Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2412.08959 · Journal of High Energy Physics

Grassmann tensor renormalization group for the massive Schwinger model with a θ term using staggered fermions

Hayato Kanno, Shinichiro Akiyama, Kotaro Murakami, Shinji Takeda

Published Nov 10, 2025• 5 citations
arXivHTMLPDF

Abstract

A bstract We use the Grassmann tensor renormalization group method to investigate the N f = 2 Schwinger model with the staggered fermions in the presence of a 2 π periodic θ term in a broad range of mass. The method allows us to deal with the massive staggered fermions straightforwardly and to study the θ dependence of the free energy and topological charge in the thermodynamic limit. Our calculation provides consistent results with not only the analytical solution in the large mass limit but also the previous Monte Carlo studies in the small mass regime. Our numerical results also suggest that the N f = 2 Schwinger model on a lattice has a different phase structure, than the model in the continuum limit.

DOI
10.1007/jhep11(2025)036

Related papers

Grassmann Tensor Renormalization Group for two-flavor massive Schwinger model with a theta term

Hayato Kanno, Shinichiro Akiyama, Kotaro Murakami +1 more

We investigate the $N_f=2$ Schwinger model with the massive staggered fermions in the presence of a $2\pi$ periodic $\theta$ term, using the Grassmann tensor renormalization group. Thanks to the Grassmann tensor network formulation, there is no difficulty in dealing with the massive staggered fermions. We study the $\theta$ dependence of the free energy in the thermodynamic limit. Our calculation provides consistent results with the analytical solution in the large mass limit. The results also suggest that the $N_f=2$ Schwinger model on a lattice has a different phase structure from that described by the continuum theory.

arXiv:2501.14086•International Symposium on Lattice Field Theory (LATTICE)•Jan 23, 2025•0 citations

Tensor network formulation of the massless Schwinger model with staggered fermions

Nouman Butt, Simon M. Catterall, Yannick Meurice +2 more

We construct a tensor network representation of the partition function for the massless Schwinger model on a two-dimensional lattice using staggered fermions. The tensor network representation allows us to include a topological term. Using a particular implementation of the tensor renormalization group we calculate the average plaquette and topological charge density for the theory. For a range of values of the coupling constant for the topological term, $\mathrm{\ensuremath{\Theta}}$, and the gauge coupling, $\ensuremath{\beta}$, we compare with results from hybrid Monte Carlo simulations when possible and find good agreement. In order to further understand the role of fermions and topology in this model, we compare calculations of the same observables in a similar model, the Abelian Higgs model.

arXiv:1911.01285•Physical review. D/Physical review. D.•May 26, 2020•49 citations

Computing the Mass Shift of Wilson and Staggered Fermions in the Lattice Schwinger Model with Matrix Product States

Takis Angelides, Lena Funcke, Karl Jansen +1 more

Simulations of lattice gauge theories with tensor networks and quantum computing have so far mainly focused on staggered fermions. In this paper, we use matrix product states to study Wilson fermions in the Hamiltonian formulation and present a novel method to determine the additive mass renormalization. Focusing on the single-flavor Schwinger model as a benchmark model, we investigate the regime of a nonvanishing topological θ-term, which is inaccessible to conventional Monte Carlo methods. We systematically explore the dependence of the mass shift on the volume, the lattice spacing, the θ-parameter, and the Wilson parameter. This allows us to follow lines of constant renormalized mass, and therefore to substantially improve the continuum extrapolation of the mass gap and electric field density. For small values of the mass, our continuum results agree with the theoretical prediction from mass perturbation theory. Going beyond Wilson fermions, our technique can also be applied to staggered fermions, and we demonstrate that the results of our approach agree with a recent theoretical prediction for the mass shift at sufficiently large volumes.

arXiv:2303.11016•Jan 1, 2023•0 citations

Density matrix renormalization group approach to the massive Schwinger model

Tim Byrnes, P. Sriganesh, Robert J. Bursill +1 more

The massive Schwinger model is studied using a density matrix renormalization group approach to the staggered lattice Hamiltonian version of the model. Lattice sizes up to 256 sites are calculated, and the estimates in the continuum limit are almost two orders of magnitude more accurate than previous calculations. Coleman's picture of ``half-asymptotic'' particles at a background field $\ensuremath{\theta}=\ensuremath{\pi}$ is confirmed. The predicted phase transition at finite fermion mass $(m/g)$ is accurately located and demonstrated to belong in the 2D Ising universality class.

arXiv:hep-lat/0202014•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Jul 1, 2002•178 citations

Computing the mass shift of Wilson and staggered fermions in the lattice Schwinger model with matrix product states

Takis Angelides, Lena Funcke, Karl Jansen +1 more

Simulations of lattice gauge theories with tensor networks and quantum computing have so far mainly focused on staggered fermions. In this paper, we use matrix product states to study Wilson fermions in the Hamiltonian formulation and present a novel method to determine the additive mass renormalization. Focusing on the single-flavor Schwinger model as a benchmark model, we investigate the regime of a nonvanishing topological $\ensuremath{\theta}$-term, which is inaccessible to conventional Monte Carlo methods. We systematically explore the dependence of the mass shift on the volume, the lattice spacing, the $\ensuremath{\theta}$-parameter, and the Wilson parameter. This allows us to follow lines of constant renormalized mass, and therefore to substantially improve the continuum extrapolation of the mass gap and electric field density. For small values of the mass, our continuum results agree with the theoretical prediction from mass perturbation theory. Going beyond Wilson fermions, our technique can also be applied to staggered fermions, and we demonstrate that the results of our approach agree with a recent theoretical prediction for the mass shift at sufficiently large volumes.

Physical review. D/Physical review. D.•Jul 26, 2023•25 citations

Tensor renormalization group study of two-dimensional U(1) lattice gauge theory with a θ term

Yoshinobu Kuramashi, Yusuke Yoshimura

Abstract We make an analysis of the two-dimensional U(1) lattice gauge theory with a θ term by using the tensor renormalization group. Our numerical result for the free energy shows good consistency with the exact one at finite coupling constant. The topological charge density generates a finite gap at θ = π toward the thermodynamic limit. In addition finite size scaling analysis of the topological susceptibility up to V = L × L = 1024 × 1024 allows us to determine the phase transition at θ = π is the first order.

arXiv:1911.06480•Journal of High Energy Physics•Apr 1, 2020•37 citations
A bstract We use the Grassmann tensor renormalization group method to investigate the N f = 2 Schwinger model with the staggered fermions in the presence of a 2 π periodic θ term in a broad range of mass. The method allows us to deal with the massive staggered fermions straightforwardly and to study the θ dependence of the free energy and topological charge in the thermodynamic limit. Our calculation provides consistent results with not only the analytical solution in the large mass limit but also the previous Monte Carlo studies in the small mass regime. Our numerical results also suggest that the N f = 2 Schwinger model on a lattice has a different phase structure, than the model in the continuum limit.
We investigate the Nf=2N_f=2Nf​=2 Schwinger model with the massive staggered fermions in the presence of a 2π2\pi2π periodic θ\thetaθ term, using the Grassmann tensor renormalization group. Thanks to the Grassmann tensor network formulation, there is no difficulty in dealing with the massive staggered fermions. We study the θ\thetaθ dependence of the free energy in the thermodynamic limit. Our calculation provides consistent results with the analytical solution in the large mass limit. The results also suggest that the Nf=2N_f=2Nf​=2 Schwinger model on a lattice has a different phase structure from that described by the continuum theory.
We construct a tensor network representation of the partition function for the massless Schwinger model on a two-dimensional lattice using staggered fermions. The tensor network representation allows us to include a topological term. Using a particular implementation of the tensor renormalization group we calculate the average plaquette and topological charge density for the theory. For a range of values of the coupling constant for the topological term, $\mathrm{\ensuremath{\Theta}}$, and the gauge coupling, $\ensuremath{\beta}$, we compare with results from hybrid Monte Carlo simulations when possible and find good agreement. In order to further understand the role of fermions and topology in this model, we compare calculations of the same observables in a similar model, the Abelian Higgs model.
Simulations of lattice gauge theories with tensor networks and quantum computing have so far mainly focused on staggered fermions. In this paper, we use matrix product states to study Wilson fermions in the Hamiltonian formulation and present a novel method to determine the additive mass renormalization. Focusing on the single-flavor Schwinger model as a benchmark model, we investigate the regime of a nonvanishing topological θ-term, which is inaccessible to conventional Monte Carlo methods. We systematically explore the dependence of the mass shift on the volume, the lattice spacing, the θ-parameter, and the Wilson parameter. This allows us to follow lines of constant renormalized mass, and therefore to substantially improve the continuum extrapolation of the mass gap and electric field density. For small values of the mass, our continuum results agree with the theoretical prediction from mass perturbation theory. Going beyond Wilson fermions, our technique can also be applied to staggered fermions, and we demonstrate that the results of our approach agree with a recent theoretical prediction for the mass shift at sufficiently large volumes.
The massive Schwinger model is studied using a density matrix renormalization group approach to the staggered lattice Hamiltonian version of the model. Lattice sizes up to 256 sites are calculated, and the estimates in the continuum limit are almost two orders of magnitude more accurate than previous calculations. Coleman's picture of ``half-asymptotic'' particles at a background field $\ensuremath{\theta}=\ensuremath{\pi}$ is confirmed. The predicted phase transition at finite fermion mass (m/g)(m/g)(m/g) is accurately located and demonstrated to belong in the 2D Ising universality class.
Simulations of lattice gauge theories with tensor networks and quantum computing have so far mainly focused on staggered fermions. In this paper, we use matrix product states to study Wilson fermions in the Hamiltonian formulation and present a novel method to determine the additive mass renormalization. Focusing on the single-flavor Schwinger model as a benchmark model, we investigate the regime of a nonvanishing topological $\ensuremath{\theta}$-term, which is inaccessible to conventional Monte Carlo methods. We systematically explore the dependence of the mass shift on the volume, the lattice spacing, the $\ensuremath{\theta}$-parameter, and the Wilson parameter. This allows us to follow lines of constant renormalized mass, and therefore to substantially improve the continuum extrapolation of the mass gap and electric field density. For small values of the mass, our continuum results agree with the theoretical prediction from mass perturbation theory. Going beyond Wilson fermions, our technique can also be applied to staggered fermions, and we demonstrate that the results of our approach agree with a recent theoretical prediction for the mass shift at sufficiently large volumes.
Abstract We make an analysis of the two-dimensional U(1) lattice gauge theory with a θ term by using the tensor renormalization group. Our numerical result for the free energy shows good consistency with the exact one at finite coupling constant. The topological charge density generates a finite gap at θ = π toward the thermodynamic limit. In addition finite size scaling analysis of the topological susceptibility up to V = L × L = 1024 × 1024 allows us to determine the phase transition at θ = π is the first order.