Kurt Langfeld

• Professor, Dr habil, PhD (TUM)
• Chair at University of Leeds

Wang-Landau simulations offer the possibility to integrate explicitly over a collective coordinate and stochastically over the remainder of configuration space. We propose to choose the so-called “slow mode,” which is responsible for large autocorrelation times and thus critical slowing down, for collective integration. We study this proposal for t...

Wang-Landau simulations offer the possibility to integrate explicitly over a collective coordinate and stochastically over the remainder of configuration space. We propose to choose the so-called "slow mode", which is responsible for large autocorrelation times and thus critical slowing down, for collective integration. We study this proposal for t...

The pandemic of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) suggests a novel type of disease spread dynamics. We here study the case where infected agents recover and only develop immunity if they are continuously infected for some time τ . For large τ , the disease model is described by a statistical field theory. Hence, the phase...

We apply the linear logarithmic relaxation (LLR) method, which generalizes the Wang-Landau algorithm to quantum systems with continuous degrees of freedom, to the fermionic Hubbard model with repulsive interactions on the honeycomb lattice. We compute the generalized density of states of the average Hubbard field and devise two reconstruction schem...

The global SARS-CoV-2 pandemic suggests a novel type of disease spread dynamics. WHO states that there is currently no evidence that people who have recovered from COVID-19 and have antibodies are immune from a second infection [WHO]. Conventional mathematical models consider cases for which a recovered individual either becomes susceptible again o...

We apply the Linear Logarithmic Relaxation (LLR) method, which generalizes the Wang-Landau algorithm to quantum systems with continuous degrees of freedom, to the fermionic Hubbard model with repulsive interactions on the honeycomb lattice. We compute the generalized density of states of the average Hubbard field and divise two reconstruction schem...

The virtual source method (VSM) has been developed to simulate water waves based upon the solution of Laplace's equation for the velocity potential integral equations with full nonlinear surface conditions. The basis of the method is the use of specific Green's functions for a rectangular ‘virtual domain’ which is an extension of the physical domai...

Z3 gauge theory with dynamical (bosonic) matter is studied in 4 dimensions with a finite chemical potential. This theory could be viewed as an effective theory describing the centre vortex picture of QCD colour confinement, but it is studied here with local interactions as theory in its own right. It is shown that the sign-problem can be solved by...

The virtual source method (VSM) developed by Langfeld et al., (2016) is based upon the integral equations derived by using Green's identity with Laplace's equation for the velocity potential. These authors presented preliminary results using the method to simulate standing waves. In this paper, we numerically model a non-linear standing wave by usi...

Quantum field theories at finite matter densities generically possess a partition function that is exponentially suppressed with the volume compared to that of the phase quenched analogue. The smallness arises from an almost uniform distribution for the phase of the fermion determinant. Large cancellations upon integration is the origin of a poor s...

Quantum field theories at finite matter densities generically possess a partition function that is exponentially suppressed with the volume compared to that of the phase quenched analogue. The smallness arises from an almost uniform distribution for the phase of the fermion determinant. Large cancellations upon integration is the origin of a poor s...

Heavy-Dense QCD (HDQCD) is a popular theory to investigate the sign problem in quantum field theory. Besides its physical applications, HDQCD is relatively easy to implement numerically: the fermionic degrees of freedom are integrated out, and the fermion determinant factorises into local ones. The theory has a sign problem, the severeness of which...

Although Monte Carlo calculations using Importance Sampling have matured into the most widely employed method for determining first principle results in QCD, they spectacularly fail for theories with a sign problem or for which certain rare configurations play an important role. Non-Markovian Random walks, based upon iterative refinements of the de...

In previous work, it has been shown that the recently proposed LLR method is very efficient at overcoming strong metastabilities that arise near first-order phase transition points. Here we present a systematic study of the performance of the algorithm near (pseudo-)critical points for $q$-state Potts models with $q$ as large as 20, in two and thre...

In previous work, it has been shown that the recently proposed LLR method is very efficient at overcoming strong metastabilities that arise near first-order phase transition points. Here we present a systematic study of the performance of the algorithm near (pseudo-)critical points for $q$-state Potts models with $q$ as large as 20, in two and thre...

