arXiv subjects

Christof Gattringer

Publications and source records attributed to Christof Gattringer.

At least 55 records · Page 3Linked to original sources

arXiv2016

Dual representation for 1+1 dimensional fermions interacting with 3+1 dimensional U(1) gauge fields

We study a system of nanowires, i.e., the theory of 1+1 dimensional massless fermions interacting with 3+1 dimensional U(1) gauge fields. When allowing for non-zero chemical potentials, this system has a complex action problem in the conventional formulation. We show that the partition sum can be mapped to a dual representation where the fermions correspond to dimers and oriented loops on 2-dimensional planes embedded in 4 dimensions. The dual degrees of freedom for the gauge fields are surfaces that either are closed or bounded by the fermion loops. In terms of the dual variables the complex action problem is overcome and Monte Carlo simulations are possible for arbitrary chemical potentials.

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arXiv2015

Finite density $\mathbf{O(3)}$ non-linear sigma model and low energy physics

We present lattice results for simulations of the $O(3)$ non-linear sigma model at finite chemical potential. The complex action problem is overcome by a dual variable representation of the model. We discuss two aspects of the theory at finite density: 1) The relation of the finite density data to scattering phases and wave-functions. 2) The phase-structure of the theory as a function of chemical potential and the possibility of a Kosterlitz-Thouless phase transition.

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arXiv2015

Grand canonical ensemble, multi-particle wave functions, scattering data, and lattice field theories

We show that information about scattering data of a quantum field theory can be obtained from studying the system at finite density and low temperatures. In particular we consider models formulated on the lattice which can be exactly dualized to theories of conserved charge fluxes on lattice links. Apart from eliminating the complex action problem at nonzero chemical potential mu, these dualizations allow for a particle world line interpretation of the dual fluxes from which one can extract data about the 2-particle wave function. As an example we perform dual Monte Carlo simulations of the 2-dimensional O(3) model at nonzero mu and finite volume, whose non-perturbative spectrum consists of a massive triplet of particles. At nonzero mu particles are induced in the system, which at sufficiently low temperature give rise to sectors of fixed particle number. We show that the scattering phase shifts can be obtained either from the critical chemical potential values separating the sectors or directly from the wave function in the 2-particle sector. We find that both methods give excellent agreement with the exact result. We discuss the applicability and generality of the new approaches.

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arXiv2015

Dual representation for massless fermions with chemical potential and U(1) gauge fields

Complex action problems coming from either a chemical potential or a topological term have been solved for several models in recent years by mapping them to so-called dual degrees of freedom. In terms of these dual variables the partition sum has only real and positive contributions such that a Monte Carlo simulation is possible. In this paper we discuss a dual representation for massless staggered fermions in two dimensions coupled to a U(1) gauge field. We include a topological term, and for the case of several flavors with vanishing total charge also a chemical potential. We show that the real and positive dualization can also be generalized to a system of nanowires (1+1 dimensional fermions) coupled to a 3+1 dimensional U(1) gauge field.

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arXiv2015

Density of states techniques for lattice field theories using the functional fit approach (FFA)

We discuss a variant of density of states (DoS) techniques for lattice field theories, the so-called "functional fit approach" (FFA). The DoS FFA is based on a density of states rho(x) which is parameterized on small intervals of the argument x of rho(x). On these intervals restricted Monte Carlo simulations with an additional Boltzmann factor exp(lambda x) allow to determine rho(x) very precisely by obtaining its parameters from fitting the Monte Carlo data to a known function of lambda. We describe the method in detail and show its applicability in four different systems, three of which have a complex action problem: The SU(3) spin model with a chemical potential, U(1) lattice gauge theory, the Z(3) spin model with chemical potential, and 2-dimensional U(1) lattice gauge theory with a topological term. In all cases we compare to reference calculations, which partly were done in a dual formulation where the complex action problem is absent. In all four cases we find a very encouraging performance of the DoS FFA.

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arXiv2015

Dual simulation of the 2-dimensional lattice U(1) gauge-Higgs model with a topological term

The 2-dimensional U(1) gauge-Higgs model with a topological term is a simple example of a lattice field theory where the complex action problem comes from the topological term. We show that the model can be exactly rewritten in terms of dual variables, such that the dual partition sum has only real and positive contributions. Using suitable algorithms the dual formulation allows for Monte Carlo simulations at arbitrary values of the vacuum angle. We demonstrate the feasibility of the dual simulation and study the continuum limit, as well as the phase diagram of the system.

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arXiv2015

Dual lattice representations for O(N) and CP(N-1) models with a chemical potential

We derive dual representations for O(N) and CP(N-1) models on the lattice. In terms of the dual variables the partition sums have only real and positive contributions also at finite chemical potential. Thus the complex action problem of the conventional formulation is overcome and using the dual variables Monte Carlo simulations are possible at arbitrary chemical potential.

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arXiv2015

Solving the sign problems of the massless lattice Schwinger model with a dual formulation

We derive an exact representation of the massless Schwinger model on the lattice in terms of dual variables which are configurations of loops, dimers and plaquette occupation numbers. When expressed with the dual variables the partition sum has only real and positive terms also when a chemical potential or a topological term are added -- situations where the conventional representation has a complex action problem. The dual representation allows for Monte Carlo simulations without restrictions on the values of the chemical potential or the vacuum angle.

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arXiv2015

Density of states method for the Z(3) spin model

We apply the density of states approach to the Z(3) spin model with a chemical potential mu. For determining the density of states we use restricted Monte Carlo simulations on small intervals of the variable for the density. In each interval we probe the response of the system to the variation of a free parameter in the Boltzmann factor. This response is a known function which we fit to the Monte Carlo data and the parameters of the density are obtained from that fit (functional fit approch; FFA). We evaluate observables related to the particle number and the particle number susceptibility, as well as the free energy. We find that for a surprisingly large range of mu the results from the FFA agree very well with the results from a reference simulation in the dual formulation of the Z(3) spin model which is free of the complex action problem.

