Related papers: More about the Grassmann tensor renormalization gr…
We investigate composite models of gravity and explore how dynamical tensor fields can emerge within the functional renormalization group framework. We consider two prototype models: a fermionic theory and a scalar theory. In both cases, an…
We present a unified framework to describe lattice gauge theories by means of tensor networks: this framework is efficient as it exploits the high amount of local symmetry content native of these systems describing only the gauge invariant…
We formulate lattice fermions in a way that encompasses Wilson fermions as well as the static and non-relativistic approximations. In particular, we treat $m_qa$ systematically ($m_q$ is the fermion mass) showing how to understand the…
We present a new tensor network algorithm for calculating the partition function of interacting quantum field theories in 2 dimensions. It is based on the Tensor Renormalization Group (TRG) protocol, adapted to operate entirely at the level…
A compact general integral formula is derived from which the fermionic contribution to the one-loop coefficient in the perturbative expansion of the MSbar coupling in powers of the bare lattice coupling can be extracted. It is seen to…
We systematically examine various proposals which aim at increasing the accuracy in the determination of the renormalization of two-fermion lattice operators. We concentrate on three finite quantities which are particularly suitable for our…
Making a combined use of bosonization and fermionization techniques, we build nonlocal transformations between dual fermion operators, describing junctions of strongly interacting spinful one-dimensional quantum wires. Our approach allows…
A perturbative study of a general class of lattice Dirac operators is reported, which is based on an algebraic realization of the Ginsparg-Wilson relation in the form $\gamma_{5}(\gamma_{5}D)+(\gamma_{5}D)\gamma_{5} =…
We present our progress in the non-perturbative O(a) improvement and renormalization of tensor currents in three-flavor lattice QCD with Wilson-clover fermions and tree-level Symanzik improved gauge action. The mass-independent O(a)…
We introduce fermionic neural network field theories via Grassmann-valued neural networks. Free theories are obtained by a generalization of the Central Limit Theorem to Grassmann variables. This enables the realization of the free Dirac…
We consider the two-dimensional N=(2,2) Wess-Zumino model with a cubic superpotential at weak and intermediate couplings. Refined algorithms allow for the extraction of reliable masses in a region where perturbation theory no longer…
We construct a hierarchy of lattice fermions, where the coarser lattice Dirac operator is the Schur complement of the block UL decomposition of the finer lattice operator. We show that the construction is an exact gauged renormalisation…
We give a general derivation of Ginsparg-Wilson relations for both Dirac and Majorana fermions in any dimension. These relations encode continuous and discrete chiral, parity and time reversal anomalies and will apply to the various classes…
The lattice Wess-Zumino model written in terms of the Ginsparg-Wilson relation is invariant under a generalized supersymmetry transformation which is determined by an iterative procedure in the coupling constant. By studying the associated…
A generalized idea of gauge invariance, that embodies into the Wilson lines the spin-dependent Pauli term $\sim F^{\mu\nu}[\gamma_\mu, \gamma_\nu]$, is applied to set up a new framework for the operator definition of…
We describe an algebraic algorithm which allows to express every one-loop lattice integral with gluon or Wilson-fermion propagators in terms of a small number of basic constants which can be computed with arbitrary high precision. Although…
Differential structure of lattices can be defined if the lattices are treated as models of noncommutative geometry. The detailed construction consists of specifying a generalized Dirac operator and a wedge product. Gauge potential and field…
Results on the computational efficiency of 2-flavor staggered Wilson fermions compared to usual Wilson fermions in a quenched lattice QCD simulation on $16^3\times32$ lattice at $\beta=6$ are reported. We compare the cost of inverting the…
We consider a lattice regularization, preserving Ward Identities (WI) and with a Wilson term, of the Massive QED$_2$, describing a fermion with mass $m$ and charge $\mathsf{e}$ interacting with a vector field with mass $M$, in the regime…
We study a systematic improvement of perturbation theory for gauge fields on the lattice [hep-lat/0606001]; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method,…