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E. Seiler

Publications and source records attributed to E. Seiler.

At least 19 recordsLinked to original sources
arXiv2019

Controlling Complex Langevin simulations of lattice models by boundary term analysis

One reason for the well known fact that the Complex Langevin (CL) method sometimes fails to converge or converges to the wrong limit has been identified long ago: it is insufficient decay of the probability density either near infinity or near poles of the drift, leading to boundary terms that spoil the formal argument for correctness. To gain a deeper understanding of this phenomenon, in a previous paper we have studied the emergence of such boundary terms thoroughly in a simple model, where analytic results can be compared with numerics. Here we continue this type of analysis for more physically interesting models, focusing on the boundaries at infinity. We start with abelian and non-abelian one-plaquette models, then we proceed to a Polyakov chain model and finally to high density QCD (HDQCD) and the 3D XY model. We show that the direct estimation of the systematic error of the CL method using boundary terms is in principle possible.

hep-lat↗
arXiv2016

On complex Langevin dynamics and zeroes of the measure II: Fermionic determinant

Lattice QCD at non-vanishing chemical potential is studied using the complex Langevin equation (CLE). One of the conditions for the correctness of the results of the CLE is that the zeroes of the measure coming from the fermionic determinant are outside of the distribution of the configurations, or at least in a region where support for the distribution is very much suppressed. We investigate this issue for Heavy Dense QCD (HDQCD) and full QCD at high temperatures. In HDQCD it is found that the configurations move closest to the zeroes of the measure around the critical chemical potential of the onset transition, where the sign problem is diminished, but results remain largely unaffected. In full QCD at high temperatures the investigation of the spectrum of the Dirac operator yields a similar observation: the results are unaffected by the issue of the poles.

hep-lat↗
arXiv2015

Hopping parameter expansion to all orders using the complex Langevin equation

We propose two novel formulations of the hopping parameter expansion for finite density QCD using Wilson fermions, while keeping the gauge action intact. We use the complex Langevin equation to circumvent the sign problem in the theory. We perform simulations at very high order of the expansion, such that convergence is directly observable. We compare results to the full QCD results, and see agreement at sufficiently high orders. These results provide support for the use of complex Langevin dynamics to study QCD at nonzero density, both in the full and the expanded theory, and for the convergence of the latter.

hep-lat↗
arXiv2008

Further discussion of Tomboulis' approach to the confinement problem

We discuss in some detail certain gaps and open problems in the recent paper by E. T. Tomboulis, which claims to give a rigorous proof of quark confinement in 4D lattice Yang-Mills theory for all values of the bare coupling. We also discuss what would be needed to fill the gaps in his proof.

hep-th↗
arXiv2007

The High Density Region of QCD from an Effective Model

We study the high density region of QCD within an effective model obtained in the frame of the hopping parameter expansion and choosing Polyakov-type loops as the main dynamical variables representing the fermionic matter. This model still shows the so-called sign problem, a difficulty peculiar to non-zero chemical potential, but it permits the development of algorithms which ensure a good overlap of the simulated Monte Carlo ensemble with the true one. We review the main features of the model and present results concerning the dependence of various observables on the chemical potential and on the temperature, in particular of the charge density and the Polykov loop susceptibility, which may be used to characterize the various phases expected at high baryonic density. In this way, we obtain information about the phase structure of the model and the corresponding phase transitions and cross over regions, which can be considered as hints about the behaviour of non-zero density QCD.

hep-lat↗
arXiv2007

A Model for QCD at High Density and Large Quark Mass

We study the high density region of QCD within an effective model obtained in the frame of the hopping parameter expansion and choosing Polyakov type of loops as the main dynamical variables representing the fermionic matter. To get a first idea of the phase structure, the model is analyzed in strong coupling expansion and using a mean field approximation. In numerical simulations, the model still shows the so-called sign problem, a difficulty peculiar to non-zero chemical potential, but it permits the development of algorithms which ensure a good overlap of the Monte Carlo ensemble with the true one. We review the main features of the model and present calculations concerning the dependence of various observables on the chemical potential and on the temperature, in particular of the charge density and the diquark susceptibility, which may be used to characterize the various phases expected at high baryonic density. We obtain in this way information about the phase structure of the model and the corresponding phase transitions and cross over regions, which can be considered as hints for the behaviour of non-zero density QCD.

hep-lat↗
arXiv2006

Does the XY Model have an integrable continuum limit?

The quantum field theory describing the massive O(2) nonlinear sigma-model is investigated through two non-perturbative constructions: The form factor bootstrap based on integrability and the lattice formulation as the XY model. The S-matrix, the spin and current two-point functions, as well as the 4-point coupling are computed and critically compared in both constructions. On the bootstrap side a new parafermionic super selection sector is found; in the lattice theory a recent prediction for the (logarithmic) decay of lattice artifacts is probed.

hep-lat↗
arXiv2006

Structure of the space of ground states in systems with non-amenable symmetries

We investigate classical spin systems in $d\geq 1$ dimensions whose transfer operator commutes with the action of a nonamenable unitary representation of a symmetry group, here ${\rm SO}(1,N)$; these systems may alternatively be interpreted as systems of interacting quantum mechanical particles moving on hyperbolic spaces. In sharp contrast to the analogous situation with a compact symmetry group the following results are found and proven: (i) Spontaneous symmetry breaking already takes place for finite spatial volume/finitely many particles and even in dimensions $d=1,2$. The tuning of a coupling/temperature parameter cannot prevent the symmetry breaking. (ii) The systems have infinitely many non-invariant and non-normalizable generalized ground states. (iii) the linear space spanned by these ground states carries a distinguished unitary representation of ${\rm SO}(1,N)$, the limit of the spherical principal series. (iv) The properties (i)--(iii) hold universally, irrespective of the details of the interaction.

math-ph↗
arXiv2004

Vacuum orbit and spontaneous symmetry breaking in hyperbolic sigma models

We present a detailed study of quantized noncompact, nonlinear SO(1,N) sigma-models in arbitrary space-time dimensions D \geq 2, with the focus on issues of spontaneous symmetry breaking of boost and rotation elements of the symmetry group. The models are defined on a lattice both in terms of a transfer matrix and by an appropriately gauge-fixed Euclidean functional integral. The main results in all dimensions \geq 2 are: (i) On a finite lattice the systems have infinitely many nonnormalizable ground states transforming irreducibly under a nontrivial representation of SO(1,N); (ii) the SO(1,N) symmetry is spontaneously broken. For D =2 this shows that the systems evade the Mermin-Wagner theorem. In this case in addition: (iii) Ward identities for the Noether currents are derived to verify numerically the absence of explicit symmetry breaking; (iv) numerical results are presented for the two-point functions of the spin field and the Noether current as well as a new order parameter; (v) in a large N saddle-point analysis the dynamically generated squared mass is found to be negative and of order 1/(V \ln V) in the volume, the 0-component of the spin field diverges as \sqrt{\ln V}, while SO(1,N) invariant quantities remain finite.

hep-th↗
arXiv2004

Some new results on an old controversy: is perturbation theory the correct asymptotic expansion in nonabelian models?

Several years ago it was found that perturbation theory for two-dimensional O(N) models depends on boundary conditions even after the infinite volume limit has been taken termwise, provided $N>2$. There ensued a discussion whether the boundary conditions introduced to show this phenomenon were somehow anomalous and there was a class of `reasonable' boundary conditions not suffering from this ambiguity. Here we present the results of some computations that may be interpreted as giving some support for the correctness of perturbation theory with conventional boundary conditions; however the fundamental underlying question of the correctness of perturbation theory in these models and in particular the perturbative $β$ function remain challenging problems of mathematical physics.

hep-lat↗
arXiv2003

Study of coupling loss on bi-columnar BSCCO/Ag tapes by a.c. susceptibility measurements

Coupling losses were studied in composite tapes containing superconducting material in the form of two separate stacks of densely packed filaments embedded in a metallic matrix of Ag or Ag alloy. This kind of sample geometry is quite favorable for studying the coupling currents and in particular the role of superconducting bridges between filaments. By using a.c. susceptibility technique, the electromagnetic losses as function of a.c. magnetic field amplitude and frequency were measured at the temperature T = 77 K for two tapes with different matrix composition. The length of samples was varied by subsequent cutting in order to investigate its influence on the dynamics of magnetic flux penetration. The geometrical factor $χ_0$ which takes into account the demagnetizing effects was established from a.c. susceptibility data at low amplitudes. Losses vs frequency dependencies have been found to agree nicely with the theoretical model developed for round multifilamentary wires. Applying this model, the effective resistivity of the matrix was determined for each tape, by using only measured quantities. For the tape with pure silver matrix its value was found to be larger than what predicted by the theory for given metal resistivity and filamentary architecture. On the contrary, in the sample with a Ag/Mg alloy matrix, an effective resistivity much lower than expected was determined. We explain these discrepancies by taking into account the properties of the electrical contact of the interface between the superconducting filaments and the normal matrix. In the case of soft matrix of pure Ag, this is of poor quality, while the properties of alloy matrix seem to provoke an extensive creation of intergrowths which can be actually observed in this kind of samples.

cond-mat.supr-con↗
arXiv2000

Discrete Symmetry Enhancement in Nonabelian Models and the Existence of Asymptotic Freedom

We study the universality between a discrete spin model with icosahedral symmetry and the O(3) model in two dimensions. For this purpose we study numerically the renormalized two-point functions of the spin field and the four point coupling constant. We find that those quantities seem to have the same continuum limits in the two models. This has far reaching consequences, because the icosahedron model is not asymptotically free in the sense that the coupling constant proposed by L"uscher, Weisz and Wolff [1] does not approach zero in the short distance limit. By universality this then also applies to the O(3) model, contrary to the predictions of perturbation theory.

hep-lat↗
arXiv2000

Absence of Asymptotic Freedom in Non-Abelian Models

The percolation properties of equatorial strips of the two dimensional O(3) nonlinear $σ$ model are investigated numerically. Convincing evidence is found that a sufficently narrow strip does not percolate at arbitrarily low temperatures. Rigorous arguments are used to show that this result implies both the presence of a massless phase at low temperature and lack of asymptotic freedom in the massive continuum limit. A heuristic estimate of the transition temperature is given which is consistent with the numerical data.

hep-th↗
arXiv2000

The Intrinsic Coupling in Integrable Quantum Field Theories

The intrinsic 4-point coupling, defined in terms of a truncated 4-point function at zero momentum, provides a well-established measure for the interaction strength of a QFT. We show that this coupling can be computed non-perturbatively and to high accuracy from the form factors of an (integrable) QFT. The technique is illustrated and tested with the Ising model, the XY-model and the O(3) nonlinear sigma-model. The results are compared to those from high precision lattice simulations.

hep-th↗
arXiv1996

The Problem of Asymptotic Freedom

There is a growing body of evidence that the running of $α_s$ predicted by perturbation (PT) theory is not correctly describing the accelerator experiments at the highest energies. A natural explanation is provided by the authors' 1992 proposal that in fact the true running predicted by the nonperturbatively defined lattice QCD is different, leading to an ultraviolet fixed point near $α_s=.1$. It is explained how this can be understood from the fact that the conventional perturbative method is ambiguous and does not provide the correct asymptotic expansion. It is pointed out that there is a large amount of lattice data that are supporting this scenario rather than the conventional one.

hep-ph↗