arXiv subjects

Matej Hrmo

Publications and source records attributed to Matej Hrmo.

4 recordsLinked to original sources

arXiv2026

Numerical Study of Scalar Field Theory on the Fuzzy Onion

We study the behaviour of the scalar field theory on the fuzzy onion model -- a three-dimensional matrix model consisting of concentric fuzzy spheres of gradually increasing radii. We use a numerical method of Hamiltonian Monte Carlo simulations to study the phase structure of this theory. We identify the field phases, investigate and describe a phenomenon of dynamical phase transitions and attempt to reconstruct phase transition lines. We compare the results with the well-studied phase structure of the fuzzy sphere. Finally, we identify two boundaries on the phase transitions of the theory, a uniform phase boundary and a critical boundary between the disordered and non-uniform phase.

hep-th↗

arXiv2026

Eigenvalue-cluster Algorithm for Matrix Monte Carlo

Various physical models can be expressed in terms of matrices. A valuable tool for analysing matrix models is numerical simulations, often the Metropolis algorithm with various improvements. The downside of this approach is that the simulation may become stuck in a vacuous state, and probing the relevant parts of the configuration space might be difficult. Here, we propose an algorithm that moves around a cluster of eigenvalues and show that it converges to the true vacuum state.

hep-lat↗

arXiv2025

Hydrogen Atom in a Fuzzy Spherical Cavity

The fuzzy onion model formed by connecting a set of concentric fuzzy spheres of increasing radius is motivated by studies of quantum space but can also be used to study standard physics. The main feature of the model is that functions in three-dimensional space -- like scalar fields or wavefunctions -- are expressed in terms of Hermitian matrices of a certain structure. Relevant equations are then matrix equations, and some problems, such as searching for the energy spectrum for fixed quantum numbers $(l,m)$, can be expressed as an eigenvalue problem. We show how this simple approach can reproduce the results of other studies analyzing the hydrogen atom in a spherical cavity. We also test the effect of the short-distance quantum structure of the space on these solutions -- not looking for the phenomenological consequences, as the scale of quantum space is many orders below the order of the Bohr radius, but to understand the effect of quantum space in general. We observe a set of solutions without a classical counterpart which have been suggested also in a former theoretical study.

hep-th↗

arXiv2024

The Fuzzy Onion: An Initial Study

In our previous contribution, we introduced a matrix formulation of a three-dimensional quantum space named the fuzzy onion. The novel part of the construction is the radial derivative term, which has been defined to recover the correct continuum limit. Here, we describe a numerical simulation of the scalar field theory in this space and test some physical properties of the model with emphasis on the interaction between neighbouring layers.

hep-th↗