arXiv subjects

Oliwier Urbański

Publications and source records attributed to Oliwier Urbański.

5 recordsLinked to original sources

arXiv2026

Standard basis operator method for ground-state and temperature properties of single and two-component Bose-Hubbard model

We formulate an improved standard basis operator (SBO) method for the single and two-component Bose-Hubbard model in three dimensions. In the first case, nonzero temperature predictions are qualitatively and quantitatively enhanced by taking into account necessary number of on-site states, not just three as in previous works. Performance of the final numerical calculations is also improved by asymptotic analysis of the self-consistent equations near the critical line. Obtained results are compared with Monte-Carlo, tensor networks, Quantum Rotor Approach and experimental data. In the two-component case, SBO generalizes rather poorly, being able to account for intra-species thermal and quantum fluctuations, but not the inter-species ones. Deeper reasons for this situation are discussed. Still however, non-trivial deformation of the phase diagrams is predicted, together with first-order phase transitions steered by the changes in chemical potential.

cond-mat.quant-gas↗

arXiv2026

Resolving problems with the continuum limit in coherent-state path integrals

The paper solves the problem of continuum limit in bosonic thermal coherent-state path integrals. For this purpose, exact discrete versions of the path integral are constructed for three different orderings of the Hamiltonian: normal, anti-normal and symmetric (Weyl order). Subsequently, their different continuum versions are checked on the harmonic oscillator, to choose the symmetric ordering as a possibly correct choice for all polynomial Hamiltonians. Spotted mathematical subtleties in the simple case serve as a clue to the general solution. Finally, a general justification for the symmetric order is provided by deriving the continuum path integral starting from the exact discrete case using a renormalization procedure in the imaginary time frequency domain. While the role of Weyl order has already been found, the paper provides the missing proof of its suitability for every polynomial Hamiltonian and simplifies the previously established construction by referring only to creation and annihilation operators (without position and momentum operators).

quant-ph↗

arXiv2026

Quantum phase transition in transverse-field Ising model on Sierpiński gasket lattice

We investigate the quantum phase transition in the transverse-field Ising model on the Sierpiński gasket using finite-size scaling (FSS) and numerical renormalization group (NRG). Since next generations of the fractal lattice contain exponentially more spins, which in turn increase exponentially the Hilbert space dimension, we challenge and prove usefulness of small systems in FSS. We identified a quantum critical point at $λ_c \approx 2.63 - 2.93$, with critical exponents $ ν\approx 0.64 - 0.71, β\approx 0.30, γ\approx 1.67$ and $z \approx 1.33$. The numerical renormalization group method produced results consistent with finite-size scaling approach ($λ_c = 2.766$$, β= 0.316$), supporting our findings. Compared to the values reported so far in the literature, critical field is in a strong disagreement, while exponents are generally similar excluding $β$ and $γ$. However, it should be noted, that the lattice investigated in previous works is different from ours, while the latter is in our opinion the standard Sierpiński gasket.

cond-mat.stat-mech↗

arXiv2025

Exploring the variational method for thermodynamic models

This work explores the possibilities of the Gibbs-Bogoliubov-Feynman variational method, aiming at finding room for designing various drawing schemes. For example, mean-field approximation can be viewed as a result of using site-independent drawing in the variational method. In subsequent sections, progressively complex drawing procedures are presented, starting from site-independent drawing in the $k$-space. In the next, each site in the real-space is again drawn independently, which is followed by an adjustable linear transformation $T$. Both approaches are presented on the discrete Ginzburg-Landau model. Subsequently, a percolation-based procedure for the Ising model is developed. It shows a general way of handling multi-stage drawing schemes. Critical inverse temperatures are obtained in two and three dimensions with a few percent discrepancy from exact values. Finally, it is shown that results in the style of the real-space renormalization group can be achieved by suitable fractal-like drawing. This facilitates a new straight-forward approach to establishing the renormalization transformation, but primarily provides a new view on the method. While the first two approaches are capable of capturing long-range correlations, they are not able to reproduce the critical behavior accurately. The main findings of the paper are developing the method of handling intricate drawing procedures and identifying the need of fractality in these schemes to grasp the critical behavior.

cond-mat.stat-mech↗

arXiv2025

An infinite grid of mesoscopic resistors: investigation and visualization of ballistic conduction

A square lattice of mesoscopic resistors is considered. Each bond is modeled as a narrow waveguide, while junctions are sources of elastic scattering given by a scattering matrix \mathbf{S}. Symmetry and unitarity constraints are used in a detailed way to simplify all possible matrices \mathbf{S}. Energetic band structure of the system is determined and visualized for exemplary parameters. Conductance between external electrodes attached to two arbitrary nodes is given by the Landauer formula. Thus the transmittance between the electrodes is calculated. The rest of the paper is devoted to studying wave function patterns arising from an electron injected through one electrode into the system. It is observed that depending on its energy both dull and localized or intricate and expansive patterns occur. It is justified mathematically that fitting electron energy into an energy band can be associated with emergence of complex patterns. Finally, possible experimental realizations of the considered model are briefly mentioned.

cond-mat.mes-hall↗