Related papers: Snowmass White Paper: Hamiltonian Truncation
Computationally efficient and accurate quantum mechanical approximations to solve the many-electron Schr\"odinger equation are at the heart of computational materials science. In that respect the coupled cluster hierarchy of methods plays a…
We calculate a renormalized Hamiltonian for pure-glue QCD and diagonalize it. The renormalization procedure is designed to produce a Hamiltonian that will yield physical states that rapidly converge in an expansion in free-particle…
Quantum electrodynamics in strong background fields provides an interesting class of problems for classical and quantum simulation. In this paper we formulate simulations of polarization (helicity) flip for a photon colliding with a…
We review recent progress and a number of future directions for applications of effective field theory methods to condensed matter systems broadly defined. Our emphasis is on areas that have allowed a fertile exchange of ideas between high…
Unitarity is a cornerstone of quantum theory, ensuring the conservation of probability and information. Although non-Hermitian Hamiltonians are typically associated with open or dissipative systems, pseudo-Hermitian quantum mechanics shows…
Quantum systems with constraints are often considered in modern theoretical physcics. All realistic field models based on the idea of gauge symmetry are of this type. A partial case of constraints being linear in coordinate and momenta…
The performance of computational methods for many-body physics and chemistry is strongly dependent on the choice of basis used to cast the problem; hence, the search for better bases and similarity transformations is important for progress…
We introduce a new diagonalization method called quasi-sparse eigenvector diagonalization which finds the most important basis vectors of the low energy eigenstates of a quantum Hamiltonian. It can operate using any basis, either orthogonal…
In this introductory article a brief description of Quantum Field Theories (QFT) is presented with emphasis on the distinction between strongly and weakly coupled theories. A case is made for using numerical simulations to solve QCD, the…
The evolution of hard probes in a medium is a complex multiscale problem that significantly benefits from the use of Effective Field Theories (EFTs). Within the EFT framework, we aim to define a series of EFTs in a way that addresses each…
A quantum field theory is described which is a supersymmetric classical model. -- Supersymmetry generators of the system are used to split its Liouville operator into two contributions, with positive and negative spectrum, respectively. The…
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus…
This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these…
Quantum simulation is one of the methods that have been proposed and used in practice to bypass computational challenges in the investigation of lattice gauge theories. While most of the proposals rely on truncating the infinite dimensional…
A novel approach to the Hamiltonian formulation of quantum field theory at finite temperature is presented. The temperature is introduced by compactification of a spatial dimension. The whole finite-temperature theory is encoded in the…
Problems connected with non-Hamiltonian nature of low energy nucleon dynamics in the effective field theory (EFT) of nuclear forces is investigated by using the formalism of the generalized quantum dynamics (GQD) developed in [J. Phys. A,…
We develop methods for computing the effective action at infinite momentum for $1+1d$ QFTs at finite volume which do not rely on the theory having a Lagrangian description. We do this by taking the infinite momentum limit of equal-time…
Microscopically conserving reduced models of many-body systems have a long, highly successful history. Established theories of this type are the random-phase approximation for Coulomb fluids and the particle-particle ladder model for…
The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple…
Quantum field theory (QFT) for interacting many-electron systems is fundamental to condensed matter physics, yet achieving accurate solutions confronts computational challenges in managing the combinatorial complexity of Feynman diagrams,…