolution of two electrons nonlinearly coupled to quantum phonons and simulate the dynamical response of the system subject to a short spatially uniform optical pulse that couples to dipole-active vibrational modes. Nonlinear electron-phonon coupling can either soften or stiffen the phonon frequency in the presence of electron density. In the former case, an external optical pulse tuned just below the phonon frequency generates attraction between electrons and leads to a long-lived bound state even after the optical pulse is switched off. It originates from a dynamical modification of the self-trapping potential that induces a metastable state. By increasing the pulse frequency, the attractive electron-electron interaction changes to repulsive. Two sequential optical pulses with different frequencies can switch between attractive and repulsive interaction. Finally, we show that the pulse-induced binding of electrons is shown to be efficient also for weakly dispersive optical phonons, in the presence anharmonic phonon spectrum and in two dimensions.

cond-mat.stat-mech↗

arXiv2023

Transition to the Haldane phase driven by electron-electron correlations

One of the most famous quantum systems with topological properties, the spin $\mathcal{S}=1$ antiferromagnetic Heisenberg chain, is well-known to display exotic $\mathcal{S}=1/2$ edge states. However, this spin model has not been analyzed from the more general perspective of strongly correlated systems varying the electron-electron interaction strength. Here, we report the investigation of the emergence of the Haldane edge in a system of interacting electrons -- the two-orbital Hubbard model -- with increasing repulsion strength $U$ and Hund interaction $J_\mathrm{H}$. We show that interactions not only form the magnetic moments but also form a topologically nontrivial fermionic many-body ground-state with zero-energy edge states. Specifically, upon increasing the strength of the Hubbard repulsion and Hund exchange, we identify a sharp transition point separating topologically trivial and nontrivial ground-states. Surprisingly, such a behaviour appears already at rather small values of the interaction, in a regime where the magnetic moments are barely developed.

cond-mat.str-el↗

arXiv2023

Slow diffusion and Thouless localization criterion in modulated spin chains

In recent years the ergodicity of disordered spin chains has been investigated via extensive numerical studies of the level statistics or the transport properties. However, a clear relationship between these results has yet to be established. We present the relation between the diffusion constant and the energy-level structure, which leads to the Thouless localization criterion. Together with the exponential-like dependence of the diffusion constant on the strength of quasiperiodic or random fields, the Thouless criterion explains the nearly linear drift with the system size of the crossover/transition to the nonergodic regime. Moreover, we show that the Heisenberg spin chain in the presence of the quasiperiodic fields can be well approached via a sequence of simple periodic systems, where diffusion remains finite even at large fields.

cond-mat.dis-nn↗

arXiv2022

Spin diffusion in perturbed isotropic Heisenberg spin chain

The isotropic Heisenberg chain represents a particular case of an integrable many-body system exhibiting superdiffusive spin transport at finite temperatures. Here, we show that this model has distinct properties also at finite magnetization $m\ne0$, even upon introducing the SU(2) invariant perturbations. Specifically, we observe nonmonotonic dependence of the diffusion constant ${\cal D}_0(\Delta)$ on the spin anisotropy $\Delta$, with a pronounced maximum at $\Delta =1$. The latter dependence remains true also in the zero magnetization sector, with superdiffusion at $\Delta=1$ that is remarkably stable against isotropic perturbation (at least in finite-size systems), consistent with recent experiments with cold atoms.

cond-mat.str-el↗

arXiv2022

Restoring ergodicity in a strongly disordered interacting chain

We consider a chain of interacting fermions with random disorder that was intensively studied in the context of many-body localization. We show that only a small fraction of the two-body interaction represents a true local perturbation to the Anderson insulator. While this true perturbation is nonzero at any finite disorder strength W, it decreases with increasing W. This establishes a view that the strongly disordered system should be viewed as a weakly perturbed integrable model, i.e., a weakly perturbed Anderson insulator. As a consequence, the latter can hardly be distinguished from a strictly integrable system in finite-size calculations at large W. We then introduce a rescaled model in which the true perturbation is of the same order of magnitude as the other terms of the Hamiltonian, and show that the system remains ergodic at arbitrary large disorder.

cond-mat.stat-mech↗

arXiv2022

Quasiballistic transport in long-range anisotropic Heisenberg model

Purely ballistic transport is a rare feature even for integrable models. By numerically studying the Heisenberg chain with the power-law exchange, \mbox{$J\propto1/r^\alpha$}, where $r$ is a distance, we show that for spin anisotropy $\Delta \simeq \exp(-\alpha+2)$ the system exhibits a quasiballistic spin transport and the presence of fermionic excitation which do not decay up to extremely long times $\sim10^3/J$. This conclusion is reached on the base of the dynamics of spin domains, the dynamical spin conductivity, inspecting the matrix elements of the spin-current operator, and by the analysis of most conserved operators. Our results smoothly connects two models where fully ballistic transport is present: free particles with nearest-neighbor hopping and the isotropic Haldane-Shastry model.

cond-mat.str-el↗

arXiv2022

From dissipationless to normal diffusion in easy-axis Heisenberg spin chain

The anomalous spin diffusion of the integrable easy-axis Heisenberg chain originates in the ballistic transport of symmetry sectors with nonzero magnetization. Ballistic transport is replaced by normal dissipative transport in all magnetization sectors upon introducing the integrability-breaking perturbations, including external driving. Such behavior implies that the diffusion constant obtained for the integrable model is relevant for the spread of spin excitations but not for the spin conductivity. We present numerical results for closed systems and driven open systems, indicating that the diffusion constant shows a discontinuous variation as the function of perturbation strength.

cond-mat.str-el↗

arXiv2021

Multiple relaxation times in perturbed XXZ chain

We numerically study the relaxation of correlation functions in weakly perturbed integrable XXZ chain. The decay of the spin-current and the energy-current correlations at zero magnetization are well described by single, but quite distinct, relaxation rates governed by the square of the perturbation strength $g$. However, at finite magnetization a single correlation function reveals multiple relaxation rates. The result can be understood in terms of multi-scale relaxation scenario, where various relaxation times are linked with various quantities which are conserved in the reference integrable system. On the other hand, the correlations of non-commuting quantities, being conserved at particular anisotropies $\Delta$, decay non-exponentially with characteristic time scale linear in $g$.

cond-mat.str-el↗

arXiv2021

Relaxation at different length-scales in models of many-body localization

We study dynamical correlation functions in the random-field Heisenberg chain, which probes the relaxation times at different length scales. Firstly, we show that the relaxation time associated with the dynamical imbalance (examining the relaxation at the smallest length scale) decreases with disorder much faster than the one determined by the dc conductivity (probing the global response of the system). We argue that the observed dependence of relaxation on the length scale originates from local nonresonant regions. The latter have particularly long relaxation times or remain frozen, allowing for nonzero dc transport via higher-order processes. Based on the numerical evidence, we introduce a toy model that suggests that the nonresonant regions asymptotic dynamics are essential for the proper understanding of the disordered chains with many-body interactions.

cond-mat.str-el↗