Related papers: The sign problem and Abelian lattice duality
We discuss recent developments for exact reformulations of lattice field theories in terms of worldlines and worldsheets. In particular we focus on a strategy which is applicable also to non-abelian theories: traces and matrix/vector…
We present a solution to the sign problem in a class of particle-hole symmetric Hamiltonian lattice fermion models on bipartite lattices using the idea of fermion bags. The solution remains valid when the particle-hole symmetry is broken…
We consider the fermion spectrum in the strong coupling vortex phase of a lattice fermion-scalar model with a global $U(1)_L\times U(1)_R$, in 2D, in the context of a recently proposed two-cutoff lattice formulation. The fermion doublers…
Recently a class of supersymmetric gauge theories have been successfully implemented on the lattice. However, there has been an ongoing debate on whether lattice versions of some of these theories suffer from a sign problem, with…
It has been a long-standing open problem to construct a general framework for relating the spectra of dual theories to each other. Here, we solve this problem for the case of one-dimensional quantum lattice models with symmetry-twisted…
We discuss a general framework for the realization of a family of abelian lattice gauge theories, i.e., link models or gauge magnets, in optical lattices. We analyze the properties of these models that make them suitable to quantum…
We investigate the possible classification of zero-temperature spin-gapped phases of multicomponent electronic systems in one spatial dimension. At the heart of our analysis is the existence of non-perturbative duality symmetries which…
The solutions that describe the motion of the classical simple pendulum have been known for very long time and are given in terms of elliptic functions, which are doubly periodic functions in the complex plane. The independent variable of…
A method for implementing non-Abelian duality on string backgrounds is given. It is shown that a direct generalisation of the familiar Abelian duality induces an extra local symmetry in the gauge invariant theory. The non-Abelian isometry…
Wegner duality is essential for Z2 lattice gauge theory, yet the duality on non-trivial topologies has remained implicit. We extend Wegner duality to arbitrary topology and dimension, obtaining a new class of Ising models, in which topology…
We study U(1) gauge theories with a modified Villain action. Such theories can naturally be coupled to electric and magnetic matter, and display exact electric-magnetic duality. In their simplest formulation without a $\theta$-term, such…
The $SU(3)\otimes SU(2) \otimes U(1)$ standard model maps smoothly onto a conventional lattice gauge formulation, including the parity violation of the weak interactions. The formulation makes use of the pseudo-reality of the weak group and…
We introduce the basics of the nonabelian duality transformation of SU(N) or U(N) vector-field models defined on a lattice. The dual degrees of freedom are certain species of the integer-valued fields complemented by the symmetric groups'…
The study of periodic solutions with constant sign in the Abel equation of the second kind can be made through the equation of the first kind. This is because the situation is equivalent under the transformation $x\mapsto x^{-1}$, and there…
We study a three-dimensional abelian lattice model in which the analogue of a theta term can be defined. This term is defined by introducing a neutral scalar field and its effect is to couple magnetic monopoles to the scalar field and…
Quantum link models provide an alternative non-perturbative formulation of Abelian and non-Abelian lattice gauge theories. They are ideally suited for quantum simulation, for example, using ultracold atoms in an optical lattice. This holds…
Starting from a microscopic t-J like model and a SU(2) spin-charge separation ansatz, a relativistic continuum gauge lagrangian is obtained in the vicinity of a nodal point of the Fermi surface. The excitations in the pseudogap phase are…
Lattice four-fermion models containing $N$ flavors of staggered fermions, that are invariant under $Z_2$ and U(1) chiral symmetries, are known to suffer from sign problems when formulated using the auxiliary field approach. Although these…
We propose an exact map from commuting lattice spin systems with gauge interactions to fermionic models in an arbitrary number of dimensions.
We introduce a generalization of conventional lattice gauge theory to describe fracton topological phases, which are characterized by immobile, point-like topological excitations, and sub-extensive topological degeneracy. We demonstrate a…