arXiv subjects

Marcin Mierzejewski

Publications and source records attributed to Marcin Mierzejewski.

At least 19 recordsLinked to original sources

arXiv2026

Diffusion in interacting two-dimensional systems under a uniform magnetic field

The dynamics of interacting particles in orbital magnetic fields are notoriously difficult to study, as this physics is inherently connected to electronic correlations in two-dimensional systems, for which no straightforward theoretical methods are available. Here, we report on the diffusive relaxation dynamics of two-dimensional interacting fermionic systems under a uniform magnetic field in the infinite temperature regime. We first show that the fermionic truncated Wigner approximation captures the equilibration dynamics unexpectedly well for intermediate interaction strengths when going beyond one dimension. This high accuracy holds at least for relatively small ladder systems, which are accessible to the Lanczos method that we use to benchmark the reliability of the Wigner approximation. We find that strong interactions, which exceed the hopping energy, suppress magnetic-field effects on diffusive transport. However, when the interactions are comparable to the kinetic energy, the diffusion is significantly reduced by the magnetic flux. This is observed for sufficiently large systems (above approximately 400 lattice sites), where finite-size effects weakly affect particle transport. We suggest that our results should be directly accessible on current optical lattice platforms.

cond-mat.quant-gas↗

arXiv2026

Spin subdiffusion in perturbed infinite-U Hubbard chain

The $t$-model represents the Hubbard model in the limit $U \to \infty$ and is one of the basic models of strongly correlated electrons. On a one-dimensional chain, the model is integrable, and the charge dynamics corresponds to that of free spinless fermions. However, the sequence of spins is frozen, leading to the Hilbert space fragmentation and nontrivial spin dynamics. We consider integrable and perturbed models with perturbations that break integrability while preserving fragmentation, and show that they exhibit various types of spin dynamics, from ballistic transport to anomalous diffusion in the integrable case, and from diffusion to subdiffusion in the perturbed case. Due to fragmentation, in all cases considered, spin transport is mediated by charge transport, with a particular magnetization dependence, most notably leading to subdiffusion in the grandcanonical average of the perturbed model, with a mechanism distinct from subdiffusion in disordered or dipole-conserving models.

cond-mat.str-el↗

arXiv2025

Tunable Hilbert space fragmentation and extended critical regime

Systems exhibiting the Hilbert-space fragmentation are nonergodic, and their Hamiltonians decompose into exponentially many blocks in the computational basis. In many cases, these blocks can be labeled by eigenvalues of statistically localized integrals of motion (SLIOM), which play a similar role in fragmented systems as local integrals of motion in integrable systems. While a nonzero perturbation eliminates all nontrivial conserved quantities from integrable models, we demonstrate for the $t$-$J_z$ chain that an appropriately chosen perturbation may gradually eliminate SLIOMs (one by one) by progressively merging the fragmented subspaces. This gradual recovery of ergodicity manifests as an extended critical regime characterized by multiple peaks of the fidelity susceptibility. Each peak signals a change in the number of SLIOMs and blocks, as well as an ultra-slow relaxation of local observables.

cond-mat.str-el↗

arXiv2024

Dependence of the charge transport in tilted chains on the choice of two-body interaction

We study tilted chains of spinless fermions in the presence of the nearest-neighbor density-density interaction for which the noninteracting counterpart displays Stark localization. We demonstrate that the latter two-body interaction can be decomposed into two (orthogonal) parts which, respectively, commute and do not commute with the single-particle Hamiltonian. We derive an explicit form of the noncommuting part that decreases with tilt and describes the nearest-neighbor correlated hopping and the pair-hopping interaction. When the density-density coupling is replaced by the pair-hopping interaction of the same magnitude then the charge dynamics may be faster by a few orders of magnitude than in the original model.

