Relativistic continuous matrix product states for quantum fields without cutoff

Abstract

I introduce a modification of continuous matrix product states (CMPS) that makes them adapted to relativistic quantum field theories (QFT). These relativistic CMPS can be used to solve genuine 1+1 dimensional QFT without UV cutoff and directly in the thermodynamic limit. The main idea is to work directly in the basis that diagonalizes the free part of the model considered, which allows to fit its short distance behavior exactly. This makes computations slightly less trivial than with standard CMPS. However, they remain feasible and I present all the steps needed for the optimization. The asymptotic cost as a function of the bond dimension remains the same as for standard CMPS. I illustrate the method on the self-interacting scalar field, a.k.a. the ${\varphi }_2^4$ model. Aside from providing unequaled precision in the continuum, the numerical results obtained are truly variational, and thus provide rigorous energy upper bounds.

v2 - major update on the algorithm v1 - 14 pages - a shorter companion article in the same posting, "Variational method in relativistic quantum field theory without cutoff" presents the results more succinctly , without the details of some computations

References in corpus (7)

• Continuous Matrix Product States for Quantum Fields
• Approximating Gibbs states of local Hamiltonians efficiently with PEPS
• Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States
• An improved lattice measurement of the critical coupling in phi^4_2 theory
• High-Precision Calculations in Strongly Coupled Quantum Field Theory with Next-to-Leading-Order Renormalized Hamiltonian Truncation
• Computing energy density in one dimension
• Variational method in relativistic quantum field theory without cutoff

Cited by in corpus (5)

• Towards a nonperturbative construction of the $S$-matrix
• Approximating Relativistic Quantum Field Theories with Continuous Tensor Networks
• Variational method in relativistic quantum field theory without cutoff
• Entanglement Renormalization of the class of Continuous Matrix Product States
• Symmetries and field tensor network states