We present a systematic approach to unitarise the Bethe Ansatz, enabling the construction of quantum circuits that exactly prepare eigenstates of a class of integrable models. The key step is a change of basis in the auxiliary space of the algebraic Bethe Ansatz to the ‘F-basis’, known from the theory of integrable models. The F-basis, which ensures symmetry under exchange of auxiliary qubits,...
While in the general framework of quantum resource theories one typically only distinguishes between operations that can or cannot generate the resource of interest, in a many-body setting one can further characterize quantum operations based on underlying geometrical constraints. For instance, a natural question is to understand the power of resource-generating operations that preserve...
The emergence of hydrodynamics is one of the deepest phenomena in many-body systems. Arguably, the hydrodynamic equations are also the most important tools for predicting large-scale behaviour. Understanding how such equations emerge from microscopic deterministic dynamics is a century-old problem, despite recent progress in fine-tuned integrable systems. Due to the universality of...
Confinement is a central concept in the theory of strong interactions, which leads to the absence of quarks (and gluons) from the spectrum of experimentally observed particles. The underlying mechanism is based on a linear potential, which can also be realised in condensed matter systems. A one-dimensional example with a great analogy to quantum chromodynamics is the mixed-field three-state...
We investigate dynamical quantum phase transitions (DQPTs) in the transverse field Ising model on ensembles of random Erdős-Rényi networks of size $N$. We analytically show that dynamical critical points are independent of the edge generation probability $p$, and matches that of the integrable fully connected network ($p=1$). This is due to the $O(N^{-1/2})$ bound on the overlap between the...
Novel approach to integrable one-dimensional many-body systems with or without interactions is Generalized Hydrodynamics (GHD). According to GHD, excitations in the system can be described by quasi particles. The key postulate of the GHD is the assumption of a mesoscopic scale for time and space (fluid cells) which state maximizes local entropy. GHD provides evolution of the system over large...
The Blume-Capel model, a spin chain system exhibiting a tricritical point described by a conformal field theory with central charge $c=7/10$, serves as a rich framework for studying its thermal perturbation, the $E_7$ integrable quantum field theory. In my work, I investigate both numerical and analytical aspects of the $E_7$ model, aiming to validate theoretical predictions and explore new...
Quantum integrable models possess a sufficiently large number of conserved quantities in involution. As a result, these models often admit mathematical methods that enable the construction of exact solutions, even in the presence of complex physical properties such as nonlinearity and dispersion. Consequently, they are of great interest across various areas of theoretical and mathematical...
I present recent progress in computing finite-temperature dynamical correlation functions in the 1+1 dimensional Ising field theory, an integrable quantum field theory. Leveraging the fact that in the Ising model, the finite-temperature form factor expansion can be recast as a Fredholm determinant, I develop a numerical approach based on evaluating these determinants. This representation is...
We derive a systematic construction for form factors of relevant fields in the thermal perturbation of the tricritical Ising model, an integrable model with scattering amplitudes described by the $E_7$ bootstrap. We find a new type of recursive structure encoding the information in the bound state fusion structure, which fully determines the form factors of the perturbing field and the...
We present results from plaquette models with ground states coming from both linear and nonlinear constraint rules. For the linear case, we study the triangular plaquette spin model, which we also study in the presence of an external longitudinal magnetic field. For the latter case, we study spin models whose ground state constraints come from nonlinear elementary cellular automaton rules. We...
We consider quantum or classical many-body Hamiltonian systems characterized by integrable
contact interactions supplemented by a generic two-body potential, potentially long-range. We
show how the hydrodynamics of local observables is given in terms of a generalised version of Bogoliubov–Born–Green–Kirkwood–Yvon
hierarchy, which we denote as gBBGKY, which is built for the
densities, and...
Generalised Hydrodynamics (GHD) has proven successful to describe thermodynamics and hydrodynamics of integrable systems (See see Castro-Alvaredo, O. et al. Phys. Rev. X 6, 041065 (2016)). These systems present infinitely many constants of motion in involution and thus do not relax to a classical Gibbs Ensemble, but to a Generalised Gibbs Ensemble (GGE), taking into account all these...
Mathematical models of non-abelian anyons can be constructed using the data of fusion categories. In this context anyon species are labelled by objects in the category, and projectors can be constructed which describe the fusion of neighbouring anyons into a third anyon. The boost operator formalism provides a robust way to construct and classify integrable models based on fusion categories....
In this talk, we will discuss [arxiv:2502.19504]: Long-range nonstabilizerness can be defined as the amount of nonstabilizerness which cannot be removed by shallow local quantum circuits (QCs). We study long-range nonstabilizerness in the context of many-body quantum physics, a task with possible implications for quantum-state preparation protocols and implementation of quantum-error...
The study of correlation functions of integrable models at their free fermion points often leads to expressions involving Fredholm determinants of integrable integral operators. This occurs, for example, in dynamical two-point correlation functions of the impenetrable Bose gas, the XY and XX spin chains at finite temperature. In this talk, we address the problem of obtaining the long-time and...
We investigate the entanglement properties of the Quantum Six-Vertex Model on a cylinder, focusing on the Shannon-Renyi entropy in the limit of Renyi order $n = \infty$.
This entropy, calculated from the ground state amplitudes of the equivalent XXZ spin-1/2 chain, allows us to determine the Renyi entanglement entropy of the corresponding Rokhsar-Kivelson wavefunctions, which describe the...
The linear growth of entanglement after a quench from a state with short-range correlations is a universal feature of many body dynamics.
It has been shown to occur in integrable and chaotic systems undergoing either Hamiltonian, Floquet or circuit dynamics and has also been observed in experiments.
The entanglement dynamics emerging from long-range correlated states is far less studied,...
The linear growth of entanglement after a quench from a state with short-range correlations is a universal feature of many body dynamics.
It has been shown to occur in integrable and chaotic systems undergoing either Hamiltonian, Floquet or circuit dynamics and has also been observed in experiments.
The entanglement dynamics emerging from long-range correlated states is far less studied,...
It is widely accepted that local subsystems in isolated integrable quantum systems equilibrate to generalized Gibbs ensembles. Here, we identify a particular class of initial states in interacting integrable models that evade canonical generalized thermalization. Particularly, we demonstrate that in the easy-axis regime of the quantum XXZ chain, pure nonequilibrium initial states that lack...
This poster presents a novel class of subleading Regge trajectories (with non-orthogonal intercepts) in $\mathcal{N}=4$ SYM using the Quantum Spectral Curve (QSC), an integrability-based technique. I show how the standard application of the QSC, valid for leading trajectories, fails for the examined cases, and propose some crucial modifications to the method, which pass non-trivial consistency...
The Lieb-Liniger model is a fundamental example of an interacting integrable system, describing bosons in one dimension with point-like interactions. A key challenge in its study is solving the linear integral equations that govern the rapidity density and its moments. In this talk, I will present a trans-series approach to solving these equations, which systematically encodes both...
In our work, we consider a two-component fermionic system on a lattice with anticorrelated disorder. Due to the locality of interspecies attractive interaction, it turns out that the disorder for composite pairs is supressed. This makes the transport of pairs to be possible. Within our study, we investigate the temperature dependence of particle 'conductivity'.
