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We study the particle creation process in the Schwinger model coupled with an external classical source. One can approach the problem by taking advantage that the full quantized model is solvable and equivalent to a (massive) gauge field with a non-local effective action. Alternatively, one can also face the problem following the standard semiclassical route. This means quantizing the massless Dirac field and considering the electromagnetic field as a classical background. We evaluate the energy created by a generic, homogeneous, and time-dependent source. The results exactly match in both approaches. This proves in a very direct and economical way the validity of the semiclassical approach for the (massless) Schwinger model, in agreement with previous analysis based on the linear response equation. Our discussion suggests that a similar analysis for the massive Schwinger model could be used as a non-trivial laboratory to confront a fully quantized solvable model with its semiclassical approximation, therefore mimicking the long-standing confrontation of quantum gravity with quantum field theory in curved spacetime., 10 pages; This article belongs to the Special Issue Black Holes, Cosmology, Quantum Gravity, and Their Symmetries

39th International Symposium on Lattice Field Theory, Lattice 2022, Bonn, Germany, 8 Aug 2022 - 13 Aug 2022; Proceedings of Science / International School for Advanced Studies (LATTICE2022), 020 (2022)., We propose a variational quantum eigensolver suitable for exploring the phase structure of the multi-flavor Schwinger model in the presence of a chemical potential. The parametric ansatz circuit we design is capable of incorporating the symmetries of the model, present in certain parameter regimes, which allows for reducing the number of variational parameters substantially. Moreover, the ansatz circuit can be implementated on both measurement-based and circuit-based quantum hardware. We numerically demonstrate that our ansatz circuit is able to capture the phase structure of the model and allows for faithfully approximating the ground state. Our results show that our approach is suitable for current intermediate-scale quantum hardware and can be readily implemented on existing quantum devices., Published by SISSA, Trieste

We consider the Schwinger model with two degenerate, light fermion flavors by means of lattice simulations. At finite temperature, we probe the viability of a bosonization method by Hosotani et al. Next we explore an analogue to the pion decay constant, which agrees for independent formulations based on the Gell-Mann--Oakes--Renner relation, the 2-dimensional Witten--Veneziano formula and the $\delta$-regime. Finally we confront several conjectures about the chiral condensate with lattice results., Comment: 5 pages, LaTex, 4 figures, 1 table, presented at the "XXXV Reuni\'{o}n Anual de la Divisi\'{o}n de Part\'{i}culas y Campos", of the "Socieded Mexicana de F\'{i}sica", accepted for publication in Suplemento de la Revista Mexicana de F\'{i}sica

39th International Symposium on Lattice Field Theory, Lattice 2022, Bonn, Germany, 8 Aug 2022 - 13 Aug 2022; Proceedings of Science / International School for Advanced Studies (LATTICE2022), 046 (2022). doi:10.22323/1.430.0046, Lattice computations in the Hamiltonian formulation have so far mainly focused on staggered fermions. In these proceedings, we study Wilson fermions in the Hamiltonian formulation and propose a new method to determine the resulting mass shift. As a benchmark study, we examine the one-flavour Schwinger model with Wilson fermions and a topological $\theta$-term using matrix product states. Wilson fermions explicitly break chiral symmetry; thus, the bare mass of the lattice model receives an additive renormalization. In order to measure this mass shift directly, we develop a method that is suitable for the Hamiltonian formulation, which relies on the fact that the vacuum expectation value of the electric field density vanishes when the renormalized mass is zero. We examine the dependence of the mass shift on the lattice spacing, the lattice volume, the $\theta$-parameter, and the Wilson parameter. Using the mass shift, we then perform the continuum extrapolation of the electric field density and compare the resulting mass dependence to the analytical predictions of mass perturbation theory. We demonstrate that incorporating the mass shift significantly improves the continuum extrapolation. Finally, we apply our method to the same model using staggered fermions instead of Wilson fermions and compare the resulting mass shift to recent theoretical predictions., Published by SISSA, Trieste

