Related papers: Simulating strongly correlated multiparticle syste…
The low-lying bound states of a microscopic quantum many-body system of $n$ particles and the related physical observables can be worked out in a truncated $n$--particle Hilbert space. We present here a non-perturbative analysis of this…
The energies of low-lying bound states of a microscopic quantum many-body system of particles can be worked out in a reduced Hilbert space. We present here and test a specific non-perturbative truncation procedure. We also show that real…
A new efficient numerical algorithm for interacting fermion systems is proposed and examined in detail. The ground state is expressed approximately by a linear combination of numerically chosen basis states in a truncated Hilbert space. Two…
Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is a numerical technique for solving strongly coupled QFTs, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is…
When seeking a numerical representation of a quantum-mechanical multiparticle problem it is tempting to replace a singular short-range interaction by a smooth finite-range pseudopotential. Finite basis set expansions, e.g.~in Fock space,…
In view of recent experiments on ultra-cold polarized fermions, the zero-range potential approach is generalized to situations where two-body scattering is resonant in the p-wave channel. We introduce a modified scalar product which reveals…
The elastic neutron-${}^3\mathrm{H}$ scattering at intermediate energies is studied using rigorous integral equations solved in the momentum-space partial-wave basis. The four-particle transition operators are expanded into…
The configuration interaction (CI) method for calculating the exact eigenstates of a quantum-mechanical few-body system is problematic when applied to particles interacting through contact forces. In dimensions higher than one the approach…
A simple two-level model is developed and used to test the properties of effective interactions for performing nuclear structure calculations in truncated model spaces. It is shown that the effective many-body interactions sensitively…
Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is an efficient numerical technique to solve strongly coupled QFTs in d=2 spacetime dimensions. Further theoretical developments are needed to increase its accuracy and the range…
A number of problems arise when long-range forces, such as those governed by Bessel functions, are used in particle-particle simulations. If a simple cut-off for the interaction is used, the system may find an equilibrium configuration at…
The development of numerical methods capable of simulating realistic materials with strongly correlated electrons, with controllable errors, is a central challenge in quantum many-body physics. Here we describe how a hybrid between…
A numerical algorithm for studying strongly correlated electron systems is proposed. The groundstate wavefunction is projected out after numerical renormalization procedure in the path integral formalism. The wavefunction is expressed from…
The interacting shell model, a configuration-interaction method, is a venerable approach for low-lying nuclear structure calculations; but it is hampered by the exponential growth of its basis dimension as one increases the single-particle…
For one-dimensional systems with delta-contact interactions, the convergence of the exact-diagonalization method is tested with a basis of harmonic oscillator eigenfunctions with frequency $\Omega$ optimized through the minimization of the…
Background: Ab initio many-body methods have been developed over the past ten years to address mid-mass nuclei... As progress in the design of inter-nucleon interactions is made, further efforts must be made to tailor many-body methods.…
We carry out an interacting shell-model study of binding energies and spectra in the $sd$-shell nuclei to examine the effect of truncation of the shell-model spaces. Starting with a Hamiltonian defined in a larger space and truncating to…
We investigate few-boson systems with resonant interactions in a narrow harmonic trap within an effective theory framework. The size of the model space is identified with the effective theory cutoff. In the universal regime, the…
Nucleon capture cross sections enter various astrophysical processes. The measurement of proton capture on nuclei at astrophysically relevant low energies is a challenge, and theoretical computations in this long-wavelength regime are…
We theoretically investigate the properties of two interacting ultracold highly magnetic atoms trapped in a one-dimensional harmonic potential. The atoms interact via an anisotropic long-range dipole-dipole interaction, which in one…