Related papers: Lattice fermions with solvable wide range interact…
Using the method of finite differences a scheme is proposed to solve exactly the Klein-Gordon and Dirac free field equations, in a (1+1)-dimensional lattice. The hamiltonian of the Dirac field is translational invariant, hermitian, avoids…
Based upon the lattice Dirac operator satisfying the Ginsparg-Wilson relation, we investigate canonical formulation of massless fermion on the spatial lattice. For free fermion system exact chiral symmetry can be implemented without species…
We define Weyl fermions on a finite lattice in such a way that in the path integral the action is gauge invariant but the functional measure is not. Two variants of such a formulation are tested in perturbative calculation of the fermion…
Exact solutions for local equilibrium and nonequilibrium out-of-time-ordered correlation (OTOC) functions are obtained for a lattice fermion model with on-site interactions, namely the Falicov-Kimball (FK) model, in the large dimensional…
In this paper we present a new solution of the star-triangle relation having positive Boltzmann weights. The solution defines an exactly solvable two-dimensional Ising-type (edge interaction) model of statistical mechanics where the local…
We present an exact analytical solution for quantum strong long-range models in the canonical ensemble by extending the classical solution proposed in [Campa et al., J. Phys. A 36, 6897 (2003)]. Specifically, we utilize the equivalence…
The entanglement of non-complementary regions is investigated in an inhomogeneous free-fermion chain through the lens of the fermionic logarithmic negativity. Focus is on the Krawtchouk chain, whose relation to the eponymous orthogonal…
It is widely believed that the spectral gap above the Fermi sea ground state of lattice free fermions is stable against generic weak interactions. Quite recently, Hastings presented a new interesting idea to prove the stability for Majorana…
We discuss certain quadratic models of spinless fermions on a 1D lattice, and their corresponding spin chains. These were studied by Keating and Mezzadri in the context of their relation to the Haar measures of the classical compact groups.…
In the continuum a skyrmion is a topological nontrivial map between Riemannian manifolds, and a stationary point of a particular energy functional. This paper describes lattice analogues of the aforementioned skyrmions, namely a natural way…
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…
We show how a path integral for reduced K\"{a}hler-Dirac fermions suffers from a phase ambiguity associated with the fermion measure that is an analog of the measure problem seen for chiral fermions. However, unlike the case of chiral…
Spinless fermions on highly frustrated lattices are characterized by a lowest single-particle band which is completely flat. Concrete realizations are provided by the sawtooth chain and the kagome lattice. For these models a real-space…
We study the strong coupling limit of the 2-flavor massless Schwinger model on a lattice using staggered fermions and the Hamiltonian approach to lattice gauge theories. Using the correspondence between the low-lying states of the 2-flavor…
We study the fermion sign problem in a theory of non-relativistic fermions with a spin-independent repulsive interaction. We work in polar co-ordinates in momentum space, which makes it straightforward to keep only the low-energy degrees of…
Lieb-Robinson-type bounds are reported for a large class of classical Hamiltonian lattice models. By a suitable rescaling of energy or time, such bounds can be constructed for interactions of arbitrarily long range. The bound quantifies the…
We present a new exact renormalization approach for quantum lattice models leading to long-range interactions. The renormalization scheme is based on wavelets with an infinite support in such a way that the excitation spectrum at the fixed…
By placing fermions only on the even sites of a lattice, one may halve the momentum spectrum and construct a theory without doublers. The interaction is nonlocal. The fermion propagator is not a sparse matrix, but because the unwanted…
We study lattice fermions from the viewpoint of spectral graph theory (SGT). We find that a fermion defined on a certain lattice is identified as a spectral graph. SGT helps us investigate the number of zero eigenvalues of lattice Dirac…
Proposed is a generalization of Jordan-Wigner transform that allows to exactly fermionize a large family of quantum spin Hamiltonians in dimensions higher than one. The key new steps are to enlarge the Hilbert space of the original model by…