Student Workshop Integrability 2023

Formal begin of workshop. Introduction to the venue, schedule and giving other important information.

The presence of unconventional symmetries in quantum systems can result in ergodicity breaking and the prevention of the usual thermalization process. One example is the class of Hilbert space fragmented models which possess an exponentially growing number of kinematically disconnected sectors in the Hilbert space. The phenomenon originates from a symmetry algebra of similarly increasing...

We investigate finite temperature spin transport in one spatial dimension by considering the spin-spin correlation function of the Hubbard model in the limiting case of infinitely strong repulsion. We find that in the absence of bias the transport is diffusive, and derive the spin diffusion constant. Our approach is based on asymptotic analysis of a Fredholm determinant representation, which...

It is well established that the large-scale behaviour of integrable models is captured by Generalized Hydrodynamics (GHD). Inserting an impurity into an integrable model typically breaks integrability and therefore its effect is hard to analyse analytically. In this talk I will first briefly introduce a GHD viewpoint on impurities: An impurity is given by a boundary condition in the GHD...

The sine-Gordon field theory is a paradigmatic integrable model that shows up in the most diverse contexts, emerging as the low-energy description of a wealth of systems. Depending on the experimental platform, the sine-Gordon realization may be close to its classical limit: this is the case, for example, in the interference pattern of two weakly-coupled quasicondensates, as it is realized in...

The theory of Generalized Hydrodynamics (GHD) was introduced in order to describe the non-equilibrium transport properties of integrable quantum systems. It builds on the (infinitely many) continuity equations, that can be written for the conserved quantities present in these systems. Even though GHD itself does not rely on particle conservation on a fundamental level, all previous works...

Random tiling problems, or perfect matchings, constitute a certain class of exactly solvable models studied by both mathematicians and mathematical-physicists since the 20-th century. These models can be viewed as a playground where some universal behaviours take place, and they are particularly interesting as much for their links with other statistical models as for their rich mathematical...

We consider the four-vertex model, which is a special case of the six-vertex model in which two vertices are set to zero. Under specific choices of fixed boundary conditions, this model exhibits spatial phase separation, between frozen and disordered regions, sharply separated by a smooth curve, known as arctic curve. The most interesting aspect of the four-vertex model is that, even though it...

In this talk, we are interested in an integrable spin-1 XYZ chain with twisted boundary conditions. We show that the XYZ Hamiltonian possesses the remarkably simple eigenvalue E=0. In some regime, it is conjectured to be the ground-state eigenvalue. Moreover, we express a sum rule involving the zero-energy states in terms of special polynomials. These polynomials have connections to other...

We study reduced density matrices of the integrable critical RSOS
model in a particular topological sector containing the ground state.
Similar as in the spin-$1/2$ Heisenberg model correlation functions of this model on
short segments can be `factorized': they are completely determined by
a single nearest-neighbour two-point function $\omega$ capturing the
dependence on the system size...

In this talk, we will discuss a large class of Interaction-Round-a-Face (IRF) solvable lattice models that are based on the symmetry algebras of WZW models, namely, the affine Lie algebras $\widehat{\mathfrak{su}}(n)$, $\widehat{\mathfrak{so}}(2n+1)$, $\widehat{\mathfrak{sp}}(n)$, $\widehat{\mathfrak{so}}(2n)$, and ${\hat{G}}_2$ (studied by Jimbo et al., and Kuniba, respectively). We have derived a general...

Novel paradigms of ergodicity breaking have been mushrooming in recent years, most notably in the form of quantum many-body scars. Here I present yet another mechanism of weak ergodicity breaking, in a partially integrable spin chain. Breakdown of integrability in the generic subspaces is manifested with the violation of the Yang-Baxter equation for scattering matrices, but we were...

Spin transport in the paramagnetic XXZ model exhibits simultaneous ballistic and diffusive transport at all non-zero temperatures, which stems from the partial conservation of the local spin current. At T=0 the absence of Bethe bounds states, or strings, yields purely ballistic spin transport, however investigations at non-zero temperatures suggest that the Bethe strings play a key role. High...

A hallmark of integrable systems is the purely elastic scattering of their excitations. Such systems posses an extensive number of local conserved charges, leading to the conservation of the number of scattered excitations, as well as their set of individual momenta. In this talk, I will show that inelastic decay can nevertheless be observed in circuit QED realizations of integrable boundary...

