Lattice Gauge Theory group

CUDA Research Center 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. Since 2011 we are a CUDA Research Center.

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 {at} bodri {dot} elte {dot} hu or Daniel Nogradi at nogradi {at} bodri {dot} elte {dot} hu.

Our activities are funded by the Lendulet grant of the Hungarian Academy of Sciences and by the OTKA-NF-104034 grant of OTKA.

We are also grateful to our past funding agencies, the EU Framework Programme 7 grant (FP7/2007-2013)/ERC No 208740.


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 of the Department of Theoretical Physics

Location: 2nd floor, 2.54, Novobatzky room

Time: Wednesdays at 14:15

  • 10 September 2014, Mate Lencses (Eotvos University, Hungary)

    Excited state TBA and renormalized TCSA in the scaling Potts model slides

    We consider the field theory describing the scaling limit of the Potts quantum spin chain using a combination of two approaches. The first is the renormalized truncated conformal space approach (TCSA), while the second one is a new thermodynamic Bethe Ansatz (TBA) system for the excited state spectrum in finite volume. For the TCSA we investigate and clarify several aspects of the renormalization procedure and counter term construction. The TBA system is first verified by comparing its ultraviolet limit to conformal field theory and the infrared limit to exact S-matrix predictions. We then show that the TBA and the renormalized TCSA match each other to a very high precision for a large range of the volume parameter, providing both a further verification of the TBA system and a demonstration of the efficiency of the TCSA renormalization procedure. We also discuss the lessons learned from our results concerning recent developments regarding the low-energy scattering of quasi-particles in the quantum Potts spin chain. See arXiv:1405.3157

  • 17 September 2014, Marton Kormos (BME, Hungary)

    Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble slides

    The topic of thermalization of isolated quantum systems has enjoyed a lot of attention lately, partially due to the fast evolving experimental techniques in cold atom systems. Until recently, it was generally accepted that even completely isolated many-body systems self-thermalize to a certain extent: their evolution from a non-equilibrium initial state leads to a local thermal equilibrium (Gibbs ensemble) or to the Generalized Gibbs Ensemble (GGE) for integrable systems that have extra conserved quantities. We studied the non-equilibrium time evolution of the integrable spin-1/2 anisotropic Heisenberg (XXZ) spin chain, and we found that various short-ranged spin correlators in the long-time limit deviate significantly from predictions based on the GGE hypothesis. By computing the asymptotic spin correlators within the recently proposed quench action formalism, however, we find excellent agreement with the numerical data. We therefore conclude that the GGE cannot give a complete description even of local observables. This surprising result reopens the quest for the correct statistical description of the equilibrium state of integrable systems.

  • 24 September 2014, Attila Pasztor (Eotvos University, Hungary)

    Heavy quarkonium at finite temperature from 2+1 flavour lattice QCD slides

    Heavy quarkonium states are of great interest as a possible thermometer of hot QCD matter. For this idea to work, the determination of the dissociation temperatures of the different states is necessary. In this talk I will review some recent results from lattice QCD with 2+1 dynamical quarks that gives input to this long-standing problem. In the first part of the talk I will discuss the direct Maximum Entropy determination of spectral functions and to how much extent the lattice data depend on the heavy quark diffusion coefficient. In the the second part I will present continuum results on the static quark-antiquark pair free energies and the electric and magnetic screening masses in the QGP.

  • 1 October 2014, Guido Franchetti (Heriot-Watt University, UK)

    Geometric models of matter slides

    Geometric models of matter is a framework introduced by Atiyah, Manton and Schroers with the aim of modelling particles by means of 4-dimensional Riemannian manifolds. In this talk I will review the original proposal as well as more recent work about ALF gravitational instantons as models for multi-particle systems. Harmonic forms on these spaces have interesting properties which will be also discussed.

  • 8 October 2014, Gergo Zarand (BME, Hungary)

    Mott skyrmions: stabilizing the false vacuum slides

    Topological excitations keep fascinating physicists since many decades. While individual vortices and solitons emerge and have been observed in many areas of physics, their most intriguing higher dimensional topological relatives, skyrmions and magnetic monopoles remained mostly elusive. Here we propose that loading a three-component nematic superfluid such as 23Na into a deep optical lattice and thereby creating an insulating core, one can create topologically stable skyrmion textures and investigate their properties in detail. We show furthermore that the spectrum of the excitations of the superfluid and their quantum numbers change dramatically in the presence of the skyrmion, and they reflect the presence of a trapped monopole, as imposed by the skyrmion's topology. Signatures of the presence of the skyrmion in time of flight experiments as well as experimental protocols to create it shall also be discussed.

