Related papers: Fermionic Wave Functions from Neural-Network Const…
We present a general formalism that allows for the computation of large-order renormalized expansions in the spacetime representation, effectively doubling the numerically attainable perturbation order of renormalized Feynman diagrams. We…
Our understanding of quantum field theory rests largely on explicit and controlled calculations in perturbation theory. Because of this, much recent effort has been devoted to improve our grasp of perturbative techniques on cosmological…
The Gutzwiller projection of fermionic wave functions is a well-established method for generating variational wave functions describing exotic states of matter, such as quantum spin liquids. We investigate the conditions under which a…
Many-body Hilbert space is a functional vector space with the natural structure of an algebra, in which vector multiplication is ordinary multiplication of wave functions. This algebra is finite-dimensional, with exactly $N!^{d-1}$…
From known phase diagram regions of different model Hamiltonians describing strongly correlated systems we deduced new domains of the ground state phase diagram of the same model by an unitary transformation. Different types of extended…
We build the coherent states for a family of solvable singular Schr\"odinger Hamiltonians obtained through supersymmetric quantum mechanics from the truncated oscillator. The main feature of such systems is the fact that their…
Local Hamiltonians of fermionic systems on a lattice can be mapped onto local qubit Hamiltonians. Maintaining the locality of the operators comes at the expense of increasing the Hilbert space with auxiliary degrees of freedom. In order to…
Many quantum algorithms, including recently proposed hybrid classical/quantum algorithms, make use of restricted tomography of the quantum state that measures the reduced density matrices, or marginals, of the full state. The most…
There is no unique and widely accepted definition of the complexity measure (CM) of a many-fermion wave function in the presence of interactions. The simplest many-fermion wave function is a Slater determinant. In shell-model or…
Variations in distinct restricted spaces of wave functions generate distinct density functionals. In particular, angular momentum projected Slater determinants define a new density functional, compatible simultaneously with angular momentum…
We present a model for spectral theory of families of selfadjoint operators, and their corresponding unitary one-parameter groups (acting in Hilbert space.) The models allow for a scale of complexity, indexed by the natural numbers…
We analyse some features of the class of discrete Wigner functions that was recently introduced by Gibbons et al. to represent quantum states of systems with power-of-prime dimensional Hilbert spaces [Phys. Rev. A 70, 062101 (2004)]. We…
In this paper, we show that there is a large class of fermionic systems for which it is possible to find, for any dimension, a finite closed set of eigenoperators and eigenvalues of the Hamiltonian. Then, the hierarchy of the equations of…
We demonstrate a versatile method to create state-dependent optical lattices by applying a magnetic field gradient modulated in time. This allows for tuning the relative amplitude and sign of the tunnelling for different internal states. We…
Variational methods have proven to be excellent tools to approximate ground states of complex many body Hamiltonians. Generic tools like neural networks are extremely powerful, but their parameters are not necessarily physically motivated.…
We propose to describe bulk wave functions of fractional quantum Hall states in terms of correlators of non-unitary b/c-spin systems. These yield a promising conformal field theory analogon of the composite fermion picture of Jain.…
We prove that the Hilbert-Schmidt norm of $k$-particle reduced density matrices of $N$-body fermionic states is bounded by $C_kN^{k/2}$ - matching the scaling behaviour of Slater determinant states. This generalises a recent result of…
A deep-learning approach to optimize the selection of Slater determinants in configuration interaction calculations for condensed-matter quantum many-body systems is developed. We exemplify our algorithm on the discrete version of the…
We develop a Hilbert space framework for a number of general multi-scale problems from dynamics. The aim is to identify a spectral theory for a class of systems based on iterations of a non-invertible endomorphism. We are motivated by the…
Lattice simulations on SU(2) and SU(3) gauge theories with matter fields in the fundamental, adjoint and two index symmetric representations are needed to determine if these theories are near or within the conformal window as required for…