QCD at finite densities of heavy quarks is investigated using the density-of-states method. The phase factor expectation value of the quark determinant is calculated to unprecedented precision as a function of the chemical potential. Results are validated using those from a reweighting approach where the latter can produce a significant signal-to-n...

Quantum field theories (QFTs) at finite densities of matter generically involve complex actions. Standard Monte Carlo simulations based upon importance sampling, which have been producing quantitative first principle results in particle physics for almost forty years, cannot be applied in this case. Various strategies to overcome this so-called sig...

During the last 40 years, Monte Carlo calculations based upon Importance Sampling have matured into the most widely employed method for determinig first principle results in QCD. Nevertheless, Importance Sampling leads to spectacular failures in situations in which certain rare configurations play a non-secondary role as it is the case for Yang-Mil...

During the last 40 years, Monte Carlo calculations based upon Importance Sampling have matured into the most widely employed method for determinig first principle results in QCD. Nevertheless, Importance Sampling leads to spectacular failures in situations in which certain rare configurations play a non-secondary role as it is the case for Yang-Mil...

QCD at finite densities of heavy quarks is investigated using the density-of-states method. The phase factor expectation value of the quark determinant is calculated to unprecedented precision as a function of the chemical potential. Results are validated using those from a reweighting approach where the latter can produce a significant signal-to-n...

QCD at finite densities of heavy quarks is investigated using the density-of-states method. The phase factor expectation value of the quark determinant is calculated to unprecedented precision as a function of the chemical potential. Results are validated using those from a reweighting approach where the latter can produce a significant signal-to-n...

Quantum field theories (QFTs) at finite densities of matter generically involve complex actions. Standard Monte-Carlo simulations based upon importance sampling, which have been producing quantitative first principle results in particle physics for almost fourty years, cannot be applied in this case. Various strategies to overcome this so-called Si...

Recently, a novel algorithm for computing the density of states in statistical systems and quantum field theories has been proposed. The same method can be applied to theories at finite density affected by the notorious sign problem, reducing a high-dimensional oscillating integral to a more tractable one-dimensional one. As an example we applied t...

In this paper, we develop the Virtual Source Method for simulation of incompressible and irrotational fluid flows. The method is based upon the integral equations derived by using Green’s identity with Laplace’s equation for the velocity potential. The velocity potential within the fluid domain is completely determined by the potential on a virtual...

In Wang-Landau type algorithms, Monte-Carlo updates are performed with respect to the density of states, which is iteratively refined during simulations. The partition function and thermodynamic observables are then obtained by standard integration. In this work, our recently introduced method in this class (the LLR approach) is analysed and furthe...

In Wang-Landau type algorithms, Monte-Carlo updates are performed with respect to the density of states, which is iteratively refined during simulations. The partition function and thermodynamic observables are then obtained by standard integration. In this work, our recently introduced method in this class (the LLR approach) is analysed and furthe...

Finite density quantum field theories have evaded first principle Monte-Carlo simulations due to the notorious sign-problem. The partition function of such theories appears as the Fourier transform of the generalised density-of-states, which is the probability distribution of the imaginary part of the action. With the advent of Wang-Landau type sim...

We present a novel algorithm to compute the density of states, which is proven to converge to the correct result. The algorithm is very general and can be applied to a wide range of models, in the frameworks of Statistical Mechanics and Lattice Gauge Theory. All the thermal or quantum expectation values can then be obtained by a simple integration...

Recently, a new and efficient algorithm (the LLR method) has been proposed for computing densities of states in statistical systems and gauge theories. In this talk, we explore whether this novel density of states method can be applied to numerical computations of observables in systems for which the action is complex. To this purpose, we introduce...

We develop a first-principle generalised density of state method for studying numerically quantum field theories with a complex action. As a proof of concept, we show that with our approach we can solve numerically the strong sign problem of the $Z_3$ spin model at finite density. Our results are confirmed by standard simulations of the theory dual...

Motivated by the sign problem, we calculate the effective Polyakov line action corresponding to certain SU(3) lattice gauge theories on a ${16^3 \times 6}$ lattice via the "relative weights" method introduced in our previous articles. The calculation is carried out at $\beta=5.6,5.7$ for the pure gauge theory, and at $\beta=5.6$ for the gauge field...