The Schwinger model is often used as a testbed for conceptual and numerical approaches in lattice field theory. Still, some of its rich physical properties in anisotropic volumes have not yet been explored. For the multi-flavor finite temperature Schwinger model there is an approximate solution by Hosotani et al. based on bosonization. We perform lattice simulations and check the validity of this approximation in the case of two flavors. Next we exchange the r\^{o}le of the coordinates to enter the $\delta$-regime, and measure the dependence of the residual "pion" mass on the spatial size, at zero temperature. Our results show that universal features, which were derived by Leutwyler, Hasenfratz and Niedermayer referring to quasi-spontaneous symmetry breaking in $d>2$, extend even to $d=2$. This enables the computation of the Schwinger model counterpart of the pion decay constant $F_{\pi}$. It is consistent with an earlier determination by Harada et al. who considered the divergence of the axial current in a light-cone formulation, and with analytical results that we conjecture from 2d versions of the Witten--Veneziano formula and the Gell-Mann--Oakes--Renner relation, which suggest $F_{\pi} = 1/ \sqrt{2\pi}$., Comment: 9 pages, LaTex, 4 figures, talk presented at the 38th International Symposium on Lattice Field Theory, LATTICE2021, July 36-30, 2021 Zoom/Gather@Massachusetts Institute of Technology

Physical review / D D 101(5), 054507 (2020). doi:10.1103/PhysRevD.101.054507, We numerically study the single-flavour Schwinger model in the Hamiltonian formulation with a topological $\theta$-term corresponding to a constant electric background field. By using numerical methods based on tensor networks, especially the one-dimensional matrix product states, we explore the non-trivial $\theta$-dependence of several lattice and continuum quantities. In particular, we compute the ground-state energy, the electric field, the chiral fermion condensate, and the topological vacuum susceptibility for positive, zero, and even negative fermion mass. In the chiral limit, we demonstrate that the continuum model becomes independent of the vacuum angle $\theta$, thus respecting CP invariance, while lattice artifacts still depend on $\theta$. We also confirm that negative masses can be mapped to positive masses by shifting $\theta\rightarrow \theta +\pi$ due to the axial anomaly in the continuum, while lattice artifacts non-trivially distort this mapping., Published by Inst.302363, Melville, NY

We numerically study the single-flavor Schwinger model with a topological $\theta$-term, which is practically inaccessible by standard lattice Monte Carlo simulations due to the sign problem. By using numerical methods based on tensor networks, especially the one-dimensional matrix product states, we explore the non-trivial $\theta$-dependence of several lattice and continuum quantities in the Hamiltonian formulation. In particular, we compute the ground-state energy, the electric field, the chiral fermion condensate, and the topological vacuum susceptibility for positive, zero, and even negative fermion mass. In the chiral limit, we demonstrate that the continuum model becomes independent of the vacuum angle $\theta$, thus respecting CP invariance, while lattice artifacts still depend on $\theta$. We also confirm that negative masses can be mapped to positive masses by shifting $\theta\rightarrow \theta +\pi$ due to the axial anomaly in the continuum, while lattice artifacts non-trivially distort this mapping. This mass regime is particularly interesting for the (3+1)-dimensional QCD analog of the Schwinger model, the sign problem of which requires the development and testing of new numerical techniques beyond the conventional Monte Carlo approach., Comment: 15 pages, 10 figures

We propose a discrete spacetime formulation of quantum electrodynamics in one-dimension (a.k.a the Schwinger model) in terms of quantum cellular automata, i.e. translationally invariant circuits of local quantum gates. These have exact gauge covariance and a maximum speed of information propagation. In this picture, the interacting quantum field theory is defined as a "convergent" sequence of quantum cellular automata, parameterized by the spacetime lattice spacing---encompassing the notions of continuum limit and renormalization, and at the same time providing a quantum simulation algorithm for the dynamics., 15 pages, 4 figures, v2: typo corrected

We introduced in a previous paper a general notion of asymptotic morphism of a given local net of observables, which allows to describe the sectors of a corresponding scaling limit net. Here, as an application, we illustrate the general framework by analyzing the Schwinger model, which features confined charges. In particular, we explicitly construct asymptotic morphisms for these sectors in restriction to the subnet generated by the derivatives of the field and momentum at time zero. As a consequence, the confined charges of the Schwinger model are in principle accessible to observation. We also study the obstructions, that can be traced back to the infrared singular nature of the massless free field in d=2, to perform the same construction for the complete Schwinger model net. Finally, we exhibit asymptotic morphisms for the net generated by the massive free charged scalar field in four dimensions, where no infrared problems appear in the scaling limit., 36 pages; no figures

