Related papers: Ising model as Wilson-Majorana Fermions
Lattice gauge theories are a powerful language to theoretically describe a variety of strongly correlated systems, including frustrated magnets, high-$T_c$ superconductors, and topological phases. However, in many cases gauge fields couple…
We show how to compute the exact partition function for lattice statistical-mechanical models whose Boltzmann weights obey a special "crossing" symmetry. The crossing symmetry equates partition functions on different trivalent graphs,…
After briefly reviewing the potential for the $N$-flavor Thirring model, formulated with reducible fermions in 2+1$d$, to exhibit a strongly-coupled UV-stable fixed point where U($2N$) symmetry is spontaneously broken by a fermion bilinear…
The spin-1/2 Ising model on the bow-tie lattice is exactly solved by establishing a precise mapping relationship with its corresponding free-fermion eight-vertex model. Ground-state and finite-temperature phase diagrams are obtained for the…
We develop a Hamiltonian formalism for simulating interacting chiral fermions on the lattice while preserving unitarity and locality and without breaking the chiral symmetry. The fermion doubling problem is circumvented by constructing a…
A method is proposed for exactly calculating the partition function of a rectangular Ising lattice with the presence of a uniform external field. This approach is based on the method of the transfer matrix developed about seventy years ago…
The lattice regularized Schwinger model for one fermion flavor and in the strong coupling limit is studied through its equivalent representation as a restricted 8-vertex model. The Monte Carlo simulation on lattices with torus-topology is…
We describe a 3d analog of the Jordan-Wigner transformation which maps an arbitrary fermionic system on a 3d spatial lattice to a 2-form $\mathbb{Z}_2$ gauge theory with an unusual Gauss law. An important property of this map is that it…
We study the formation of Majorana fermions in honeycomb-lattice structures in the presence of a Zeeman field, Rashba spin-orbit coupling, and in the proximity of an s-wave superconductor. We show that an exact mapping exists between an…
We present numerical methods to solve the Generalized Hartree-Fock theory for fermionic systems in lattices, both in thermal equilibrium and out of equilibrium. Specifically, we show how to determine the covariance matrix corresponding to…
A spin-$\frac{1}{2}$ Kitaev sublattice interacting with a subsystem of spinless fermions is studied on a honeycomb lattice when the fermion band is half filled. The model Hamiltonian describes a topological Kondo lattice with the Kitaev…
We propose and test an algorithm to simulate a lattice system of interacting fermions in two spatial dimensions. The approach is an extension of the entanglement renormalization technique [Phys. Rev. Lett. 99, 220405 (2007)] and the related…
We describe non-relativistic fermions on the lattice (Hubbard model) in the canonical formulation using transfer matrices in fixed fermion number sectors such that the partition function becomes fully factorized in time. By analytically…
We consider two dimensional U(N) QCD on the cylinder with a timelike Wilson line in an arbitrary representation. We show that the theory is equivalent to N fermions with internal degrees of freedom which interact among themselves with a…
We present preliminary numerical results from a lattice study of the two-dimensional O(3) non-linear sigma model. In the continuum this model possesses N=2 supersymmetry. The lattice formulation we use retains an exact (twisted)…
The modular (or entanglement) Hamiltonian correspondent to the half-space-bipartition of a quantum state uniquely characterizes its entanglement properties. However, in the context of lattice models, its explicit form is analytically known…
We describe ground states of correlated electron systems in which the electron fractionalizes into separate quasiparticles which carry its spin and its charge, and into real Majorana fermions which carry its Fermi statistics. Such parent…
We study the two dimensional lattice Thirring model in the presence of a fermion chemical po- tential. Our model is asymptotically free, contains massive fermions that mimic a baryon and light bosons that mimic pions. Hence it is a useful…
It is shown that the Wilson fermion doubling phenomenon on irregular lattices (simplicial complexes) does exist. This means that the irregular (not smooth) zero or soft modes exist. The statement is proved on 4 Dimensional lattice by means…
The surface states in three-dimensional (3D) topological insulators (TIs) can be described by a two-dimensional (2D) continuous Dirac Hamiltonian. However, there exists the Fermion doubling problem when putting the continuous 2D Dirac…