We describe the "relative weights" method used to compute the effective Polyakov line action corresponding to a given lattice gauge theory, and present some results that have been obtained so far. The main motivation is the sign problem, which may be easier to address in the effective theory than in the underlying gauge theory.

The density-of-states method (Phys.Rev.Lett. 109 (2012) 111601) features an exponential error suppression and is not restricted to theories with positive probabilistic weight. It is applied to the SU(2) gauge theory at finite densities of heavy quarks. The key ingredient here is the Polyakov line probability distribution, which is obtained of over...

We extend the density-of-states approach to gauge systems (LLR method) to QCD at finite temperature and density with heavy quarks. The approach features an exponential error suppression and yields the Polyakov loop probability distribution function over a range of more than hundred orders of magnitude. SU(2) gauge theory is considered in the confin...

We calculate the effective Polyakov line action corresponding to SU(2) lattice gauge theory on a 16^3 X 4 lattice via the "relative weights" method. We consider a variety of lattice couplings, ranging from beta=1.2 in the strong-coupling domain, to beta=2.3 at the deconfinement transition, in order to study how the effective action evolves with bet...

The quantum O(2) model in 2+1 dimensions is studied by simulating the 3d O(2) model near criticality. Finite densities are introduced by a non-zero chemical potential mu, and the worm algorithm is used to circumvent the sign problem. The renormalisation is discussed in some detail. We find that the onset value of the chemical potential coincides wi...

We apply the relative weights method (arXiv:1209.5697) to determine the effective Polyakov line action for SU(2) lattice gauge theory in the confined phase, at lattice coupling beta=2.2 and N_t=4 lattice spacings in the time direction. The effective action turns out to be bilinear in the fundamental representation Polyakov line variables, with a ra...

The density of states is calculated for the SU(2), SU(3), and a compact U(1) lattice gauge theories using a modified version of the Wang-Landau algorithm. We find that the density of states of the SU(2) gauge theory can be reliably calculated over a range of 120 000 orders of magnitude for lattice sizes as big as ${20}^{4}$. We demonstrate the pote...

Transitions between centre sectors are related to confinement in pure Yang–Mills theories. We study the impact of these transitions in QCD (quantum chromodynamics) like theories for which the centre symmetry is explicitly broken by the presence of matter. For low temperatures, we provide numerical evidence that centre transitions do occur, with mat...

Centre sector transitions in QCD-like theories with dynamical quark matter are investigated. In the hadronic phase, these transitions still take place in the infinite volume at zero temperature limit despite of the explicit breaking of the centre symmetry by the matter fields. This finding is supported by simulations of the SU(2) Yang-Mills theory...

It is shown that the nonperturbative dynamics of a phase change to the nontrivial phase of λφ4-theory in the early universe can give rise to slow-rollover inflation without recourse to unnaturally small couplings.

The quark condensate which enters the Gell-Mann-Oakes-Renner (GMOR) relation, is investigated in the framework of one-gluon-exchange models. The usual definition of the quark condensate via the trace of the quark propagator produces a logarithmic divergent condensate. In the product of current mass and condensate, this divergence is precisely compe...

Transitions between centre sectors are related to confinement in pure Yang-Mills theories. We study the impact of these transitions in QCD-like theories for which centre symmetry is explicitly broken by the presence of matter. For low temperatures, we provide numerical evidence that centre transitions do occur with matter merely providing a bias to...

While pure Yang-Mills theory feature the centre symmetry, this symmetry is explicitly broken by the presence of dynamical matter. We study the impact of the centre symmetry in such QCD-like theories. In the analytically solvable Schwinger model, centre transitions take place even under extreme conditions, temperature and/or density, and we show tha...

The frustrated Ising model on a two-dimensional lattice with open boundary conditions is revisited. A hidden Z2 gauge symmetry relates models with different frustrations which, however, share the same partition function. By means of a duality transformation, it is shown that the partition function only depends on the distribution of gauge invariant...

We develop a numerical formulation to calculate the classical motion of charges in strong electromagnetic fields, such as those occurring in high-intensity laser beams. By reformulating the dynamics in terms of SL(2,C) matrices representing the Lorentz group, our formulation maintains explicit covariance, in particular the mass-shell condition. Con...

Semi-classical configurations in Yang-Mills theory have been derived from lattice Monte Carlo configurations using a recently proposed constrained cooling technique which is designed to preserve every Polyakov line (at any point in space-time in any direction). Consequently, confinement was found sustained by the ensemble of semi-classical configur...