We follow up on a suggestion by Adams and construct explicit domain wall fermion operators with staggered kernels. We compare different domain wall formulations, namely the standard construction as well as Borici's modified and Chiu's optimal construction, utilizing both Wilson and staggered kernels. In the process, we generalize the staggered kernels to arbitrary even dimensions and introduce both truncated and optimal staggered domain wall fermions. Some numerical investigations are carried out in the (1+1)-dimensional setting of the Schwinger model, where we explore spectral properties of the bulk, effective and overlap Dirac operators in the free-field case, on quenched thermalized gauge configurations and on smooth topological configurations. We compare different formulations using the effective mass, deviations from normality and violations of the Ginsparg-Wilson relation as measures of chirality., Comment: 23 pages, 22 figures, 2 tables; major revision, matches published version

The Schwinger model with $N_f \geq 2$ flavors is a simple example for a fermionic model with zero chiral condensate Sigma (in the chiral limit). We consider numerical data for two light flavors, based on simulations with dynamical chiral lattice fermions. We test properties and predictions that were put forward in the recent literature for models with Sigma = 0, which include IR conformal theories. In particular we probe the decorrelation of low lying Dirac eigenvalues, and we discuss the mass anomalous dimension and its IR extrapolation. Here we encounter subtleties, which may urge caution with analogous efforts in other models, such as multi-flavor QCD., 19 pages, LaTex, 6 figures, 5 tables, final version to appear in Int. J. Mod. Phys. C

Numerical investigations of the XY model, the Heisenberg model and the J-J' Heisenberg model are conducted, using the exact diagonalisation, the numerical renormalisation and the density matrix renormalisation group approach. The low-lying energy levels are obtained and finite size scaling is performed to estimate the bulk limit value. The results are found to be consistent with the exact values. The DMRG results are found to be most promising.The Schwinger model is also studied using the exact diagonalisation and the strong coupling expansion. The massless, the massive model and the model with a background electric field are explored. Ground state energy, scalar and vector particle masses and order parameters are examined. The achieved values are observed to be consistent with previous results and theoretical predictions. Path to the future studies is outlined.

We present numerical results for the 2-flavour Schwinger model with dynamical chiral lattice fermions. We insert an approximately chiral hypercube Dirac operator into the overlap formula to construct the overlap hypercube operator. This is an exact solution to the Ginsparg-Wilson relation, with an excellent level of locality and scaling. Due to its similarity with the hypercubic kernel, a low polynomial in this kernel provides a numerically efficient Hybrid Monte Carlo force. We measure the microscopic Dirac spectrum and discuss the corresponding scale-invariant parameter, which takes a surprising form. This is an interesting case, since Random Matrix Theory is unexplored for this setting, where the chiral condensate {\Sigma} vanishes in the chiral limit. We also measure {\Sigma} and the "pion" mass, in distinct topological sectors. In this context we discuss and probe the topological summation of observables by various methods, as well as the evaluation of the topological susceptibility. The feasibility of this summation is essential for the prospects of dynamical overlap fermions in QCD., Comment: 44 pages, LaTex, 12 tables, 17 figures, final version published in Eur. Phys. J. C

