Research

Classically simulating quantum field theories—especially real-time dynamics—remains challenging, yet it is essential for questions spanning cosmology, black-hole and particle physics. This work introduces a new numerical technique that combines Hamiltonian truncation with Tensor-Networks, yielding a tool designed for both low-energy properties and out-of-equilibrium dynamics in continuous QFTs. The method is benchmarked on sine-Gordon ground-state properties and applied to the massive Schwinger model to locate its critical point and to study quench dynamics.

[arXiv:2312.12506]

Why do isolated quantum systems typically “self-thermalize,” and when do they fail? This paper tests the eigenstate thermalisation hypothesis (ETH)—a leading explanation for quantum thermalisation—in a non-integrable relativistic quantum field theory, using Hamiltonian truncation techniques. The key finding is an infinite sequence of exceptional energy eigenstates that behave like quantum many-body scars: they strongly deviate from thermal expectations even at energies where typical states look thermal and are identified as one-quasiparticle eigenstates. Our analysis suggests that in the thermodynamic limit the spectrum fills a wedge between a “quasiparticle line” fixed by relativistic kinematics and the thermal prediction. The result points to a generic mechanism by which strong ETH can be violated in relativistic QFTs that admit a quasiparticle description.

[PRL 2024]

Entanglement is a defining feature of quantum matter and quantum fields, but directly measuring entanglement measures in extended many-body systems is notoriously hard as it typically requires near-complete knowledge of the quantum state. In this experiment, the von Neumann entropy of spatial subsystems is measured in an ultracold-atom simulator of one-dimensional quantum field theories, allowing an experimental test of a fundamental theoretical prediction: in gapped systems at thermal equilibrium, the mutual information between different subsystems obeys an area law, i.e. it scales with the size of their interface, not their volume. Beyond verifying this scaling, the work shows how mutual information depends on temperature and on the separation between subsystems, providing an operational route to quantify correlations and entanglement, a key step toward using cold atoms to probe quantum-field entanglement in the laboratory.

[Nat. Phys. 2023]

Quantum chaos is often diagnosed through universal statistical patterns—especially Random-Matrix-like energy level statistics—but establishing and interpreting such signatures in interacting quantum field theories is subtle. This work studies chaos indicators in several (1+1)D non-integrable QFTs using Hamiltonian truncation to compute spectra and eigenstates with high precision. The level spacings are found to closely follow the Gaussian Orthogonal Ensemble, consistent with chaotic behaviour, and intriguingly this transition occurs already in the perturbative regime. At the same time, the statistics of eigenvector components do not match the naïvely expected Gaussian distribution and appear remarkably robust against changing the model, basis, or increasing the perturbation strength. Together these results sharpen what “quantum chaos” means in QFT settings and show that different chaos diagnostics can behave very differently even within the same theory.

[PRL 2021]

Complete information on the equilibrium behaviour and dynamics of a quantum field theory is given by multipoint correlation functions. However, their theoretical calculation is a challenging problem, even for exactly solvable models. Using the so-called Truncated Conformal Space Approach, we numerically compute correlation functions of the quantum sine-Gordon model, a prototype integrable model of central interest from both theoretical and experimental point of view. We measure deviations from Gaussianity due to interaction, as expressed by the kurtosis of thermal states, and analyse their dependence on temperature, explaining recent experimental observations. 

[PRL 2018]

The expansion of an ultra-cold atomic gas from a confining trap is a common experiment for the study of quantum dynamics. We analytically derive the non-equilibrium dynamics of a hard-core boson gas released from a parabolic trap to a circle, showing that at large times it equilibrates locally to a generalised Gibbs ensemble, a non-thermal statistical ensemble characterised by an extensive number of conserved quantities.

[PRL 2013]

A standard way of bringing a quantum system away from equilibrium is by abruptly changing a dynamical parameter, i.e. by performing what is known as a "quantum quench". Such processes induce complex and highly-energetic excitations into the system. We develop a diagrammatic method for determining the excitation content of quench initial states in integrable quantum field theories from first principles. Our method is essentially based on the form-factor bootstrap, a set of rules dictated by fundamental requirements and consistency criteria applicable to relativistically invariant integrable models.

[Nucl Phys B 2016]

After a “quantum quench”, a sudden parameter change, isolated many-body systems often relax locally to a steady state—but in integrable settings this steady state is expected to be a Generalised Gibbs Ensemble (GGE) rather than an ordinary thermal ensemble. Most analytic checks of this idea had assumed both the initial and post-quench models were essentially noninteracting. This paper tackles a less trivial case: the system starts in an equilibrium state of an interacting model, but after the quench evolves under a noninteracting model. Our work proves that the GGE still correctly describes the long-time values of local observables and correlation functions, unveiling the physical principles underlying this information scrambling mechanism: while for noninteracting initial states the argument relies merely on Wick’s theorem, for generic interacting initial states it follows from the cluster decomposition property, the physically natural requirement that far-apart regions are uncorrelated.

[J Stat Mech 2014]