We consider the reformulation the sigma-models as a generalized Gross-Neveu models. In fact, this representation crucially simplifies the analisys of quantum aspects of sigma-models. We show, as simplest application, that in this formulation the derivation of the $\beta$-function of the sigma-models reduces to ordinary calculation of Feynman diagrams (as in ${\varphi }^4$ model), while in the usual...

We study ${\mathcal{W}}_3$ toroidal conformal blocks for degenerate primary fields in AdS/CFT context.
In the large central charge limit ${\mathcal{W}}_3$ algebra reduces to ${\mathfrak{sl}}_3$ algebra and ${\mathfrak{sl}}_3$ blocks are defined as contributions to ${\mathcal{W}}_3$ blocks coming from the generators of ${\mathfrak{sl}}_3$ subalgebra.
We consider the construction of ${\mathfrak{sl}}_3$...

Several one-dimensional models (both relativistic and
non-relativistic) can be solved - at least numerically - by a linear,
thermodynamic Bethe ansatz-like integral equation in specific
settings. Excellent examples are the nonlinear sigma models in an
external field coupled to a conserved charge or the
Lieb-Liniger/Gaudin-Yang models for different couplings. In these
scenarios, it is...

We consider the dynamics of a one-dimensional quantum system in the presence of a localized defect. We prepare the system in a short-range entangled state, we let it evolve ballistically, and we study the entanglement across the defect. Linear growth of the entanglement entropy is observed, whose slope depends both on the scattering properties of the defect and the initial state. The protocol...

In this talk I will present the results obtained with my supervisor Dr. Olalla Castro-Alvaredo and other collaborators on the symmetry resolution of entanglement measures in excited states of (1+1)d massive integrable quantum field theory (IQFT). This work generalises the results known to hold for excited states of massive IQFT with no internal symmetry to the case in which the theory enjoys...

The concept of space-evolution (or space-time duality) has emerged as a promising approach for studying quantum dynamics. The basic idea involves exchanging the roles of space and time and evolving the system using a space transfer matrix whose fixed points, also known as influence matrices, describe the interaction of the rest of the system acting as a bath on a subsystem. To evaluate the...

The Floquet Baxterization was introduced as a bridge between quantum integrable models and quantum circuits. In this work we revisit the Floquet Baxterization extending it to graded $\mathbf{R}$ matrices, introducing an integrable supersymmetric brick-wall quantum circuit. The brick-wall circuit is made up by the $\mathbf{S}$-matrix of a supersymmetric particle theory in 1+1 dimensions as...

We consider the spin-1/2 XXX chain weakly perturbed away from integrability by an isotropic next-to-nearest neighbor exchange interaction. Recently, it was conjectured that this model possesses an infinite tower of quasiconserved integrals of motion (charges) [D. Kurlov et al., Phys. Rev. B 105, 104302 (2022)]. In this work we first test this conjecture by investigating how the norm of the...

We introduce and discuss dynamical universality of charge fluctuations in charged single-file systems. The full counting statistics of such systems out of equilibrium generically undergoes first and second order dynamical phase transitions, while equilibrium typical fluctuations are given by a universal non-Gaussian distribution. Similar phenomenology of dynamical criticality is observed in...

Out of equilibrium dynamics of integrable systems have been intensively studied in the past 20 years. However, a full characterisation of time evolution of an integrable field theory after a quantum quench is still missing. We investigate many processes occurring during relaxation towards a steady state and describe them in terms of analytical properties of form factors of operators in the...

The domain wall melting offer a paradigmatic example of an out-of-equilibrium problem. In the past years the application of many techniques has made possible to investigate the entanglement properties of this problem, by allowing the computation of the entanglement entropies. In this work we move forward, by deriving the Entanglement Hamiltonian (the logarithm of the reduced density matrix) in...

The study of the dynamics of entanglement measures after a quench has become a very active area of research in the last two decades, motivated by the development of experimental techniques. However, exact results in this context are available in only very few cases. In this talk, I present the results of a work done in collaboration with Gilles Parez, in which we provide the proof of the...

The study of symmetric space sigma models and their integrable Yang-Baxter deformations in the context of the AdS/CFT correspondence has led to many important results. However, the quantization of these models remains a challenging problem. To gain new insights into the quantum structure of these models, we propose to study Yang-Baxter deformations of the flat space string. The advantage of...

We consider the problem of the development of steady states in one-dimensional Bose gas tubes modelled by the integrable Lieb-Liniger model. The tubes are weakly coupled to one another through a density-density interaction, which weakly breaks the integrability of the system. We analyze this development through a Boltzmann collision integral approach. We argue that when the leading order of...