Die vorliegende Arbeit untersucht das Skalierungsverhalten von Wilsonfermionen in einem Modell ohne spontane Brechung der chiralen Symmetrie (SXSB). Wilsonfermionen sind eine Regularisierung der fermionischen Wirkung, die in Gittersimulationen der Quantenchromodynamik (QCD) oft zur Anwendung kommt. Zur Umgehung der Fermionenverdopplung enthaelt sie einen Term, der selbst im masselosen Limes die chirale Symmetrie explizit bricht. Infolgedessen treten bei Simulationen der QCD in grossem Volumen Gitterartefakte auf, die linear mit dem Gitterabstand skalieren. Mit Hilfe einer so genannten spurionischen Symmetrie der Gitterwirkung, die verschiedene (Wilson-) Regularisierungen miteinander verknuepft, kann jedoch gezeigt werden, dass die fuehrenden Cutoffeffekte im chiralen Limes einer Theorie ohne SXSB zweiter Ordnung sind. Bei endlicher Quark Masse kommen Effekte der Ordnung O(am_q) dazu. Diese Hypothese konnte hier erfolgreich numerisch gestest werden. Zur Ueberpruefung des Arguments wurde eine Skalierungsstudie in der zwei dimensionalen Quantenelektrodynamik, dem sog. Schwinger Modell, mit zwei Massen entarteten Fermionen durchgefuehrt. Dieses Modell wurde als Testlaboratorium ausgewaehlt, da es sowohl ueber die noetige Flavor Struktur verfuegt, als auch, infolge des Theorems vom Mermin und Wagner, keine spontane Brechung einer kontinuierlichen Symmetrie auftreten kann. Vor diesem Hintergrund scheinen Skalierungsstudien im Schwinger Modell nur in sehr beschraenktem Masse auf die QCD in grossem Volumen, wo die chirale Symmetrie spontan gebrochen ist, uebertragbar zu sein., This work investigates the scaling of Wilson fermions in a set up without spontaneous chiral symmetry breaking (SXSB). Wilson fermions are a lattice regularization which is widely used in lattice simulations of Quantum Chromodynamics (QCD). In order to avoid the notorious fermion doubling problem, it contains a term which breaks chiral symmetry explicitly even in the massless limit. As a consequence, in simulations of QCD in large volume lattice artifacts which scale linear in the lattice spacing do appear.However, with the help of a spurionic lattice symmetry, it has been shown, that those effects are closely connected to the phenomenon of spontaneous chiral symmetry breaking. In the chiral limit of a theory where this phenomenon is absent, leading cutoff effects are of second order. At finite quark masses corrections of O(am_q) do appear. We confirmed this argument numerically by a scaling study in the two dimensional Schwinger model. We use two degenerate, dynamical Wilson fermions in our simulations, since this version of the model not only provides the flavor structure needed to define the spurionic symmetry but, more importantly, due to the Mermin-Wagner theorem, no SXSB can occur.As a consequence of the result, scaling studies in the Schwinger Model are only of very limited use if one wants to learn something for the phenomenologically very different case of QCD in large volume where chiral symmetry is spontaneously broken.

Physical review / D 71(5), 054501 (2005). doi:10.1103/PhysRevD.71.054501, We present a scaling analysis in the 1-flavor Schwinger model with the full overlap and the rooted staggered determinant. In the latter case the chiral and continuum limit of the scalar condensate do not commute, while for overlap fermions they do. For the topological susceptibility a universal continuum limit is suggested, as is for the partition function and the Leutwyler-Smilga sum rule. In the heavy-quark force no difference is visible even at finite coupling. Finally, a direct comparison between the complete overlap and the rooted staggered determinant yields evidence that their ratio is constant up to $O(a^2)$ effects., Published by Inst., Woodbury, NY

Diplomarbeit in Theoretischer Physik. [Thesis for integrated MSc in Theoretical Physics]. Institut für Theoretische Physik, Universität Göttingen. 1999.

We construct a number of lattice fermions, which fulfill the Ginsparg-Wilson relation either exactly or approximately, and test them in the framework of the 2-flavor Schwinger model. We start from explicit approximations within a short range, and study this formulation, as well as its correction to an exact Ginsparg-Wilson fermion by the ``overlap formula''. Then we suggest a new method to realize this correction perturbatively, without using the tedious square root operator. In this way we combine many favorable properties: good chiral behavior, small mass renormalization, excellent scaling and rotational invariance, as well as a relatively modest computational effort, which makes such formulations most attractive for QCD., Comment: 31 pages, 21 figures, replaced by final version to appear in Nucl. Phys. B

We present a detailed study of the interplay between chiral symmetry and spectral properties of the Dirac operator in lattice gauge theories. We consider, in the framework of the Schwinger model, the fixed point action and a fermion action recently proposed by Neuberger. Both actions show the remnant of chiral symmetry on the lattice as formulated in the Ginsparg-Wilson relation. We check this issue for practical implementations, also evaluating the fermion condensate in a finite volume by a subtraction procedure. Moreover, we investigate the distribution of the eigenvalues of a properly defined anti-hermitian lattice Dirac operator, studying the statistical properties at the low lying edge of the spectrum. The comparison with the predictions of chiral Random Matrix Theory enables us to obtain an estimate of the infinite volume fermion condensate., 13 figures, 33 pages; minor changes, update to version accepted for publication

We perform a comparison between different lattice regularizations of the Dirac operator for massless fermions in the framework of the single and two flavor Schwinger model. We consider a) the Wilson-Dirac operator at the critical value of the hopping parameter; b) Neuberger's overlap operator; c) the fixed point operator. We test chiral properties of the spectrum, dispersion relations and rotational invariance of the mesonic bound state propagators., Revised version; 13 pages (LaTeX), 3 figures (EPS)