The diagonalization of quantum field Hamiltonians

Abstract

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 or non-orthogonal, and any sparse Hamiltonian, either Hermitian, non-Hermitian, finite-dimensional, or infinite-dimensional. The method is part of a new computational approach which combines both diagonalization and Monte Carlo techniques.

12 pages, 8 figures, new material added

References in corpus (2)

• A non-perturbative analysis of symmetry breaking in two-dimensional phi^4 theory using periodic field methods
• Modal expansions and non-perturbative quantum field theory in Minkowski space

Cited by in corpus (25)

• Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions
• A Cheap Alternative to the Lattice?
• Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions II. The Z_2-Broken Phase and the Chang Duality
• Tensor network analysis of critical coupling in two dimensional ${\varphi }^4$ theory
• A Conformal Truncation Framework for Infinite-Volume Dynamics
• Monte Carlo determination of the critical coupling in ${\varphi }_2^4$ theory
• RG Flow from ${\varphi }^4$ Theory to the 2D Ising Model
• Two-dimensional light-front ${\varphi }^4$ theory in a symmetric polynomial basis
• New MC determination of the critical coupling in ${\varphi }_2^4$ theory
• Introduction to Lightcone Conformal Truncation: QFT Dynamics from CFT Data
• Critical mass renormalization in renormalized phi4 theories in two and three dimensions
• Monte Carlo Hamiltonian from Stochastic Basis
• The renormalized Hamiltonian truncation method in the large $E_T$ expansion
• Simulating scalar field theories on quantum computers with limited resources
• Cut-Off Kinks
• Fast quantum state preparation and bath dynamics using non-Gaussian variational ansatz and quantum optimal control
• Light-front ${\varphi }_{1+1}^4$ theory using a many-boson symmetric-polynomial basis
• Light-front ${\varphi }_2^4$ theory with sector-dependent mass
• Open quantum dynamics with variational non-Gaussian states and the truncated Wigner approximation
• Rényi entropy of quantum anharmonic chain at non-zero temperature
• Light-front versus equal-time quantization in ${\varphi }^4$ theory
• Critical Coupling for Two-dimensional ${\varphi }^4$ Theory in Discretized Light-Cone Quantization
• On computing non-equilibrium dynamics following a quench
• A First Step Towards Effectively Nonperturbative Scattering Amplitudes in the Perturbative Regime
• Nonperturbative dynamics of (2+1)d ${\varphi }^4$-theory from Hamiltonian truncation