DMRG study of the higher-charge Schwinger model and its 't Hooft anomaly

Abstract

The charge-$q$ Schwinger model is the $(1+1)$-dimensional quantum electrodynamics (QED) with a charge-$q$ Dirac fermion. It has the ${\mathbb{Z}}_q$ $1$-form symmetry and also enjoys the ${\mathbb{Z}}_q$ chiral symmetry in the chiral limit, and there is a mixed 't Hooft anomaly between those symmetries. We numerically study the charge-$q$ Schwinger model in the lattice Hamiltonian formulation using the density-matrix renormalization group (DMRG). When applying DMRG, we map the Schwinger model to a spin chain with nonlocal interaction via Jordan-Wigner transformation, and we take the open boundary condition instead of the periodic one to make the Hilbert space finite-dimensional. When computing the energy density or chiral condensate, we find that using local operators significantly reduces the boundary effect compared with the computation of corresponding extensive quantities divided by the volume. To discuss the consequence of the 't Hooft anomaly, we carefully treat the renormalization of the chiral condensates, and then we confirm that Wilson loops generate the discrete chiral transformations in the continuum limit.

33 pages, 12 figures

References in corpus (7)

• Generalized Global Symmetries
• Grassmann Tensor Renormalization Group Approach to One-Flavor Lattice Schwinger Model
• Vacuum structure of bifundamental gauge theories at finite topological angles
• Abelian gauge theories on the lattice: $\theta$-terms and compact gauge theory with(out) monopoles
• Classically emulated digital quantum simulation for screening and confinement in the Schwinger model with a topological term
• Fractional $\theta$ angle, 't Hooft anomaly, and quantum instantons in charge-$q$ multi-flavor Schwinger model
• Semiclassics with 't Hooft flux background for QCD with $2$-index quarks

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• End-to-end complexity for simulating the Schwinger model on quantum computers
• Monopole-vortex continuity of $\mathcal{N}=1$ super Yang-Mills theory on ${\mathbb{R}}^2\times S^1\times S^1$ with 't Hooft twist