Related papers: Fourier transform of fermionic systems and the spe…
The tensor network representation of the ground state of a Bethe chain is analytically obtained and studied in relation to its entanglement distribution. Block entanglement displays a maximum at the interplay between single- and…
We introduce a systematic mathematical language for describing fixed point models and apply it to the study to topological phases of matter. The framework is reminiscent of state-sum models and lattice topological quantum field theories,…
We decompose the counting statistics of many-body interference experiments into contributions associated with distinct irreducible exchange symmetries. To do so, we perform a Fourier transform over the symmetric group $S_N$ on the…
The Jordan-Wigner transformation establishes a duality between $su(2)$ and fermionic algebras. We present qualitative arguments and numerical evidence that when mapping spins to fermions, the transformation makes strong correlation weaker,…
The Jordan-Wigner transformation is a powerful tool for converting systems of spins into systems of fermions, or vice versa. While this mapping is exact, the transformation itself depends on the labeling of the spins. One consequence of…
We discuss a scheme for performing Jordan-Wigner transformation for various lattice fermion systems in two and three dimensions which keeps internal and spatial symmetries manifest. The correspondence between fermionic and bosonic operators…
Jordan-Wigner-type transformations connecting the spin-3/2 operators and two kinds of fermions are derived. A general condition of fermionizability of spins is obtained and a theorem establishing connection between half integer spins and…
As the new results for the massive Thirring model the L-matrix and the algebraic relations for its action angle variables are given. So it is shown most directly that this model which describes self-interacting relativistic Fermions in…
Deep learning techniques have opened a new venue for electronic structure theory in recent years. In contrast to traditional methods, deep neural networks provide much more expressive and flexible wave function ansatz, resulting in better…
We present a constructive approximation framework for analyzing the expressive power of Fourier residual networks in approximating a broad class of one-dimensional functions. Our study covers both piecewise continuous functions -- including…
With the rapid growth of deep learning, there is an increasing availability of open-source models for various tasks. However, single fine-tuned models often fall short of meeting the diverse needs of users. Model merging has thus emerged as…
Once developed for quantum theory, tensor networks have been established as a successful machine learning paradigm. Now, they have been ported back to the quantum realm in the emerging field of quantum machine learning to assess problems…
Recently a Jordan-Wigner transformation was constructed for spinful fermions at S=1/2 spins in one dimension connecting the spin-1/2 operators to genuine spinful canonical Fermi operators. In the presented paper this exact transformation is…
We present a new tensor network algorithm for calculating the partition function of interacting quantum field theories in 2 dimensions. It is based on the Tensor Renormalization Group (TRG) protocol, adapted to operate entirely at the level…
We propose a simple connection between matrix quantum mechanics and tensor networks. This allows us to imbue tensor networks with some interesting additional structure. The geometry of the graph describing the tensor network state is…
The Replica Fourier Transform is the generalization of the discrete Fourier Transform to quantities defined on an ultrametric tree. It finds use in con- junction of the replica method used to study thermodynamics properties of disordered…
We propose a general framework for finding the ground state of many-body fermionic systems by using feed-forward neural networks. The anticommutation relation for fermions is usually implemented to a variational wave function by the Slater…
An approach to the simulation of locally interacting systems is demonstrated and assayed. The proposal is built upon the concept of folding of bosonic modes previously introduced in the context of linear dynamics and can be seen as an…
In this contribution we generalize the classical Fourier Mellin transform [S. Dorrode and F. Ghorbel, Robust and efficient Fourier-Mellin transform approximations for gray-level image reconstruction and complete invariant description,…
We provide an introduction to the Fractional Fourier Transform $\mathcal{F}_{\theta}$ and draw a connection between it and the unit complex number $e^{i\theta}$. Motivated by this, we define an entirely new object associated with any unit…