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arXiv2015

Generalized quark number susceptibilities from fugacity expansion at finite chemical potential for $N_f$ = 2 Wilson fermions

Generalized susceptibilities of the net quark number have been proposed to be good probes for the transitions in the QCD phase diagram and for the search of a possible critical end point. In this article we explore a new strategy for computing quark number susceptibilities from lattice QCD via an expansion in the fugacity parameter $e^{μβ}$. All quark number related bulk observables are particularly easy to access in this approach and we present results for generalized quark number susceptibilities up to 4-th order. Ratios of these quantities are studied and compared with model calculations for the high- and low temperature regions up to a chemical potential of $μβ\approx1.0$.

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arXiv2015

Dual simulation of finite density lattice QED at large mass

We discuss a mapping of lattice QED with two flavors and a chemical potential to dual variables, which are surfaces for the gauge fields and loops for the fermions. The gauge fields are completely dualized and the corresponding dual variables are integer valued plaquette occupation numbers with constraints that lead to a structure of surfaces that are either closed or bounded by fermion loops. The fermion loops are obtained from a resummed hopping expansion (large mass expansion) of the determinant of the Wilson-Dirac operator. The loops can come with both positive and negative signs. We identify a sub-class of loops, which we refer to as quasi-planar loops, where the total sign is positive. For this sub-class a dual Monte Carlo simulation is possible and we discuss its implementation and some results. In particular we address condensation phenomena at finite chemical potential.

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arXiv2015

Condensation phenomena in two-flavor scalar QED at finite chemical potential

We study condensation in two-flavored, scalar QED with non-degenerate masses at finite chemical potential. The conventional formulation of the theory has a sign problem at finite density which can be solved using an exact reformulation of the theory in terms of dual variables. We perform a Monte Carlo simulation in the dual representation and observe a condensation at a critical chemical potential $μ_c$. After determining the low-energy spectrum of the theory we try to establish a connection between $μ_c$ and the mass of the lightest excitation of the system, which are naively expected to be equal. It turns out, however, that the relation of the critical chemical potential to the mass spectrum in this case is non-trivial: Taking into account the form of the condensate and making some simplifying assumptions we suggest an adequate explanation which is supported by numerical results.

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arXiv2014

Taylor- and fugacity expansion for the effective Z(3) spin model of QCD at finite density

Series expansions in the chemical potential mu are studied for an effective theory of QCD which has a flux representation where the complex action is overcome. In particular we consider fugacity series, Taylor expansion and a modified Taylor expansion and compare the outcome of these series to the reference results from a Monte Carlo simulation in the flux representation where arbitrary mu is accessible. It is shown that for most parameter values the fugacity expansion gives the best approximation to the data from the flux simulation, followed by our newly proposed modified Taylor expansion. For the conventional Taylor expansion we find that the results coincide with the flux data only for very small mu.

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arXiv2014

Scalar QED$_2$ with a topological term - a lattice study in a dual representation

We present a dual representation for the partition function of 2-dimensional scalar quantum electrodynamics with a topological term ($θ$-term). In the dual representation the complex action problem at non-zero $θ$ is absent, which is an obstacle for Monte Carlo simulations in the conventional form of the model. We discuss the technical aspects of the dual representation and show that a dual Monte Carlo simulation can be implemented. As a first application we demonstrate how the $2π$-periodicity of physical observables is recovered in a suitable continuum limit.

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arXiv2014

The Z3 model with the density of states method

In this contribution we apply a new variant of the density of states method to the Z3 spin model at finite density. We use restricted expectation values evaluated with Monte Carlo simulations and study their dependence on a control parameter lambda. We show that a sequence of one-parameter fits to the Monte-Carlo data as a function of lambda is sufficient to completely determine the density of states. We expect that this method has smaller statistical errors than other approaches since all generated Monte Carlo data are used in the determination of the density. We compare results for magnetization and susceptibility to a reference simulation in the dual representation of the Z3 spin model and find good agreement for a wide range of parameters.

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arXiv2014

Quark number susceptibilities at finite chemical potential from fugacity expansion

Generalized quark number susceptibilities are expected to be good probes for the phase transitions in QCD and the search of a possible critical point. However, their computation in lattice QCD is plagued by the complex action problem which appears at finite chemical potential mu. In this work we explore the possibilities of an expansion in the fugacity parameter exp(mu beta) which has features that make, in particular quark number related bulk observables easily accessible. We present results at finite chemical potential for generalized susceptibilities up to the 4th order as well as their ratios and compare them to model calculations.

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arXiv2014

A test of Taylor- and modified Taylor-expansion

We compare Taylor expansion and a modified variant of Taylor expansion, which incorporates features of the fugacity series, for expansions in the chemical potential around a zero-density lattice field theory. As a first test we apply both series to the cases of free fermions and free bosons. Convergence and other properties are analyzed.

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arXiv2014

Fractality and other properties of center domains at finite temperature Part 1: SU(3) lattice gauge theory

Using finite temperature SU(3) lattice gauge theory in the fixed scale approach we analyze center properties of the local Polyakov loop L(x). We construct spatial clusters of points x where the phase of L(x) is near the same center element and study their properties as a function of temperature. We find that below the deconfinement transition the clusters form objects with a fractal dimension D < 3. As the temperature is increased, the largest cluster starts to percolate and its dimensionality approaches D=3. The fractal structure of the clusters in the transition region may have implications regarding both the small shear viscosity and the large opacity of the Quark Gluon Plasma observed in heavy-ion collision experiments.

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