We are the lattice gauge theory group at the Eotvos University in Budapest, part of the Department of Theoretical Physics at the Faculty of Science.

Currently there are nine members and we are seeking new ones. Positions are available for PhD students and postdocs for 2 - 4 years appointments. If you are interested please email Sandor Katz at katz@bodri.elte.hu or Daniel Nogradi at nogradi@bodri.elte.hu.

Our activities are and were funded by various funding agencies for which we are grateful, these include the Lendulet grant of the Hungarian Academy of Sciences, the OTKA-NF-104034 grant of OTKA and the EU Framework Programme 7 grant (FP7/2007-2013)/ERC No 208740.

Timetable of department common room.

Our primary interests are:

• Chiral symmetry restoration and deconfinement in QCD with Wilson fermions
• Finite chemical potential
• QCD hadron spectrum
• Eigenvalue distributions of the overlap Dirac operator
• Strongly interacting Higgs sector - strong dynamics
• Conformal gauge theories

Weekly seminars at the Department of Theoretical Physics

Location: 3rd floor, 3.67, Bekesy room, 1117 Budapest, Pazmany Peter setany 1/a

If you'd like to receive seminar email announcements please write to nogradi@bodri.elte.hu

Time: Tuesdays at 14:15

See the archive for seminars since 2014.

• 17 February 2025, Karoly Seller (Eotvos) slides

  Primordial magnetic fields

  There is evidence today that galactic voids are permeated by a largely homogeneous and extremely weak magnetic field. While magnetic fields are not uncommon in the Universe, their presence in the low-density voids is somewhat perplexing. There are competing theories for the origin of these fields: they may be of galactic origins or entirely primordial. In this talk, we will begin by looking at how the combined magnetic field of galaxies is unlikely to explain the observed spectra. Then we turn to the alternative, primordial explanation, and after a short review of the relevant details (in particular of electroweak topological defects), we show how a primordial magnetic field spectrum may be generated through a simple lattice model and derive analytic properties. We end by commenting on the evolution of the primordial fields through the early Universe, and their expected form today.

• 24 February 2026, David Pesznyak (Eotvos) slides

  Is it worth to find Lefschetz thimbles?

  The fermionic sign problem severely limits Monte Carlo simulations of systems with complex actions. Contour-deformation methods in complexified field space (such as Lefschetz thimbles, holomorphic flow or sign optimization) offer systematic ways to reduce phase fluctuations, but their optimal use is still under active study. In this talk, I analyze a set of exactly solvable one-dimensional integrals arising as one-site limits of Hubbard-, Gross-Neveu-, Thirring-, and Chern-Simons-like models. These toy models allow for a detailed comparison of Lefschetz thimbles, finite-time holomorphic flow contours, and numerically optimized continuous contours. We find that the convergence toward thimble results under holomorphic flow is generically non-monotonic, with an optimal finite flow time where the sign problem is weaker than on the thimbles themselves. Moreover, numerically optimized contours consistently outperform both thimbles and flowed contours, indicating that greater flexibility in contour choice can substantially improve sign-problem mitigation. The talk is based on: Phys.Rev.D 113 (2026) 1, 014506.

• 3 March 2026, Lorenz von Smekal (Giessen) slides

  Quark numbers and percolation of electric center fluxes in QCD

  We construct a gauge-invariant measure for deconfinement based on the percolation of electric center fluxes in full lattice QCD, and predict an associated geometric phase transition without a thermodynamic singularity. Our percolation measure agrees with the Z_N center-symmetry transition in the pure SU(N) gauge theory. In the corresponding Z_N-spin models, this percolation phase transition persists into the crossover region with explicit symmetry breaking along the Kertesz line, and in fact reduces to pure bond percolation for asymptotically large external fields. We therefore also predict a percolation phase transition for QCD with physical quarks, and perhaps even in the chiral limit, thus always yielding a clear distinction between confined and deconfined phases. The gauge invariance of the spanning probability as the order parameter for this geometric phase transition ensures that physical states remain colorless at all temperatures and densities. We discuss the strong and weak-coupling limits, and explicitly illustrate the mechanism in the flux-tube model representation of the effective theory for QCD at strong coupling with heavy quarks.

• 10 March 2026, Attila Pasztor (Eotvos) slides

  Lattice QCD at non-zero baryon density: a mini-review

  I will review recent lattice QCD calculations of the phase diagram of strongly interacting matter at non-zero baryochemical potential and temperature. I will focus on the crossover line in the chemical-potential -- temperature plane and on the search for the QCD critical endpoint. I will discuss how different observables can be used to map the phase diagram, including the equation of state, quantities related to chiral symmetry restoration and deconfinement, and grand canonical fluctuations of the baryon number and strangeness.

• 17 March 2026, Yunxin Ye (University of Jena) slides

  Quantum Field Theory of relativistic Luttinger fermions

  Inspired by the Luttinger fermion from condensed matter system, we generalize it to a relativistic system as a new ingredient for the construction of fundamental quantum field theory. As a higher derivative theory, Luttinger fermions exhibit canonical scaling dimension that is different from Dirac fermions, which allows the possibility to write down perturbative renormalizable QFT with fermionic four point interaction. We will then discuss the possibility of including different kinds of mass term and the analytic structure of the corresponding propagators. Some of the mass terms offer a stable quantum field theory. We then discuss the further implications for these stable models, such as the applicability of spin-statistics theorem, CPT theorem, and discuss the mean field effective potential and axial anomaly.

• 24 March 2026, Timea Vitos (Eotvos, Uppsala University) slides

  How far have we gone and can we go with machine learning in particle physics? -- Part 2

  This talk is the direct follow-up to a previous seminar. Undoubtedly, the topic that has seen the greatest increase in references and discussions today, both in science and outside of it, is the use and development of artificial intelligence. High-energy physics, historically one of the frontiers of technology, is also keeping up with this ever-growing trend by using machine learning in various approaches. In this talk, I discuss the use of machine learning in two specific areas of particle physics phenomenology. Firstly, I present our proposed efficient event generation based on colour expansion, which can be aided by machine learning in the reweighting step to obtain faster evaluation times. Secondly, I discuss the phase-space sampling of kinematic variables, which outperforms conventional phase-space mappings for most processes.

• 31 March 2026, Balazs Pozsgay (Eotvos)

  The (potential) use of LLM's in mathematical physics

  In this (informal) seminar I would like to share our experiences of working with the currently available Pro version of LLM's. Recently LLM's jumped the threshold of being actually useful for problem solving in mathematics, and we expect that similar progress will happen also in physics. In collaboration with Istvan Vona we wanted to find out what an LLM can do as a research assistant. We found that the current technology is at the level of a good PhD student or early postdoc, in problem solving, coding, and manuscript preparation. We obtained scientific results that are worth publishing, regardless of whether or not they are calculated by the AI. I will share our experiences, and discuss the opportunities and problems that this tremendous progress brings about.

• 21 April 2026, Ors Legeza (Wigner) slides

  Recent advances in tensor network state methods on high performance computing infrastructures: a journey from mathematical aspects towards industrial perspectives

  In light of major developments over the past decades in both quantum computing and simulations on classical hardware, it is a serious challenge to identify a real-world problem where quantum advantage is expected to appear. In this contribution, we present a brief overview of recent advances in tensor network state (TNS) methods that have the potential to broaden their scope of application radically for strongly correlated quantum many body systems. We show state-of-the-art results obtained for two dimensional quantum lattice systems via a joint optimization on the matrix product state (MPS) and Grassmann manifolds. Novel mathematical models for hybrid multiNode-multiGPU parallelization on high-performance computing (HPC) infrastructures will be discussed together with scaling analysis on NVIDIA DGX A100 and DXG H100 platforms reaching quarter petaflops performance on a single node. We also introduce mixed precision ab initio TNS methods by utilizing the Ozaki scheme for emulating FP64 arithmetic through the use of fixed-point compute resources. Benchmark results obtained on the NVIDIA Blackwell platform via CAS-SCF based orbital optimizations for unprecedented CAS sizes of up to 89 electrons in 102 orbitals [CAS(89,102)] for the Fe_5S_{12}H_5^{-4} molecular system comprising twenty five open shell orbitals in its sextet ground state and an active spaces size of 331 electrons in 451 orbitals will be presented as a new classical benchmark for quantum computation. Finally, we showcase recent results obtained on IBM superconducting quantum processor with up to 144 qubits, together with classical validation, using TNS-based novel Basis Update Galerkin (BUG) method, establishing agreement between quantum and classical approaches. We close our presentation discussing future possibilities via utilization of NVL72 and Blackwell technology in tree-like TNS calculations pushing performance towards the exascale limit and opening new research directions in material sciences and beyond.

• 28 April 2026, Kornel Kapas (Wigner) slides

  Real-time dynamics with tensor networks: An overview and the quantum chip benchmark

  Real-time quantum dynamics is one of the central challenges in quantum many-body physics. Tensor-network methods provide a powerful classical framework for this problem, especially when the relevant dynamics can be captured within a moderately entangled variational manifold. In this talk, I will give an overview of matrix product state based time-evolution algorithms, starting from a brief review of MPS representations of quantum states and MPO representations of Hamiltonians. I will then compare three important classes of time evolution algorithms: TEBD, TDVP, and the recently developed Basis Update and Galerkin method.