cond-mat.str-el↗

arXiv2024

Universal semiclassical dynamics in disordered two-dimensional systems

The dynamics of disordered two-dimensional systems is much less understood than the dynamics of disordered chains, mainly due to the lack of appropriate numerical methods. We demonstrate that a single-trajectory version of the fermionic truncated Wigner approximation (fTWA) gives unexpectedly accurate results for the dynamics of one-dimensional (1D) systems with moderate or strong disorder. Additionally, the computational complexity of calculations carried out within this approximation is small enough to enable studies of two-dimensional (2D) systems larger than standard fTWA. Using this method, we analyze the dynamics of interacting spinless fermions propagating on disordered 1D and 2D lattices. We find for both spatial dimensions that the imbalance exhibits a universal dependence on the rescaled time $t/\xi_W$, where in 2D the time-scale $\xi_W$ follows a stretched-exponential dependence on disorder strength.

cond-mat.stat-mech↗

arXiv2024

Normal weak eigenstate thermalization

Eigenstate thermalization has been numerically shown to occur for few-body observables in a wide range of nonintegrable models. For intensive sums of few-body observables, a weaker version of eigenstate thermalization known as weak eigenstate thermalization has been proved to occur in general. Here, we unveil a stricter weak eigenstate thermalization phenomenon that occurs in quadratic models exhibiting quantum chaos in the single-particle sector (quantum-chaotic quadratic models) and in integrable interacting models. In such models, we argue that few-body observables that have a properly defined system-size independent norm are guaranteed to exhibit at least a polynomially vanishing variance (over the entire many-body energy spectrum) of the diagonal matrix elements, a phenomenon we dub normal weak eigenstate thermalization. We prove that normal weak eigenstate thermalization is a consequence of single-particle eigenstate thermalization, i.e., it can be viewed as a manifestation of quantum chaos at the single-particle level. We report numerical evidence of normal weak eigenstate thermalization for quantum-chaotic quadratic models such as the three-dimensional Anderson model in the delocalized regime and the power-law random banded matrix model, as well as for the integrable interacting spin-1/2 XYZ and XXZ models.

cond-mat.stat-mech↗

arXiv2024

Einstein relation for subdiffusive relaxation in Stark chains

We investigate chains of interacting spinless fermions subject to a finite external field $F$ (also called Stark chains) and focus on the regime where the charge thermalization follows the subdiffusive hydrodynamics. First, we study reduced models conserving the dipole moment and derive an explicit Einstein relation which links the subdiffusive transport coefficient with the correlations of the dipolar current. This relation explains why the decay rate, $\Gamma_q$, of the density modulation with wave-vector $q$ shows $q^4$-dependence. In the case of the Stark model, a similar Einstein relation is also derived and tested using various numerical methods. They confirm an exponential reduction of the transport coefficient with increasing $F$. On the other hand, our study of the Stark model indicates that upon increasing $q$ there is a crossover from subdiffusive behavior, $\Gamma_q \propto q^4$, to the normal diffusive relaxation, $\Gamma_q \propto q^2$, at the wave vector $q^*$ which vanishes for $F \to 0$.

cond-mat.str-el↗

arXiv2024

Local integrals of motion in dipole-conserving models with Hilbert space fragmentation

Hilbert space fragmentation is an ergodicity breaking phenomenon, in which Hamiltonian shatters into exponentially many dynamically disconnected sectors. In many fragmented systems, these sectors can be labelled by statistically localized integrals of motion, which are {\em nonlocal} operators. We study the paradigmatic nearest-neighbor pair hopping (PH) model exhibiting the so-called strong fragmentation. We show that this model hosts local integrals of motion (LIOMs), which correspond to frozen density modes with long wavelengths. The latter modes become subdiffusive when longer-range pair hoppings are allowed. Finally, we make a connection with a tilted (Stark) chain. Contrary to the dipole-conserving effective models, the tilted chain is shown to support either Hamiltonian or dipole moment as an LIOM. Numerical results are obtained from a numerical algorithm, in which finding LIOMs is reduced to the data compression problem.

cond-mat.str-el↗

arXiv2023

Generalized thermalization in quantum-chaotic quadratic Hamiltonians

Thermalization (generalized thermalization) in nonintegrable (integrable) quantum systems requires two ingredients: equilibration and agreement with the predictions of the Gibbs (generalized Gibbs) ensemble. We prove that observables that exhibit eigenstate thermalization in single-particle sector equilibrate in many-body sectors of quantum-chaotic quadratic models. Remarkably, the same observables do not exhibit eigenstate thermalization in many-body sectors (we establish that there are exponentially many outliers). Hence, the generalized Gibbs ensemble is generally needed to describe their expectation values after equilibration, and it is characterized by Lagrange multipliers that are smooth functions of single-particle energies.

cond-mat.stat-mech↗

arXiv2023

Relaxation mechanisms in a disordered system with the Poisson level statistics

We discuss the interplay between many-body localization and spin-symmetry. To this end, we study the time evolution of several observables in the anisotropic t-J model. Like the Hubbard chain, the studied model contains charge and spin degrees of freedom, yet it has smaller Hilbert space and thus allows for numerical studies of larger systems. We compare the field disorder that breaks the Z_2 spin symmetry and a potential disorder that preserves the latter symmetry. In the former case, sufficiently strong disorder leads to localization of all studied observables, at least for the studied system sizes. However, in the case of symmetry-preserving disorder, we observe that odd operators under the Z_2 spin transformation relax towards the equilibrium value at relatively short time scales that grow only polynomially with the disorder strength. On the other hand, the dynamics of even operators and the level statistics within each symmetry sector are consistent with localization. Our results indicate that localization exists within each symmetry sector for symmetry preserving disorder. Odd operators' apparent relaxation is due to their time evolution between distinct symmetry sectors.

cond-mat.str-el↗

arXiv2023

Modelling sample-to-sample fluctuations of the gap ratio in finite disordered spin chains

We study sample-to-sample fluctuations of the gap ratio in the energy spectra in finite disordered spin chains. The chains are described by the random-field Ising model and the Heisenberg model. We show that away from the ergodic/nonergodic crossover, the fluctuations are correctly captured by the Rosenzweig-Porter (RP) model. However, fluctuations in the microscopic models significantly exceed those in the RP model in the vicinity of the crossover. We show that upon introducing an extension to the RP model, one correctly reproduces the fluctuations in all regimes, i.e., in the ergodic and nonergodic regimes as well as at the crossover between them. Finally, we demonstrate how to reduce the sample-to-sample fluctuations in both studied microscopic models.

cond-mat.stat-mech↗

arXiv2022

Semiclassical bounds on dynamics of two-dimensional interacting disordered fermions

Using the truncated Wigner approximation (TWA) we study quench dynamics of two-dimensional lattice systems consisting of interacting spinless fermions with potential disorder. First, we demonstrate that the semiclassical dynamics generally relaxes faster than the full quantum dynamics. We obtain this result by comparing the semiclassical dynamics with exact diagonalization and Lanczos propagation of one-dimensional chains. Next, exploiting the TWA capabilities of simulating large lattices, we investigate how the relaxation rates depend on the dimensionality of the studied system. We show that strongly disordered one-dimensional and two-dimensional systems exhibit a transient, logarithmic-in-time relaxation, which was recently established for one-dimensional chains. Such relaxation corresponds to the infamous $1/f$-noise at strong disorder.

cond-mat.stat-mech↗

arXiv2021

Phenomenology of spectral functions in disordered spin chains at infinite temperature

Studies of disordered spin chains have recently experienced a renewed interest, inspired by the question to which extent the exact numerical calculations comply with the existence of a many-body localization phase transition. For the paradigmatic random field Heisenberg spin chains, many intriguing features were observed when the disorder is considerable compared to the spin interaction strength. Here, we introduce a phenomenological theory that may explain some of those features. The theory is based on the proximity to the noninteracting limit, in which the system is an Anderson insulator. Taking the spin imbalance as an exemplary observable, we demonstrate that the proximity to the local integrals of motion of the Anderson insulator determines the dynamics of the observable at infinite temperature. In finite interacting systems our theory quantitatively describes its integrated spectral function for a wide range of disorders.

cond-mat.dis-nn↗

arXiv2020

Identification of the Majorana edge modes in tight-binding systems based on the Krylov method

Low dimensional structures in the non-trivial topological phase can host the in-gap Majorana bound states, identified experimentally as zero-bias peaks in differential conductance. Theoretical methods for studying Majorana modes are mostly based on the bulk-boundary correspondence or exact diagonalization of finite systems via, e.g., Bogoliubov-de Gennes formalism. In this paper, we develop an efficient method for identifying the Majorana in-gap (edge) states via looking for extreme eigenvalues of symmetric matrices. The presented approach is based on the Krylov method and allows for study the spatial profile of the modes as well as the spectrum of the system. The advantage of this method is the calculation cost, which shows linear dependence on the number of lattice sites. The latter problem may be solved for very large clusters of arbitrary shape/geometry. In order to demonstrate the efficiency of our approach, we study two- and three-dimensional clusters described by the Kitaev and Rashba models for which we determine the number of Majorana modes and calculate their spatial structures. Additionally, we discuss the impact of the system size on the physical properties of the topological phase of the magnetic nanoisland deposited on the superconducting surface. In this case, we have shown that the eigenvalues of the in-gap states depend on the length of the system edge.

cond-mat.mes-hall↗

arXiv2019

Majorana phase-gate based on the geometric phase

We study dynamics of a single qubit encoded in two pairs of Majorana modes, whereby each pair is hosted on a trijunction described by the Kitaev model extended by many-body interactions. We demonstrated that the challenging phase-gate may be efficiently implemented via braiding of partially overlapping modes. Although such qubit acquires both geometric and dynamical phases during the braiding protocol, the latter phase may be eliminated if the Majorana modes are hosted by systems with appropriate particle-hole symmetry.

cond-mat.supr-con↗

arXiv2019

Eigenstate thermalization hypothesis and integrals of motion

Even though foundations of the eigenstate thermalization hypothesis (ETH) are based on random matrix theory, physical Hamiltonians and observables substantially differ from random operators. One of the major challenges is to embed local integrals of motion (LIOMs) within the ETH. Here we focus on their impact on fluctuations and structure of the diagonal matrix elements of local observables. We first show that nonvanishing fluctuations entail the presence of LIOMs. Then we introduce a generic protocol to construct observables, subtracted by their projections on LIOMs as well as products of LIOMs. The protocol systematically reduces fluctuations and/or the structure of the diagonal matrix elements. We verify our arguments by numerical results for integrable and nonintegrable models.

cond-mat.stat-mech↗

arXiv2018

Dynamics of the one-dimensional Anderson insulator coupled to various bosonic baths

We study a particle which propagates in a one dimensional strong random potential and is coupled to a bosonic bath. We independently test various properties of bosons (hopping term, hard-core effects and generic boson-boson interaction) and show that bosonic itineracy is the essential ingredient governing the dynamics of the particle. Coupling of the particle to itinerant phonons or hard core bosons alike leads to delocalization of the particle by virtue of a subdiffusive (or diffusive) spread from the initially localized state. Delocalization remains in effect even when the boson frequency and the bandwidth of itinerant bosons remain an order of magnitude smaller than the magnitude of the random potential. When the particle is coupled to localized bosons, its spread remains logarithmic or even sub-logarithmic. The latter result together with the survival probability shows that the particle remains localized despite being coupled to bosons.

cond-mat.str-el↗

arXiv2018

Spin subdiffusion in disordered Hubbard chain

We derive and study the effective spin model that explains the anomalous spin dynamics in the one-dimensional Hubbard model with strong potential disorder. Assuming that charges are localized, we show that spins are delocalized and their subdiffusive transport originates from a singular random distribution of spin exchange interactions. The exponent relevant for the subdiffusion is determined by the Anderson localization length and the density of electrons. While the analytical derivations are valid for low particle density, numerical results for the full model reveal a qualitative agreement up to half-filling.

cond-mat.str-el↗