January 18, 2025
We investigate the implications of the quantized vectorial and axial charges in the lattice Hamiltonian of multi-flavor staggered fermions in $(1+1)$ dimensions. These lattice charges coincide with those of the $U(1)_V$ and $U(1)_A$ global symmetries of Dirac fermions in the continuum limit, whose perturbative chiral anomaly matches the non-Abelian Onsager algebra on the lattice. In this note, we focus on the lattice models that flow to continuum quantum field theories of Dirac fermions that are free from the perturbative chiral anomaly between $U(1)_V$ and $U(1)_A$. In a lattice model that flows to two Dirac fermions, we identify quadratic Hamiltonian deformations that can gap the system while fully preserving both the vectorial and axial charges on the lattice. These deformations flow to the usual symmetry-preserving Dirac mass terms in the continuum. Additionally, we propose a lattice model that flows to the chiral fermion $3-4-5-0$ model in the continuum by using these lattice charges, and we discuss the multi-fermion interactions that can generate a mass gap in the paradigm of symmetric mass generation.
Similar papers 1
September 18, 2024
In the 1+1D ultra-local lattice Hamiltonian for staggered fermions with a finite-dimensional Hilbert space, there are two conserved, integer-valued charges that flow in the continuum limit to the vector and axial charges of a massless Dirac fermion with a perturbative anomaly. Each of the two lattice charges generates an ordinary U(1) global symmetry that acts locally on operators and can be gauged individually. Interestingly, they do not commute on a finite lattice, but thei...
November 25, 1992
The staggered fermion approach to build models with chiral fermions is briefly reviewed. The method is tested in a U(1) model with axial vector coupling in two and four dimensions.
August 10, 1993
We investigate a proposal for the construction of models with chiral fermions on the lattice using staggered fermions. In this approach the gauge invariance is broken by the coupling of the staggered fermions to the gauge fields. Motivated by previous results in the non-gauge invariant massive Yang-Mills theory and certain gauge-fermion models we aim at a dynamical restoration of the gauge invariance in the full quantum model. If the gauge symmetry breaking is not too severe,...
October 5, 2020
We describe a proposal for constructing a lattice theory that we argue may be capable of yielding free Weyl fermions in the continuum limit. The model employs reduced staggered fermions and uses site parity dependent Yukawa interactions of Fidkowski-Kitaev type to gap a subset of the lattice fermions without breaking symmetries. The possibility for such symmetric mass generation is tied to the cancellation of certain discrete anomalies arising in the continuum limit. The latt...
November 30, 1993
We investigate a proposal for the construction of models with chiral fermions on the lattice using staggered fermions. In this approach the gauge invariance is broken by the coupling of the staggered fermions to the gauge fields. We aim at a dynamical restoration of the gauge invariance in the full quantum model. If the gauge symmetry breaking (SB) is not too severe, this procedure could lead in the continuum limit to the desired gauge invariant chiral gauge theory.
July 29, 2013
A non-perturbative lattice regularization of chiral fermions and bosons with anomaly-free symmetry $G$ in 1+1D spacetime is proposed. More precisely, we ask "whether there is a local short-range quantum Hamiltonian with a finite Hilbert space for a finite system realizing onsite symmetry $G$ defined on a 1D spatial lattice, such that its low energy physics produces a 1+1D anomaly-free chiral matter theory of symmetry $G$?" In particular, we propose that the 3$_L$-5$_R$-4$_L$-...
October 19, 2020
It is generally believed that the 1+1D model for a single chiral fermion does not exist by itself alone on lattice. The obstruction to such a lattice realization is the failure to reproduce the quantum anomalies of a chiral fermion in continuum. The conventional way to escape is to associate the anomalous 1d system with a 2d bulk, which is in a topologically non-trivial state, as the boundary of the latter. In this paper, we propose a 1+1D chiral fermion model on 1d spatial l...
June 26, 2000
The vectorlike doubling of low-energy excitations is in fact a natural consequence of the pair-production around the zero-energy (E=0) due to the quantum field fluctuations of the lattice regularized vacuum. On the 1+1 dimensional lattice, we study an anomaly-free chiral model (11112) of four left-movers and one right-mover with strong interactions. Exact computations of relevant S-matrices illustrate that for high-momentum states, a negative energy-gap (E<0) develops; the bo...
October 18, 1997
We revisit the strong coupling limit of the Schwinger model on the lattice using staggered fermions and the hamiltonian approach to lattice gauge theories. Although staggered fermions have no continuous chiral symmetry, they posses a discrete axial invari ance which forbids fermion mass and which must be broken in order for the lattice Schwinger model to exhibit the features of the spectrum of the continuum theory. We show that this discrete symmetry is indeed broken spontane...
November 28, 2001
We present a new staggered discretization of the Dirac operator. Doubling gives only a doublet of Dirac fermions which we propose to interpret as a physical (lepton or quark) doublet. If coupled with gauge fields, an $(1+\gamma^5)$ chiral interaction appears in a natural way. We define a generalization for curved background which does not require tetrad variables. The approach suggests a natural explanation for the three fermion families.