The infrared structure of SU(2) Yang–Mills theory is studied by means of lattice gauge simulations using a new constrained cooling technique. This method reduces the action while all Polyakov lines on the lattice remain unchanged. In contrast to unconstrained cooling, quark confinement remains intact. A study of the Hessian of the Yang–Mills action...

We study the behavior of the AsqTad quark propagator in Landau gauge on SU(3) Yang-Mills gauge configurations under the removal of center vortices. In SU(2) gauge theory, center vortices have been observed to generate chiral symmetry breaking and support the infrared behavior of the quark propagator. In contrast, we report a weak dependence on the...

Topological configurations, monopoles and vortices, successfully describe quark confinement and the spontaneous breakdown of chiral symmetry. Despite their infinite action, these configurations are relevant due to a subtle cancellation between action and entropy. A natural explanation for this intrinsic fine-tuning is that smooth low action configu...

Strongly-coupled fermionic systems can support a variety of low-energy phenomena, giving rise to collective condensation, symmetry breaking and a rich phase structure. We explore the potential of worldline Monte Carlo methods for analyzing the effective action of fermionic systems at large flavor number Nf, using the Gross-Neveu model as an example...

Yang-Mills theories with a gauge group SU(N_c\=3)and quark matter in the fundamental representation share many properties with the theory of strong interactions, QCD with N_c=3. We show that, for N_c even and in the confinement phase, the gluonic average of the quark determinant is independent of the boundary conditions, periodic or anti-periodic o...

The standard approach to the infra-red problem is to sum over degenerate final states to remove soft divergences (Bloch-Nordsiech), and over both initial and final states for collinear divergences (Lee-Nauenberg). We show that this division is inconsistent, and further that the Lee-Nauenberg recipe leads to ill-defined results in a variety of theor...

A new approach to gauge fixed Yang-Mills theory is derived using the Polyakov-Susskind projection techniques to build gauge invariant states. In our approach, in contrast to the Faddeev-Popov method, the Gribov problem does not prevent the gauge group from being factored out of the partition function. Lattice gauge theory is used to illustrate the...

We study the behavior of the AsqTad quark propagator in Landau gauge on quenched SU(2) gauge configurations under the removal of center vortices. In contrast to recent results in SU(3), we clearly see the infrared enhancement of the mass function disappear if center vortices are removed, a sign of the intimate relation between center vortices and c...

In this paper we describe gauge invariant multi-quark states generalising the path integral framework developed by Parrinello, Jona-Lasinio and Zwanziger to amend the Faddeev-Popov approach. This allows us to produce states such that, in a limit which we call the ice-limit, fermions are dressed with glue exclusively from the fundamental modular reg...

We study trial states modelling the heavy quark-antiquark ground state in SU(2) Yang-Mills theory. A state describing the flux tube between quarks as a thin string of glue is found to be a poor description of the continuum ground state; the infinitesimal thickness of the string leads to UV artifacts which suppress the overlap with the ground state....

Center vortices are studied in $SU(3)$ gauge theory using maximal center gauge (MCG) fixing. Stout link smearing and over-improved stout link smearing are used to construct a preconditioning gauge-field transformation which is applied to the original gauge field before fixing to MCG. We find that preconditioning successfully achieves higher maxima...

We study the behavior of the AsqTad quark propagator in Landau gauge on quenched SU(2) gauge configurations under the removal of center vortices. In contrast to recent results in SU(3), we clearly see the infrared enhancement of the mass function disappear if center vortices are removed, a sign of the intimate relation between center vortices and c...

Spectral sums of the Dirac-Wilson operator and their relation to the Polyakov loop are thoroughly investigated. The approach by Gattringer is generalized to mode sums which reconstruct the Polyakov loop locally. This opens the possibility to study the mode sum approximation to the Polyakov loop correlator. The approach is re-derived for the ab init...

It is thought that confinement and chiral symmetry breaking might be driven by the same mech-anism. Centre vortices have long been considered a promising candidate for such a mechanism. We use the Landau-gauge quark propagator as a probe of dynamical chiral symmetry breaking and show that, for SU(2) gauge theory, the infrared behaviour of the quark...

