Related papers: Many-chain Generalization of Gauge-Coupled Fermion…
We present a new approach to some four-fermion lattice field theories which we call the generalized fermion bag approach. The basic idea is to identify unpaired fermionic degrees of freedom that cause sign problems and collect them in 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…
The strongly coupled lattice gauge models with confined fermion and scalar matter fields, which in a certain phase break dynamically a global chiral symmetry, are reconsidered from the point of view of the existence of heavy fermions. If…
The spin-rotationally invariant SU(2) approach to the Hubbard model is extended to accommodate the charge degrees of freedom. Both U(1) and SU(2) gauge transformation are useed to factorize the charge and spin contribution to the original…
We consider a chain of spinful fermions with nearest neighbor hopping in the presence of a $XY$ antiferromagnetic interaction. The $XY$ term is mapped onto a Kitaev chain at half-filling such that displays a bosonic zero mode topologically…
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…
Functional renormalisation group approach is applied to a imbalanced many- fermion system with a short-range attractive force. Composite boson field is introduced to describe the pairing between different flavour fermions. A set of…
Group algebras of permutations have proved highly useful in solving a number of problems in large N gauge theories. I review the use of permutations in classifying gauge invariants in one-matrix and multi-matrix models and computing their…
Junctions of multiple one-dimensional quantum wires of interacting electrons have received considerable theoretical attention as a basic constituent of quantum circuits. While results have been obtained on these models using bosonization…
The supersymmetric generalization of a recently proposed Abelian axial gauge model with antisymmetric tensor matter fields is presented.
SU(2) gauge theory coupled to massless fermions in the adjoint representation is quantized in light-cone gauge by imposing the equal-time canonical algebra. The theory is defined on a space-time cylinder with "twisted" boundary conditions,…
We investigate a model containing two species of one-dimensional fermions interacting via a gauge field determined by the positions of all particles of the opposite species. The model can be solved exactly via a simple unitary…
Electroweak interactions based on a gauge group $\rm SU(3)_L \times U(1)_X$, coupled to the QCD gauge group $\rm SU(3)_c$, can predict the number of generations to be multiples of three. We first try to unify these models within SU(N)…
Gauge theories coupled to fermions in generation are reformulated in a modified version of extended differential geometry with the symbol $\chi$. After discussing several toy models, we will reformulate in our framework the standard model…
We study the problem of axial and gauge anomalies in a reducible theory involving vector and tensor gauge fields coupled in a topological way. We consider that vector and axial fermionic currents couple with the tensor field in the same…
We study quantum spin chains solvable via hidden free fermionic structures. We study the algebras behind such models, establishing connections to the mathematical literature of the so-called ``graph-Clifford'' or ``quasi-Clifford''…
The projective construction (the slave-particle approach) has played an very important role in understanding strongly correlated systems, such as the emergence of fermions, anyons, and gauge theory in quantum spin liquids and quantum Hall…
Quantum entanglement can be an effective diagnostic tool for probing topological phases protected by global symmetries. Recently, the notion of nontrivial topology in critical systems has been proposed and is attracting growing attention.…
We introduce a simple scenario where, by starting with a five-dimensional SU(3) gauge theory, we end up with several 4-D parallel branes with localized fermions and gauge fields. Similar to the split fermion scenario, the confinement of…
We propose quasiperiodic chains with tunable mobility edge physics, as a promising platform for engineering long-range quantum entanglement. Using the generalized Aubry-Andr\'e model, we show that the mobility edges play a key role in…