Related papers: Characterization of solvable spin models via graph…
We introduce and study an exactly solvable model of several species of fermions in which particles interact pairwise through a mutual magnetic field; the interaction operates only between particles belonging to different species. After an…
This article provides a method for constructing invariants and semi-invariants of a binary $N$-ic form over a field $k$ characteristics $0$ or $p > N$. A practical and broadly applicable sufficient condition for ensuring nontriviality of…
We study the XX model for quantum spins on the star graph with three legs (i.e., on a Y-junction). By performing a Jordan-Wigner transformation supplemented by the introduction of an auxiliary space we find a Kondo Hamiltonian of fermions,…
We relate a large class of classical spin models, including the inhomogeneous Ising, Potts, and clock models of q-state spins on arbitrary graphs, to problems in quantum physics. More precisely, we show how to express partition functions as…
General dynamic properties like controllability and simulability of spin systems, fermionic and bosonic systems are investigated in terms of symmetry. Symmetries may be due to the interaction topology or due to the structure and…
We have studied free higher spin gauge fields through an investigation of their Hamiltonian dynamics. Over a flat space-time, their Hamiltonian constraints were identified and solved through the introduction of prepotentials, enjoying both…
In this work, building up on [1] we present momentum space Ward identities related to broken higher spin symmetry as an alternate approach to computing correlators of spinning operators in interacting theories such as the quasi-fermionic…
We propose a model of an electrically charged fermion as a regular localized solution of electromagnetic and spinor fields interacting with a physical vacuum, which is phenomenologically described as a logarithmic superfluid. We…
We demonstrate an exact local transformation which maps a purely Fermionic manybody system to a system of spinfull Bosons and spinless Fermions, demonstrating a possible path to a non-Fermi liquid state. We apply this to the half-filled…
We focus on the geometrical reformulation of free higher spin supermultiplets in $4\rm{D},~\mathcal{N}=1$ flat superspace. We find that there is a de Wit-Freedman like hierarchy of superconnections with simple gauge transformations. The…
An exactly solvable model describing the dilute spin-3/2 fermion gas in one-dimensional optical trap is proposed. The diagonalization of the model Hamiltonian is derived by means of the Bethe ansatz method. Exotic spin excitations such as…
We define and study a long-range version of the XX model, arising as the free-fermion point of the XXZ-type Haldane--Shastry (HS) chain. It has a description via non-unitary fermions, based on the free-fermion Temperley--Lieb algebra, and…
We derive a rigorous, quantum mechanical map of fermionic creation and annihilation operators to continuous Cartesian variables that exactly reproduces the matrix structure of the many-fermion problem. We show how our scheme can be used to…
We study the SU(3) gauge theory with twelve flavours of fermions in the fundamental representation as a prototype of non-Abelian gauge theories inside the conformal window. Guided by the pattern of underlying symmetries, chiral and…
We study a few two-dimensional models with massive and massless fermions in the hamiltonian framework and in both conventional and light-front forms of field theory. The new ingredient is a modification of the canonical procedure by taking…
The three-dimensional (3D) Ising model is mapped into a 3D spinless fermionic model by the Jordan-Wigner transformation. The exact solution of the 3D model for spinless fermions is derived analytically by performing a diagonalization…
This review is dedicated to two-dimensional sigma models with flag manifold target spaces, which are generalizations of the familiar $CP^{n-1}$ and Grassmannian models. They naturally arise in the description of continuum limits of spin…
We construct a model of Pauli spin operators with all-to-all 4-local interactions by replacing Majorana fermions in the SYK model with spin operators. Equivalently, we replace fermions with hard-core bosons. We study this model numerically…
We introduce a family of many-body systems of distinguishable continuous-variable particles in which interparticle interactions are set by the adjacency matrix of a graph. The ground-state wavefunction of such systems is of a generalized…
In this work we presented a number of explicit examples for the cubic vertices describing an interaction of massless spin-5/2 field with massive boson and fermion including all hypertransformations necessary for the vertices to be gauge…