Related papers: New Numerical Method for Fermion Field Theory
Microscopic models of classical degrees of freedom coupled to non-interacting fermions occur in many different contexts. Prominent examples from solid state physics are descriptions of colossal magnetoresistance manganites and diluted…
This thesis addresses a fundamental problem in deformation quantization: the difficulty of calculating the star-exponential, the symbol of the evolution operator, due to convergence issues. Inspired by the formalism that connects the…
We have extended the perturbative expansion method around the Gaussian effective action to the fermionic field theory, by taking the 2-dimensional Gross-Neveu model as an example. We have computed both the zero temperature and the finite…
In this thesis, we analyze unitary conformal field theories in three dimensional spaces by applying analytic conformal bootstrap techniques to correlation functions of non-scalar operators, in particular Majorana fermions. Via the analysis…
We complete the formulation of the equations of motion of a non-Abelian gauge field coupled to fermions on a finite-element lattice in four space-time dimensions. This is accomplished by a straightforward iterative approach, in which…
This report contains both a review of recent approaches to supersymmetric lattice field theories and some new results on the deconstruction approach. The essential reason for the complex phase problem of the fermion determinant is shown to…
We present a method to compute the Fermi function of the Hamiltonian for a system of independent fermions, based on an exact decomposition of the grand-canonical potential. This scheme does not rely on the localization of the orbitals and…
We introduce the Pad\'e--Z$_2$ (PZ) stochastic estimator for calculating determinants and determinant ratios. The estimator is applied to the calculation of fermion determinants from the two ends of the Hybrid Monte Carlo trajectories with…
In this paper we show that a system of three fermions is exactly solvable for the case of a single-$j$ in the presence of an angular momentum-$J$ pairing interaction. On the basis of the solutions for this system, we obtain new sum rules…
We describe a controllable and unbiased strong-coupling diagrammatic Monte Carlo technique that is applicable to a wide range of fermionic systems and spin models. Unlike previous strong coupling methods that generally rely on the…
We study a tensor network formulation of the two dimensional lattice $\mathcal{N}=1$ Wess-Zumino model with Wilson derivatives for both fermions and bosons. The tensor renormalization group allows us to compute the partition function…
A nonlocal method to obtain discrete classical fields is presented. This technique relies on well-behaved matrix representations of the derivatives constructed on a non--equispaced lattice. The drawbacks of lattice theory like the fermion…
We present an ideal system of interacting fermions where the solutions of the many-body Schroedinger equation can be obtained without making approximations. These exact solutions are used to test the validity of two many-body effective…
Lattice computations in the Hamiltonian formulation have so far mainly focused on staggered fermions. In these proceedings, we study Wilson fermions in the Hamiltonian formulation and propose a new method to determine the resulting mass…
Lattice fermions have well-known difficulties with chiral symmetry. To evade them it is possible to couple continuum fermions to lattice gauge fields, by introducing an interpolation of the latter. Following this line of thinking, this…
I explore computer simulations of the dynamics of small multi-fermion lattice systems. The method is more general, but I concentrate on Hubbard type models where the fermions hop between a small number of connected sites. I use the natural…
We review a recently proposed approach to the problem of alternating signs for fermionic many body Monte Carlo simulations in finite temperature simulations. We derive an estimate for fermion wandering lengths and introduce the notion of…
We consider hamiltonian models representing an arbitrary number of spin $1/2$ fermion quantum fields interacting through arbitrary processes of creation or annihilation of particles. The fields may be massive or massless. The interaction…
Developing numerical exact solvers for open quantum systems is a challenging task due to the non-perturbative and non-Markovian nature when coupling to structured environments. The Feynman-Vernon influence functional approach is a powerful…
An invaluable method for probing the physics of a quantum many-body spin system is a mapping to noninteracting effective fermions. We find such mappings using only the frustration graph $G$ of a Hamiltonian $H$, i.e., the network of…