  • 15 October 2014, Istvan Nandori (ATOMKI, Hungary)

    Renormalization scheme-dependence in the FRG Method slides

    The Functional Renormalization Group (FRG) method has been constructed to perform the renormalization non-perturbatively and it has been successfully applied in many cases over the last four decades. The modern form of FRG is the Wetterich equation which can be related to the previously introduced Wegner-Houghton and Polchinski equations by the appropriate choice of the so called regulator function, i.e. the renormalization scheme. FRG equations are integro-differential equations for functionals thus their solutions require approximations. However, the approximated FRG equations depend on the choice of the regulator function thus the predictions for physical quantities could become scheme-dependent too. I discuss this renormalization scheme-dependence of the FRG method in the context of the so called compactly supported smooth (CSS) regulator function introduced recently.

  • 22 October 2014, Gabor Somogyi (CERN, Switzerland)

    Colorful NNLO -- Higher order QCD corrections via local subtraction slides

    At the LHC very high energy proton-proton collisions are measured at a level of precision which demands that the theory predictions be computed at higher orders in perturbation theory. In recent years the precision frontier for QCD calculations has moved beyond next-to-leading order and today fully differential results at next-to-next-to-leading order accuracy are available for a handful of processes. One serious bottleneck which hampers the straightforward evaluation of cross sections at higher perturbative orders is the presence of infrared singularities in intermediate stages of the computation. One possible way of dealing consistently with infrared singularities is through a so-called subtraction scheme. In this talk I will describe the Colorful NNLO algorithm, a completely local subtraction scheme for fully differential predicitions at NNLO in QCD. I will give an overview of the main conceptual issues that need to be addressed as well as present some technical aspects and a first application of the method.

  • 29 October 2014, Janos Polonyi (University of Strasbourg, France)

    Classical and quantum effective theories slides

    A generalization of the action principle of classical mechanics, motivated by the Closed Time Path (CTP) scheme of quantum field theory, is presented to deal with initial condition problems and dissipative forces. The similarities of the classical and the quantum cases are underlined. In particular, effective interactions which describe classical dissipative forces represent the system-environment entanglement. The relation between the traditional effective theories and their CTP extension is briefly discussed and few qualitative examples are mentioned.

  • 5 November 2014, Zoltan Bajnok (Wigner Center, Hungary)

    Integrability for 2 and 3pt functions in AdS5/CFT4 slides

    In my talk I review the strategy of the integrable bootstrap method. I explain how it determines the spectrum of string states on AdS5 x S5, i.e. the scaling dimensions of single trace operators in planar N=4 SYM. I emphasize its non-perturbative nature and that it starts at infinite volume and systematically calculates the finite size corrections based on the infinite volume scattering data. In the second part of the talk I outline a similar program to determine the 3pt functions via the bootstrap method.

  • 12 November 2014, Gergely Marko (Eotvos University, Hungary)

    Bose-Einstein condensation and Silver Blaze in the 2-loop Phi-derivable approximation slides

    We numerically study the chemical potential-temperature phase diagram of the O(2) model within the 2-loop truncation of the Phi-derivable formalism. We find that different parameters allow for a phase transition of either SSB or BEC type. In the BEC case we observe the Silver Blaze phenomenon, which we understand and generalize using analyticity arguments. We compare our results both with the Hartree-Fock approximation and with lattice simulations. We discuss the loss of solution strongly connected with the Goldstone-theorem.

  • 19 November 2014, Gabor Etesi (BME, Hungary)

    Gravity as a four dimensional algebraic quantum field theory slides

    Based on an indefinite unitary representation of the diffeomorphism group of an oriented 4-manifold an algebraic quantum field theory formulation of gravity is exhibited. More precisely the representation space is a Krein space therefore as a vector space it admits a family of direct sum decompositions into orthogonal pairs of maximal definite Hilbert subspaces coming from the Krein space structure. It is observed that the C*-algebra of bounded linear operators associated to this representation space contains algebraic curvature tensors. Classical vacuum gravitational fields i.e., Einstein manifolds correspond to quantum observables obeying at least one of the above decompositions of the space. In this way classical general relativity exactly in 4 dimensions naturally embeds into an algebraic quantum field theory whose net of local C*-algebras is generated by local algebraic curvature tensors and vector fields. This theory is constructed out of the structures provided by an oriented 4-manifold only hence possesses a diffeomorphism group symmetry. Motivated by the Gelfand--Naimark--Segal construction and the Dougan--Mason construction of quasi-local energy-momentum we construct certain representations of the limiting global C*-algebra what we call the ``positive mass representations''. Finally we observe that the bunch of these representations give rise to a 2 dimensional conformal field theory in the sense of G. Segal.

  • 26 November 2014, Janos Balog (Wigner Center, Hungary)

    Walking in a 3-dimensional scalar toy model slides

    The O(N) scalar field theory in the large N limit is an ideal toy model exhibiting "walking" behavior, expected in some SU(N) gauge theories with a large number of fermion flavors. We study the model using lattice regularization and show that when the ratio of the particle mass to an effective 4-point coupling (with dimension mass) is small, the beta function associated to the running 4-point coupling is ?walking?. We show the robustness of the walking phenomenon by showing that it can also be observed by studying physical observables such as the scattering phase shifts and the mass gap in finite volume.