  I will then discuss a recent application to real-time dynamics in a (2+1)-dimensional Z2-Higgs gauge theory, where tensor-network simulations using BUG were used to benchmark superconducting quantum hardware and interpret string-like dynamics. The goal was to show how modern tensor-network time evolution is not only a numerical tool, but also an essential benchmark and diagnostic framework for quantum simulators.

  J. Cobos, J. Fraxanet, C. Benito, F. di Marcantonio, P. Rivero, K. Kapas, M. A. Werner, O. Legeza, A. Bermudez, and E. Rico Real-Time Dynamics in a (2+1)-D Gauge Theory: The Stringy Nature on a Superconducting Quantum Simulator, arXiv:2507.08088 [quant-ph], 2025

• 5 May 2026, Miklos Werner (Wigner) slides

  Symmetry-adapted Matrix Product State simulation of Open Quantum Systems: From Dissipative Front Propagation to KPZ Scaling

  In my talk, I will present recent advances in simulating open quantum systems with non-Abelian symmetries using matrix product operator methods. First, I will introduce a non-Abelian time-evolving block decimation (NA-TEBD) framework for Lindbladian dynamics that exploits arbitrary Abelian and non-Abelian symmetries, enabling highly efficient simulations of strongly correlated open systems. We have demonstrated the method on the one-dimensional SU(2) Hubbard model on a semi-infinite lattice with localized particle loss, revealing ballistic front propagation with a strongly renormalized velocity, hydrodynamic current profiles, and quantum Zeno suppression of transport at large loss rates [1]. This dissipative model has a rich information-theoretic structure. In the strongly interacting regime, two-site mutual information and operator entanglement entropy display two distinct propagating fronts with superimposed quantum interference fringes. While a classical reversible cellular automaton captures the slow, classical part of the dynamics, it fails to describe a rapidly propagating quantum information jet that resembles coherent free-particle propagation, exponentially damped by spin correlations in the many-body background[2]. Finally, I will also briefly discuss two further results connecting non-Abelian symmetries to universal scaling phenomena. We have found numerical evidence for Kardar-Parisi-Zhang (KPZ) scaling in both charge and spin sectors of the half-filled Hubbard model, confirming the link between non-Abelian symmetry, integrability, and KPZ universality [3]. We have also introduced an efficient numerical method for computing quantum generating functions and full counting statistics in one-dimensional systems at high temperature, reaching timescales beyond current state-of-the-art simulations, with results that challenge the conjectured KPZ universality in isotropic integrable spin chains [4].

  [1] C. P. Moca, M. A. Werner, O. Legeza, T. Prosen, M. Kormos, and G. Zarand, Physical Review B 105, 195144 (2022).

  [2] P. Penc, C. P. Moca, O. Legeza, T. Prosen, G. Zarand, and M. A. Werner, Physical Review Letters 133, 190403 (2024).

  [3] C. P. Moca, M. A. Werner, A. Valli, T. Prosen, and G. Zarand, Physical Review B 108, 235139 (2023).

  [4] A. Valli, C. P. Moca, M. A. Werner, M. Kormos, Z. Krajnik, T. Prosen, and G. Zarand, Physical Review Letters 135, 100401 (2025).

• 12 May 2026, Sandor Katz (Eotvos) slides

  Lattice QCD on the 16-cell honeycomb

  We formulate QCD discretized on the four dimensional 16-cell honeycomb. The advantage is a higher degree of rotational symmetry as compared to a traditional cubic lattice leading to much smaller cut-off effects. We demonstrate in quenched QCD, through both gluonic and fermionic ob- servables, that the scaling properties are indeed superior to the cubic lattice and much larger lattice spacings are sufficient for controlled continuum extrapolations. Chiral and topological properties also show remarkable improvement.

Our group offers BSc/MSc diploma, PhD and TDK topics in Lattice Field Theory.

Please contact Sandor: katz@bodri.elte.hu or Daniel: nogradi@bodri.elte.hu in case you are interested.

Current topics include:

• QCD thermodynamics
• 2 and 4 dimensional CFT
• Beyond Standard Model

Since it is tricky to locate all papers by a large number of people whose names are not unique on inspire, you can try various search queries:

• Papers by Sandor Katz and Zoltan Fodor
• Papers by Sandor Katz and Gergely Endrodi
• Papers by Sandor Katz and Matteo Giordano
• Papers by Tamas Kovacs
• Papers by Daniel Nogradi

Our group has access to a number of high performance computer installations in Europe and also maintains several PC and GPU clusters on site in Budapest.

Our department is on the Buda side of the Danube very close to the Petofi Bridge, the address is Budapest 1117, Pazmany Peter setany 1/A:

The Department of Theoretical Physics is on the sixth floor opposite the Danube facing side of the building: