Density matrix renormalization group approach to the massive Schwinger model

Byrnes, Tim; Sriganesh, P.; Bursill, Robert J.; Hamer, C. J.

doi:10.1103/physrevd.66.013002

Cited by 176 publications

(245 citation statements)

References 48 publications

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“…This model is exactly solvable for massless fermions, m = 0 (Schwinger model) [1,2,7]. For massive fermions, m = 0, no analytic solution is known so that one relies on approximate solutions [8][9][10][11][12][13][14]. Below we employ realtime lattice gauge theory to calculate the time evolution of observable quantities such as the electric field or the fermion charge following the classical-statistical approach of Refs.…”

Section: Qed In 1 + 1 Dimensionsmentioning

confidence: 99%

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Connecting real-time properties of the massless Schwinger model to the massive case

Hebenstreit

Berges

2014

Phys. Rev. D

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Quantum electrodynamics in 1 + 1 space-time dimensions is analytically solvable for massless fermions, while no solution is known for massive fermions. Employing the classical-statistical approach, we simulate the real-time dynamics on a lattice using Wilson fermions with mass m at gauge coupling g. It is shown that quantitative properties of the massless Schwinger model are emerging in the limit of large g/m. We investigate two scenarios corresponding to opposite charges which are either held fixed or moving back-to-back along the light cone, as employed in effective descriptions for jet energy loss and photon production in the context of heavy-ion collisions. Remarkably, we find that the dynamics is rather well described by the massless limit for a wide range of mass values at fixed coupling. Moreover, our study shows that previous approximate scenarios with external charges on the light cone rather accurately capture the self-consistent dynamics of the energy conserving simulation.

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Section: Qed In 1 + 1 Dimensionsmentioning

confidence: 99%

“…While the massless Schwinger model is analytically solvable, no exact solution is known for massive fermions [1,2,[7][8][9][10][11][12][13][14]. The current quark masses of the light quarks are small compared to the QCD scale.…”

Section: Introductionmentioning

confidence: 99%

Connecting real-time properties of the massless Schwinger model to the massive case

Hebenstreit

Berges

2014

Phys. Rev. D

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“…We also mention that there are some related works with different approaches to the one-flavor lattice Schwinger model, where the density matrix renormalization group or variational matrix-product-state method are employed [20][21][22][23][24]. They are all based on the Hamiltonian lattice gauge theory with the Kogut-Susskind formulation.…”

Section: Introductionmentioning

confidence: 99%

Grassmann tensor renormalization group approach to one-flavor lattice Schwinger model

2014

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We apply the Grassmann tensor renormalization group to the lattice regularized Schwinger model with one-flavor of the Wilson fermion. We study the phase diagram in the ðβ; κÞ plane performing a detailed analysis of the scaling behavior of the Lee-Yang zeros and the peak height of the chiral susceptibility. Our results strongly indicate that the whole range of the phase transition line starting from ðβ; κÞ ¼ ð0.0; 0.380665ð59ÞÞ and ending at ð∞; 0.25Þ belongs to the two-dimensional Ising universality class similar to the free fermion case.

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“…These wave functions go well beyond Gaussian trial states and allow the accurate and efficient calculation of observable quantities. Thus Feynman's objections can already be regarded as having been addressed, in the case where MPS are applied to relativistic QFTs in conjunction with a lattice regulator [10].…”

Section: A New Variational Ansatz: Continuous Matrix Product Statesmentioning

confidence: 99%

Applying the Variational Principle to (1+1)-Dimensional Quantum Field Theories

et al. 2010

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We extend the recently introduced continuous matrix product state (cMPS) variational class to the setting of (1 + 1)-dimensional relativistic quantum field theories. This allows one to overcome the difficulties highlighted by Feynman concerning the variational procedure applied to relativistic theories, and provides a new way to regularize quantum field theories. A fermionic version of the continuous matrix product state is introduced which is manifestly free from fermion doubling and sign problems. We illustrate the power of the formalism with the simulation of free massive Dirac fermions, the Gross-Neveu model, and the Casimir effect. We find that cMPS can capture chiral symmetry breaking with absolute scaling of the chiral parameter, and that boundary effects can be accommodated with modest computational effort.

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Density matrix renormalization group approach to the massive Schwinger model

Cited by 176 publications

References 48 publications

Connecting real-time properties of the massless Schwinger model to the massive case

Connecting real-time properties of the massless Schwinger model to the massive case

Grassmann tensor renormalization group approach to one-flavor lattice Schwinger model

Applying the Variational Principle to (1+1)-Dimensional Quantum Field Theories

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