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We study the stochastic six-vertex model in half-space with generic integrable boundary weights, and define two families of multivariate rational symmetric functions. Using commutation relations between double-row operators, we prove a skew…
We consider the insertion of integrable boundaries for a class of supersymmetric quantum models. The generic conditions for constructing purely bosonic, purely fermionic or mixed type solutions of the graded reflection equation are…
We introduce a new mathematical object, the "fermionant" ${\mathrm{Ferm}}_N(G)$, of type $N$ of an $n \times n$ matrix $G$. It represents certain $n$-point functions involving $N$ species of free fermions. When N=1, the fermionant reduces…
Solving interacting fermionic quantum many-body problems as they are ubiquitous in quantum chemistry and materials science is a central task of theoretical and numerical physics, a task that can commonly only be addressed in the sense of…
We extend the planar Pfaffian formalism for the evaluation of the Ising partition function to lattices of high topological genus g. The 3D Ising model on a cubic lattice, where g is proportional to the number of sites, is discussed in…
This work presents a tensorial approach to constructing data-driven reduced-order models corresponding to semi-discrete partial differential equations with canonical Hamiltonian structure. By expressing parameter-varying operators with…
The Weyl fermion belonging to the real representation of the gauge group provides a simple illustrative example for L\"uscher's gauge-invariant lattice formulation of chiral gauge theories. We can explicitly construct the fermion…
This textbook introduces the basic concepts of the theory of causal fermion systems, a recent approach to the description of fundamental physics. The theory yields quantum mechanics, general relativity and quantum field theory as limiting…
We investigate the simulation of fermionic systems on a quantum computer. We show in detail how quantum computers avoid the dynamical sign problem present in classical simulations of these systems, therefore reducing a problem believed to…
In this work, we characterize the $t$-th order commutants of fermionic Gaussian unitaries and of their particle-preserving subgroup acting on $n$ fermionic modes. These commutants govern Haar averages over the corresponding groups and…
Simulating the properties of many-body fermionic systems is an outstanding computational challenge relevant to material science, quantum chemistry, and particle physics. Although qubit-based quantum computers can potentially tackle this…
Matrix determinants play an important role in data analysis, in particular when Gaussian processes are involved. Due to currently exploding data volumes, linear operations - matrices - acting on the data are often not accessible directly…
Hilbert space operators may be mapped onto a space of ordinary functions (operator symbols) equipped with an associative (but noncommutative) star-product. A unified framework for such maps is reviewed. Because of its clear probabilistic…
In the fermion loop formulation the contributions to the partition function naturally separate into topological equivalence classes with a definite sign. This separation forms the basis for an efficient fermion simulation algorithm using a…
Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by…
We develop methods for systematic construction of superintegrable polynomials in matrix/eigenvalue models. Our consideration is based on a tight connection of superintegrable property of Gaussian Hermitian model and $W_{1 + \infty}$ algebra…
We derive exact form of the piecewise-linear finite element stiffness matrix on general non-uniform meshes for the integral fractional Laplacian operator in one dimension, where the derivation is accomplished in the Fourier transformed…
We obtain the Ward identities and the gauge-dependence of Green's functions in non-Abelian gauge theories by using only the canonical commutation relations and the equations of motion for the Heisenberg operators. The consideration is…
Ab initio studies of atomic nuclei are based on Hamiltonians including one-, two- and three-body operators with very complicated structures. Traditionally, matrix elements of such operators are expanded on a Harmonic Oscillator…
A relevant signal in the quantum domain may manifest as a displacement or a squeezing operator in the bosonic phase space. For a real parameter $\beta$ embedded in such a Gaussian operator, the task of determining if $\beta \in…