Truncated Hilbert space approach to the 2d $\phi^{4}$ theory

TL;DR

This paper applies a truncated Hilbert space method to analyze the 2D $\

Contribution

It introduces a numerical approach to study the 2D $\

Findings

Finite volume spectrum determined numerically.

Infinite volume masses and scattering matrices extracted.

Critical point confirmed in the Ising universality class.

Abstract

We apply the massive analogue of the truncated conformal space approach to study the two dimensional $\phi^{4}$ theory in finite volume. We focus on the broken phase and determine the finite size spectrum of the model numerically. We interpret the results in terms of the Bethe-Yang spectrum, from which we extract the infinite volume masses and scattering matrices for various couplings. We compare these results against semiclassical analysis and perturbation theory. We also analyze the critical point of the model and confirm that it is in the Ising universality class.