After a brief introduction to the statistical description of data, these lecture notes focus on quantum field theories as they emerge from lattice models in the critical limit. For the simulation of these lattice models, Markov chain Monte-Carlo methods are widely used. We discuss the heat bath and, more modern, cluster algorithms. The Ising model...

We study the approach, initiated by Marinari et al., to the static interquark potential based on Polyakov lines of finite temporal extent, evaluated in Coulomb gauge. We show that, at small spatial separations, the potential can be understood as being between two separately gauge invariant color charges. At larger separations Gribov copies obstruct...

We investigate the effectiveness of using smearing as a means to generate a preconditioning transformation for gauge fields prior to fixing to Maximal Centre Gauge. This still leaves the gauge-fixed field in the original gauge orbit. As expected, we find that this preconditioning leads to higher maxima of the gauge-fixing condition, resulting in lo...

We propose to apply ``worldline numerics'' to a numerical calculation of quark determinants. The Gross-Neveu model with a U(1) chiral symmetry is considered as a first test. The worldline approach allows for an analytic renormalisation, and only finite parts of the determinant require a numerical calculation. It is shown that the discretisation of...

We consider two very different models of the flux tube linking two heavy quarks: a string linking the matter fields and a Coulombic description of two separately gauge invariant charges. We compare how close they are to the unknown true ground state in compact U(1) and the SU(2) Higgs model. Simulations in compact U(1) show that the string descript...

We consider two very different models of the flux tube linking two heavy quarks: a string linking the matter fields and a Coulombic description of two separately gauge invariant charges. We compare how close they are to the unknown true ground state in compact U(1) and the SU(2) Higgs model. Simulations in compact U(1) show that the string descript...

Improved actions in SU(2) and SU(3) lattice gauge theories are investigated with an emphasis on asymptotic scaling. A new scheme for tadpole improvement is proposed. The standard but heuristic tadpole improvement emerges from a mean field approximation from the new approach. Scaling is investigated by means of the large distance static quark potent...

We study the approach, initiated by Marinari et al., to the static inter-quark potential based on Polyakov lines of finite temporal extent, evaluated in Coulomb gauge. We show that, at small spatial separations, the potential can be understood as being between two separately gauge invariant colour charges. At larger separations Gribov copies obstru...

The mass and renormalization functions of the nonperturbative quark propagator are studied in SU(3) gauge field theory with a Symanzik-improved gluon action and the AsqTad fermion action. Centre vortices in the gauge field are identified by fixing to maximal centre gauge. The role of centre vortices in dynamical mass generation is explored by remov...

We argue that screening of higher-representation color charges by gluons implies a domain structure in the vacuum state of non-abelian gauge theories, with the color magnetic flux in each domain quantized in units corresponding to the gauge group center. Casimir scaling of string tensions at intermediate distances results from random spatial variat...

The frustrated Ising model in two dimensions is revisited. The frustration is quantified in terms of the number of non-trivial plaquettes which is invariant under the Nishimori gauge symmetry. The exact ground state energy is calculated using Edmond's algorithm. A novel cluster algorithm is designed which treats gauge equivalent spin glasses on equ...

The magnetic flux noise induced by vortices in thin superconducting films is studied. Rigid vortices in thin films as well as pancake vortices in the pancake gas regime are addressed. The vortex dynamics is described by a Feynman path integral which fully accounts for the balance between vortex entropy and vortex energetics. We find that vortex pai...

By using the method of center projection the center vortex part of the gauge field is isolated and its propagator is evaluated in the center Landau gauge, which minimizes the open 3-dimensional Dirac volumes of non-trivial center links bounded by the closed 2-dimensional center vortex surfaces. The center field propagator is found to dominate the g...

By using the method of center projection, the center vortex part of the gauge field is isolated and its propagator is evaluated in the center Landau gauge, which minimizes the open 3-dimensional Dirac volumes of nontrivial center links bounded by the closed 2-dimensional center vortex surfaces. The center field propagator is found to dominate the g...

SU(2) lattice gauge theory is investigated where the traces of the Wilson lines at any lattice point and along each direction is constrained to zero. Hence, each of the lattice configurations possesses a vanishing density of heavy (anti-) quarks. The results are compared with those of pure SU(2) gauge theory which can be interpreted as the grand ca...