Hamiltonian truncation approach to quenches in the Ising field theory

TL;DR

This paper demonstrates that Hamiltonian truncation methods can effectively simulate non-equilibrium dynamics in continuum quantum field theories, specifically analyzing quenches in the 1+1 dimensional Ising model with and without integrability breaking perturbations.

Contribution

It introduces a Hamiltonian truncation approach to study quantum quenches in continuum systems, extending numerical techniques beyond lattice models and capturing low-lying excitation effects.

Findings

Persistent oscillations observed in both phases after quenches.

Low-lying particle excitations dominate the dynamics.

Method enables extraction of mass spectra from quench behavior.

Abstract

In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to simulate. We demonstrate here that Hamiltonian truncation methods can be efficiently applied to this problem, by studying the quantum quench dynamics of the 1+1 dimensional Ising field theory using a truncated free fermionic space approach. After benchmarking the method with integrable quenches corresponding to changing the mass in a free Majorana fermion field theory, we study the effect of an integrability breaking perturbation by the longitudinal magnetic field. In both the ferromagnetic and paramagnetic phases of the model we find persistent oscillations with frequencies set by the low-lying particle excitations not only for small, but even for moderate size quenches. In the ferromagnetic phase these particles are the various non-perturbative confined bound states of the domain wall excitations, while in the paramagnetic phase the single magnon excitation governs the dynamics, allowing us to capture the time evolution of the magnetisation using a combination of known results from perturbation theory and form factor based methods. We point out that the dominance of low lying excitations allows for the numerical or experimental determination of the mass spectra through the study of the quench dynamics.