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.
Highlights
In this work we investigate global quantum quenches in a quantum field theory in one spatial dimension
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
We have demonstrated that for quenches of moderate size within the same phase of the Ising field theory, the truncated fermionic space approach (TFSA) method is able to reproduce the theoretical results for various quantities, including the statistics of work P (W ), the Loschmidt echo L(t), and the expectation values ε(t), σ(t) to a good accuracy
Summary
In this work we investigate global quantum quenches in a quantum field theory in one spatial dimension. Non-integrable systems are expected to relax to a thermal (Gibbs) state, at least for a suitable class of (local, or few-body) observables; the principle underlying thermalisation in closed quantum systems is the Eigenstate Thermalisation Hypothesis (ETH) [19, 20] This leads to some important questions, chief among them is what aspects of integrability are still retained after such a perturbation. As a result of the above situation, in this work we are interested in the effects of integrability breaking in quantum field theory quenches. To address this problem, we adopt a nonperturbative Hamiltonian truncation approach that has been successfully applied to study equilibrium properties of both integrable and non-integrable two-dimensional quantum field theories. Some of the more technical details regarding the cut-off extrapolation and finite size effects, and the description of the meson spectrum in the ferromagnetic phase are relegated to appendices
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