Discrete chiral symmetry and mass shift in the lattice Hamiltonian approach to the Schwinger model

Dempsey, Ross; Klebanov, Igor R.; Pufu, Silviu S.; Zan, Bernardo

doi:10.1103/physrevresearch.4.043133

Cited by 23 publications

(26 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is due to the spurious symmetry 𝜓 → 𝛾 5 𝜓, 𝑚 lat /𝑔 → −𝑚 lat /𝑔, and 𝑟 → −𝑟 of the Hamiltonian in Eq. (7).…”

Section: Resultsmentioning

confidence: 99%

“…For the one-flavour Schwinger model with a 𝜃-term and staggered fermions, Ref. [7] recently showed that this lattice model receives an additive mass renormalization given by 𝑚 𝑟 /𝑔 = 𝑚 lat /𝑔 + 1/(8 √ 𝑥). This prediction was derived by enforcing a discrete spurious chiral symmetry on the staggered-fermion lattice with periodic boundary conditions and 𝑚 𝑟 /𝑔 = 0, which is given by a translation of one site followed by a shift of 𝜃 by 𝜋.…”

Section: A Staggered Fermionsmentioning

confidence: 99%

“…Hence, while the main text focuses on Wilson fermions, in Appendix A we consider staggered fermions and compute their mass shift in the Schwinger model to compare it to the recent theoretical predictions in Ref. [7].…”

Section: Introductionmentioning

confidence: 99%

“…Figure 5: Electric field density F /𝑔 as a function of the lattice mass 𝑚 lat /𝑔 using Kogut-Susskind staggered fermions, for different volumes 𝑁/ √ 𝑥.The vertical purple dashed line is the theoretical prediction of Ref [7]…”

mentioning

confidence: 96%

See 3 more Smart Citations

Mass Renormalization of the Schwinger Model with Wilson and Staggered Fermions in the Hamiltonian Lattice Formulation

Angelides¹,

Funcke²,

Jansen³

et al. 2023

Proceedings of the 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022)

View full text Add to dashboard Cite

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 𝜃-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 𝜃-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.

show abstract

“…This is due to the spurious symmetry 𝜓 → 𝛾 5 𝜓, 𝑚 lat /𝑔 → −𝑚 lat /𝑔, and 𝑟 → −𝑟 of the Hamiltonian in Eq. (7).…”

Section: Resultsmentioning

confidence: 99%

Section: A Staggered Fermionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 96%

See 2 more Smart Citations

Mass Renormalization of the Schwinger Model with Wilson and Staggered Fermions in the Hamiltonian Lattice Formulation

Angelides¹,

Funcke²,

Jansen³

et al. 2023

Proceedings of the 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022)

View full text Add to dashboard Cite

show abstract

“…2In the conference, T. Angelides and E. Itou told me that a work[49] for chiral symmetry violation in the Schwinger model with the staggered fermion, but here we report original results as in the conference since results do not change qualitatively. This formalism has an additive mass renormalization.…”

mentioning

confidence: 96%

T-mu phase diagram using classical-quantum hybrid algorithm

Tomiya¹

2023

Proceedings of the 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022)

View full text Add to dashboard Cite

We study the Schwinger model at finite temperature and density using a variational algorithm for near-term quantum devices. We adapt 𝛽-VQE, a classical-quantum hybrid algorithm with a neural network, to evaluate thermal and quantum expectation values and study the phase diagram for the massless Schwinger model along with the temperature and density. By comparing the exact variational free energy, we find that the variational algorithm works for the Schwinger model for 𝑇 > 0 and 𝜇>0. As a result, we obtain a qualitative picture of the phase diagram for the massless Schwinger model.

show abstract

RG flows in 2d QCD

Delmastro,

Gomis

2023

J. High Energ. Phys.

View full text Add to dashboard Cite

2d QCD, Yang-Mills theory with gauge group G and massless quarks in representations (Rℓ, Rr) of G, flows in the infrared to a CFT or a TQFT depending on whether spectrum is gapless or gapped. We identify the infrared effective theory and construct the explicit RG flow map between the QCD operators in the UV and the IR, in particular identifying which operators create massive excitations and decouple in the IR, and those that create massless excitations or vacua and remain as nontrivial IR operators. We determine the exact scaling dimensions of the QCD operators that remain in the IR, which generically acquire large anomalous dimensions. We also study QCD deformed by various operators in the ultraviolet (such as mass terms or four-fermi interactions), and determine the theory that emerges at low energies. We conjecture and provide some evidence for QCD deformed by various operators developing a nonperturbative fermion condensate that dynamically breaks the gauge symmetry G, thus explicitly realizing an old idea known as “tumbling” in an exactly soluble setting.

show abstract

Discrete chiral symmetry and mass shift in the lattice Hamiltonian approach to the Schwinger model

Cited by 23 publications

References 50 publications

Mass Renormalization of the Schwinger Model with Wilson and Staggered Fermions in the Hamiltonian Lattice Formulation

Mass Renormalization of the Schwinger Model with Wilson and Staggered Fermions in the Hamiltonian Lattice Formulation

T-mu phase diagram using classical-quantum hybrid algorithm

RG flows in 2d QCD

Contact Info

Product

Resources

About