  • 17 December 2014, Kim Splittorff (Niels Bohr Institute, Copenhagen, Denmark)

    Complex Langevin in QCD with chemical potential larger than half the pion mass

    The complexification of gauge fields in the complex Langevin approach to QCD at non zero chemical potential drastically affects the Dirac spectrum. In particular, we show that the eigenvalues the Dirac operator in complex Langevin simulations of QCD at non-zero chemical potential must accumulate at the origin in order to support spontaneous breaking of chiral symmetry. This mechanism is exemplified through application of the complex Langevin method in chiral random matrix theory.

For students

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

Please contact Sandor: katz {at} bodri {dot} elte {dot} hu
or Daniel: nogradi {at} bodri {dot} elte {dot} hu
in case you are interested.

Current topics include:

  • QCD thermodynamics
  • SU(N) gauge theory with topological lattice action
  • O(3) non-linear sigma model with topological term
  • Beyond Standard Model - technicolor


Sandor Katz


2001 PhD - Eotvos University, Hungary

2001-2003 postdoc - DESY, Hamburg, Germany

2003-2005 postdoc - University of Wuppertal, Germany

2006-2012 assistant professor - Eotvos University, Hungary

2012- professor - Eotvos University, Hungary

katz {at} bodri {dot} elte {dot} hu

Santanu Mondal


2013 PhD - University of Calcutta, India

2013 postdoc - Eotvos University, Hungary

santanu {at} bodri {dot} elte {dot} hu







Daniel Nogradi

assistant professor

2005 PhD - University of Leiden, the Netherlands

2005-2007 postdoc - University of Wuppertal, Germany

2007-2009 postdoc - UCSD, USA

2009-2011 senior research fellow - Eotvos University, Budapest

2011 assistant professor - Eotvos University, Budapest

nogradi {at} bodri {dot} elte {dot} hu

Attila Pasztor

PhD student

2010 - Eotvos University, Hungary

apasztor {at} bodri {dot} elte {dot} hu








Ferenc Pittler


2013 PhD - University of Pecs, Hungary

2013- postdoc - Eotvos University, Budapest

pittler {at} bodri {dot} elte {dot} hu


Andras Saradi

MSc student

2014 - Eotvos University, Hungary







Csaba Torok

MSc student

2014 - Eotvos University, Hungary


Norbert Trombitas

PhD student

2010 - Eotvos University, Hungary

trombitas {at} ludens {dot} elte {dot} hu



Lorinc Szikszai

BSc student

2014 - Eotvos University, Hungary



Former members

Gergely Endrodi

2009 PhD - Eotvos University, Hungary

2010 postdoc - University of Regensburg, Germany

endrodi {at} general {dot} elte {dot} hu

Tamas Kovacs

1996 PhD - UCLA, USA

1996-1998 postdoc - University of Colorado, Boulder, USA

1998-2000 postdoc - University of Leiden, the Netherlands

2000-2002 postdoc - DESY, Zeuthen, Germany

2002-2011 professor - University of Pecs, Hungary

2011- senior researcher - ATOMKI, Debrecen, Hungary

kgt {at} fizika {dot} ttk {dot} pte {dot} hu

Balint Toth

2005-2006 research assistant - University of Wuppertal, Germany

2007 assistant lecturer - University of Pecs, Hungary

2010 PhD - Eotvos University, Hungary

2010 postdoc - University of Wuppertal, Germany

tothbalint {at} szofi {dot} elte {dot} hu



Recent papers


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 primary resource is a 128 node cluster with two NVIDIA GTX 275 cards in each node, hosted in Budapest. There is also a 60 node cluster with one NVIDIA GTX 8800 card per node.

In addition we also have access to the Juropa cluster and the BlueGene/P installation in Forschungszentrum Juelich, Germany.

Our collaboriation with the University of Wuppertal, Germany also allows us to use several PC and GPU clusters there.

In case you are interested you can see a map of GPU cluster installations throughout the world dedicated to Lattice Gauge Theory.

For visitors

You will most likely stay at the Peregrinus hotel in the downtown area of Pest.

The simplest way to get to/from your hotel from/to the airport is by taxi. Ask for the fixed rate which should be around 20-22 euros.

Our department is on the Buda side of the Danube very close to the Petofi Bridge and it is about a 30-35 minutes walk from the hotel:

View Larger Map

You exit your hotel, walk past the Great Market Hall (definitely worth a closer look if you have about half an hour or an hour!) and the Corvinus University, cross the Danube on the Szabadsag Bridge and walk South. You will pass the Budapest University of Technology and the Petofi Bridge and our building will be a redish seven-story building on the right. The Department of Theoretical Physics is on the first floor on the Danube facing side of the building: