arXiv subjects

Błażej Jaworowski

Publications and source records attributed to Błażej Jaworowski.

14 recordsLinked to original sources

arXiv2026

Structured Non-Locality and Emergent Locality in Cavity-QED Many-Body Dynamics

Cavity quantum electrodynamics (QED) modifies many-body systems by combining cavity-mediated collective interactions with microscopic short-range interactions. The resulting dynamics lies between the local and fully collective limits, such that neither locality nor collectivity alone provides a complete organizing principle. In the clean conceptual limit of dominant collective coupling, we show that the effective dynamics within each energetically isolated subspace is generically controlled by whether that subspace admits a local product-state basis, and identify exceptions imposed by angular-momentum selection rules. Product-state subspaces generically retain the spatial structure of the microscopic interaction. Entangled subspaces instead generically dress local processes with global operators, generating non-local but highly structured dynamics. We illustrate this by deriving the corresponding effective Hamiltonians in two representative cavity-QED spin models. The cavity-isolated subspace thus becomes a resource for generating competing short-range interactions or globally conditioned local processes, opening a class of many-body dynamics without local or fully collective counterparts.

quant-ph↗

arXiv2025

Squeezing Classical Antiferromagnets into Quantum Spin Liquids via Global Cavity Fluctuations

Cavity quantum electrodynamics with atomic ensembles is typically associated with collective spin phenomena, such as superradiance and spin squeezing, in which the atoms evolve collectively as a macroscopic spin ($S\sim N/2$) on the Bloch sphere. Surprisingly, we show that the tendency toward a collective spin description need not imply collective spin phenomena; rather, it can be exploited to generate new forms of strongly correlated quantum matter. The key idea is to use uniform cavity-mediated interactions to energetically project the system into the total-spin singlet sector ($S=0$) - a highly entangled subspace where the physics is governed entirely by cavity fluctuations. Focusing on Rydberg atom arrays coupled to a single-mode cavity, we show that global cavity fluctuations can effectively squeeze classical antiferromagnets into quantum spin liquids, characterized by non-local entanglement, fractionalized excitations, and emergent gauge fields. This work suggests that cavity QED can be a surprising resource for inducing strongly correlated phenomena, which could be explored in the new generation of hybrid tweezer-cavity platforms.

quant-ph↗

arXiv2025

Laughlin-like states of few atomic excitations in small subwavelength atom arrays

Atom arrays with sub-wavelength lattice constant can exhibit fascinating optical properties. For example, the combination of $V$-type level structure and magnetic fields can yield topological band structures, making the neutral atomic excitations behave like charged particles in a magnetic field. Up to now, much of our understanding of these systems (and arrays in general) focuses on the single-excitation regime. Here, we go beyond the single-excitation level to show that such systems can give rise to few-particle Laughlin-like states. In particular, we consider small honeycomb ``flakes,'' where the harmful divergences near the light cone can be smeared out by finite-size effects. By choosing an appropriate value of magnetic field we thereby obtain an energy spectrum and eigenstates resembling those of Landau levels. The native hard-core nature of atomic excitations then gives rise to multi-excitation Laughlin-like states. This phenomenon occurs not only in samples of tens of sites, but also in a minimal nanoring system of only six sites. Next, considering two-particle Laughlin-like states, we show that they can be driven by uniform light, and that correlations of the output light contain identifying fingerprints of these states. We believe that these results are a step towards new paradigms of engineering and understanding strongly-correlated many-body states in atom-light interfaces.

cond-mat.str-el↗

arXiv2024

Many-body localization on finite generation fractal lattices

We study many-body localization in a hardcore boson model in the presence of random disorder on finite generation fractal lattices with different Hausdorff dimensions and different local lattice structures. In particular, we consider the Vicsek, T-shaped, Sierpinski gasket, and modified Koch-curve fractal lattices. In the single-particle case, these systems display Anderson localization for arbitrary disorder strength if they are large enough. In the many-body case, the systems available to exact diagonalization exhibit a transition between a delocalized and localized regime, visible in the spectral and entanglement properties of these systems. The position of this transition depends on the Hausdorff dimension of the given fractal, as well as on its local structure.

cond-mat.dis-nn↗

arXiv2024

Dynamics of quasiholes and quasiparticles at the edges of small lattices

We study quench dynamics of bosonic fractional quantum Hall systems in small lattices with cylindrical boundary conditions and low particle density. The states studied have quasiholes or quasiparticles relative to the bosonic Laughlin state at half filling. Pinning potentials are placed at edge sites (or sites close to the edges) and are then turned off. Because the edges of fractional quantum Hall systems host chiral edge modes, we expect chiral dynamics, with motion in one direction for positive potentials pinning quasiholes, and motion in the other direction for negative potentials pinning quasiparticles. We numerically show that chiral motion of the density distribution is observed and robust for the case with positive potentials (quasiholes), but that there is no noticeable chiral motion for negative potentials (quasiparticles). The comparison of the numerical ground states with model lattice Laughlin wavefunctions suggests that both positive and negative potentials do create and pin anyons that are not necessarily well-separated on small lattices. Initializing the dynamics with the model state also shows the lack of chiral dynamics of quasiparticles. Our results suggest that, in small lattices with low particle density, quasiparticles are strongly adversely affected in dynamical processes, whereas quasiholes are dynamically robust.

cond-mat.mes-hall↗

arXiv2023

Approximate Hofstadter- and Kapit-Mueller-like parent Hamiltonians for Laughlin states on fractals

Recently, it was shown that fractional quantum Hall states can be defined on fractal lattices. Proposed exact parent Hamiltonians for these states are nonlocal and contain three-site terms. In this work, we look for simpler, approximate parent Hamiltonians for bosonic Laughlin states at half filling, which contain only onsite potentials and two-site hopping with the interaction generated implicitly by hardcore constraints (as in the Hofstadter and Kapit-Mueller models on periodic lattices). We use an ``inverse method'' to determine such Hamiltonians on finite-generation Sierpiński carpet and triangle lattices. The ground states of some of the resulting models display relatively high overlap with the model states if up to third neighbor hopping terms are considered, and by increasing the maximum hopping distance one can achieve nearly perfect overlaps. When the number of particles is reduced and additional potentials are introduced to trap quasiholes, the overlap with a model quasihole wavefunction is also high in some cases, especially for the nonlocal Hamiltonians. We also study how the small system size affects the braiding properties for the model quasihole wavefunctions and perform analogous computations for Hamiltonian models.

cond-mat.str-el↗

arXiv2022

Non-Abelian chiral spin liquid on spin-1 kagome lattice: truncation of an exact Hamiltonian and numerical optimization

We search for short-range Hamiltonians of finite spin-1 kagome systems, maximizing the overlaps with lattice Moore-Read states. Our starting point is an exact, long-range parent Hamiltonian for such a state on a finite plane, obtained from conformal field theory. A truncation procedure is applied to it, which retains only short-range terms and makes it easy to define the Hamiltonian on a torus. Finally, the remaining coefficients are optimized, to yield maximized overlaps between exact diagonalization results and model ground states. In the best cases, these overlaps exceed 0.9 and 0.8 for the three lowest states of 12- and 18-site systems, respectively, suggesting that the obtained Hamiltonians are good parent Hamiltonians for a non-Abelian topological order.

cond-mat.str-el↗

arXiv2021

Interaction-driven transition between the Wigner crystal and the fractional Chern insulator in topological flat bands

We investigate an interaction-driven transition between crystalline and liquid states of strongly correlated spinless fermions within topological flat bands at low density (with filling factors $ν=1/5$, $1/7$, $1/9$). Using exact diagonalization for finite size systems with periodic boundary conditions, we distinguish different phases, whose stability depends on the interaction range, controlled by the screening parameter of the Coulomb interaction. The crystalline phases are identified by a crystallization strength, calculated from the Fourier transforms of pair correlation density, while the Fractional Chern insulator phases are characterized using momentum counting rules, entanglement spectrum, and overlaps with corresponding Fractional Quantum Hall states. The type of the phase depends on a particular single particle model and its topological properties. We show that for $ν=1/7$ and $1/5$ it is possible to tune between the Wigner crystal and Fractional Chern insulator phase in the kagome lattice model with the band carrying the Chern number $C=1$. In contrast, in the $C=2$ models, the Wigner crystallization was absent at $ν=1/5$, and appeared at $ν=1/9$, suggesting that $C=2$ FCIs are more stable against the formation of crystalline order

cond-mat.str-el↗

arXiv2021

Model wavefunctions for an interface between lattice Laughlin and Moore-Read states

We use conformal field theory to construct model wavefunctions for a gapless interface between lattice versions of a bosonic Laughlin state and a fermionic Moore-Read state, both at $ν=1/2$. The properties of the resulting model state, such as particle density, correlation function and Rényi entanglement entropy are then studied using the Monte Carlo approach. Moreover, we construct the wavefunctions also for anyonic excitations (quasiparticles and quasiholes). We study their density profile, charge and statistics. We show that, similarly to the Laughlin-Laughlin case studied earlier, some anyons (the Laughlin Abelian ones) can cross the interface, while others (the non-Abelian ones) lose their anyonic character in such a process. Also, we argue that, under an assumption of local particle exchange, multiple interfaces give rise to a topological degeneracy, which can be interpreted as originating from Majorana zero modes.

cond-mat.str-el↗

arXiv2020

Model wavefunctions for interfaces between lattice Laughlin states

We study the interfaces between lattice Laughlin states at different fillings. We propose a class of model wavefunctions for such systems constructed using conformal field theory. We find a nontrivial form of charge conservation at the interface, similar to the one encountered in the field theory works from the literature. Using Monte Carlo methods, we evaluate the correlation function and entanglement entropy at the border. Furthermore, we construct the wavefunction for quasihole excitations and evaluate their mutual statistics with respect to quasiholes originating at the same or the other side of the interface. We show that some of these excitations lose their anyonic statistics when crossing the interface, which can be interpreted as impermeability of the interface to these anyons. Contrary to most of the previous works on interfaces between topological orders, our approach is microscopic, allowing for a direct simulation of e.g. an anyon crossing the interface. Even though we determine the properties of the wavefunction numerically, the closed-form expressions allow us to study systems too large to be simulated by exact diagonalization.

cond-mat.str-el↗

arXiv2019

Characterization of quasiholes in two-component fractional quantum Hall states and fractional Chern insulators in $|C|=2$ flat bands

We perform an exact-diagonalization study of quasihole excitations for the two-component Halperin $(221)$ state in the lowest Landau level and for several $ν=1/3$ bosonic fractional Chern insulators in topological flat bands with Chern number $|C|=2$. Properties including the quasihole size, charge, and braiding statistics are evaluated. For the Halperin $(221)$ model state, we observe isotropic quasiholes with a clear internal structure, and obtain the quasihole charge and statistics matching the theoretical values. Interestingly, we also extract the same quasihole size, charge, and braiding statistics for the continuum model states of $|C|=2$ fractional Chern insulators, although the latter possess a "color-entangled" nature that does not exist in ordinary two-component Halperin states. We also consider two real lattice models with a band having $|C|=2$. There, we find that a quasihole can exhibit much stronger oscillations of the density profile, while having the same charge and statistics as those in the continuum models.

cond-mat.str-el↗

arXiv2018

Wigner crystallization in topological flat bands

We study the Wigner crystallization on partially filled topological flat bands. We identify the Wigner crystals by analyzing the cartesian and angular Fourier transform of the pair correlation density of the many-body ground state obtained using exact diagonalization. The crystallization strength measured by the magnitude of the Fourier peaks, increases with decreasing particle density. The shape of the resulting Wigner crystals is determined by the boundary conditions of the chosen plaquette and to a large extent independent on the underlying lattice, including its topology, and follows the behavior of classical point particles.

cond-mat.str-el↗

arXiv2018

Interband excitations in the 1D limit of two-band fractional Chern insulators

We investigate the stability of the one-dimensional limit of $ν=1/3$ Laughlin-like fractional Chern insulator with respect to the interband interaction. We propose a construction for the excitations in the infinite-interaction case and show that the energy gap remains finite in the thermodynamic limit. Next, by means of exact diagonalization and Density Matrix Renormalization Group approaches, we consider deviations from ideal dimerization and show that they reduce the stability of the FCI-like states. Finally, to show that our approach is not restricted to one model, we identify the dimer structure behind the thin-torus limit of other system -- the checkerboard lattice.

cond-mat.str-el↗

arXiv2015

Fractional Chern Insulator phase at the transition between checkerboard and Lieb lattice

The stability of $ν=1/3$ Fractional Chern Insulator (FCI) phase is analysed on the example of checkerboard lattice undergoing a transition into Lieb lattice. The transition is performed by the addition of a second sublattice, whose coupling to the checkerboard sites is controlled by sublattice staggered potential. We investigate the influence of these sites on the many body energy gap between three lowest energy states and the fourth state. We consider cases with different complex phases acquired in hopping and a model with a flattened topologically nontrivial band. We find that an interaction with the additional sites either open the single-particle gap or enlarge the existing one, which translates into similar effect on the many-particle gap. Evidences of FCI phase for a region in a parameter space with larger energy gap are shown by looking at momenta of the three-fold degenerate ground state, spectral flow, and quasihole excitation spectrum.

cond-mat.str-el↗