Recent advances have introduced deterministic quantum algorithms capable of preparing Bethe states, providing a unitary realization of the Bethe Ansatz. We systematize these developments by demonstrating that such circuits naturally arise from a well-established structure in quantum integrable models: the F-basis. We hope that this approach can help to characterize the computational complexity...
W-states are quantum states possessing both bipartite and multipartite entanglement and are necessary for several relevant quantum algorithms. We propose a protocol to generate them with an arbitrary number of qubits on a Rydberg atoms platform, by exploiting ring (topological) frustration. To validate our state preparation, we develop a new Bayesian state tomography approach that leverage on...
We have initiated a study of dynamical two-point functions of arbitrary local operators in integrable lattice models by means of thermal form factor series. These are obtained as expansions in a basis of eigenstates of an appropriately defined quantum transfer matrix. The latter is different from the transfer matrix that generates the Hamiltonian. The quantum transfer matrix rather is an...
After reviewing quantum integrable models with quantum group symmetry, we focus on the models associated with $D^{(2)}$. We first review the case $D^{(2)}_2$, whose continuum limit is a non-compact CFT that is related to a black hole sigma model. We finally turn to the general case $D^{(2)}_{n+1}$, and present preliminary results of joint work with Holger Frahm, Sascha Gehrmann and Ana Retore...
The symmetry-broken phase of the N=4 super-Yang-Mills theory (SYM) is described by a D3-brane in the bulk of AdS. The D3-brane boundary conditions preserve integrability of the string, opening an avenue for applying boundary Bethe Ansatz to non-perturbative condensates (1pt functions) and possibly other observables on the Coulomb branch of SYM, which break conformal symmetry, generates a mass...
For half a century the critical points of spin glasses in two and three dimensions have been considered out of reach of analytical methods and have been studied numerically. We show how conformal invariance gives exact access to spin glass criticality in two dimensions.
We consider integrable models with $o_{2n+1}$ symmetry. Within the framework of Algebraic Bethe Ansatz,
we construct their Bethe vectors and rectangular recurrence relations.
These rectangular recurrence relations generalize the usual ones, and are new, even for models with gl(n) symmetry, which are obtained as a subcase.
We also compute the scalar products of Bethe vectors.
Based on...
We investigate large-scale fluctuations of conserved quantities and their associated currents in the sine-Gordon field theory. Our approach is based on the framework of Generalized Hydrodynamics, which has only recently become fully applicable across all regimes of the model. By combining this with Ballistic Fluctuation Theory, we analyse the distribution of conserved charges and the full...
The sine-Liouville gravity, or the sine-Gordon model coupled to 2D gravity, is discretised as a dilute vertex model on random triangulations, which in turn has a dual description as a large N matrix model referred here as vertex matrix model (VMM). It is shown that in the scaling limit, the spectral curve of the vertex matrix model is analytically connected to the spectral curve of Matrix...
The QQ-system plays a crucial role in the study of many integrable models, and it is the cornerstone of many techniques such as the Quantum Spectral Curve and the Separation of Variables. We will explore the structure of the QQ-system for the osp(4|2) super Lie algebra. Its key application will be the Quantum Spectral Curve for the study of string theory on AdSโ ร Sยณ ร Sยณ ร Sยน background with...
We study the linear problems in $z,t$ ($t$ the time) associated to the Painlev\'e III$_3$, III$_1$ and V and VI equations when the Painlevรฉ solution $q(t)$ approaches a pole or a zero. In this limit the problem in $z$ for the Painlev\'e III$_3$ reduces to the modified Mathieu equation, that for the Painlevรฉ III$_1$ to the Doubly Confluent Heun Equation and the ones for the Painlevรฉ V and VI to...
The Mpemba effect is a striking and counterintuitive phenomenon in which, under certain conditions, hotter water cools more quickly than colder water. Although originally observed in classical systems, recent theoretical and experimental studies have uncovered an analogous effect in extended quantum systems.
A specific manifestation of this quantum effect occurs when the system starts in a...
Finite temperature dynamical correlation functions of Yang-Baxter integrable quantum chains can be represented by thermal form-factor series. These are series in which every term is expressed in terms of the spectral data and the form factors of an appropriately defined dynamical quantum transfer matrix. We review the construction and exemplify its usefulness with the discussion of the leading...
The characterization of ensembles of many-qubit random states and their realization via quantum circuits are crucial tasks in quantum-information theory. In this work, we study the ensembles generated by quantum circuits that randomly permute the computational basis, thus acting classically on the corresponding states. We focus on the averaged entanglement and present two main results. First,...
Understanding thermalisation in quantum many-body systems is among the most enduring problems in modern physics. A particularly interesting question concerns the role played by quantum mechanics in this process, i.e. whether thermalisation in quantum many-body systems is fundamentally different from that in classical many-body systems and, if so, which of its features are genuinely quantum. I...
We study local quenches induced by boundary changing operators in the scaling Lee-Yang model. At the critical point, we provide explicit results for how the matrix element of a bulk field evolves between pre- and post-quench vacuum states. The quench effect propagates within a light-cone, indicating a finite velocity for the spread of information. When a bulk perturbation is added, the model...
I will discuss the integrability property of a stochastic and quantum deformation of the Rule 54 cellular automaton: the simplest microscopic (deterministic) reversible model in 1+1 discrete space and time dimensions with strong local interactions. First, I will introduce the Rule 54 model and its two deformations:
1) In the stochastic case, I couple the system to stochastic boundary...
Measurements can qualitatively alter correlations and entanglement emerging in gapless quantum matter. Using the Ising spin chain as case study, I will study the impact of measurements in an explicit protocol involving uncorrelated ancillae entangled with the critical chain and subsequently measured projectively. By varying the measurement basis, we induce renormalizationโgroup flows between...
Eigenstate thermalization hypothesis is a cornerstone of our modern understanding of thermalization and relaxation phenomena in quantum many-body systems. The studies mainly focus on chaotic dynamics, where there is solid numerical evidence supporting the standard ETH. The are however conflicting statements regarding its validity in integrable systems. By motivating and introducing a refined...
I will discuss the continuum limit of a non-Hermitian deformation of the Heisenberg XXX spin chain. This model has non-diagonalisable transfer matrix, and it appeared in the classification of 4x4 solutions of the Yang-Baxter equation. This model can also be obtained by a Drinfeld twist of the XXX spin chain and its continuum limit gives a non-unitary deformation of the Landau-Lifshitz theory....
In this talk I will discuss recent advances of integrability related to generalised symmetries and fusion categories. In particular I will show a framework on how to introduce Lax operators and R-matrices in this context. I will discuss some new models and a relation with Temperley-Lieb algebras.
In this talk I will present some recent advances on understanding RG flows between 2d CFT by employing non-invertible (generalized) symmetries.
After introducing the formalism of non-invertible symmetries, I will illustrate how the matching of their 't Hooft anomalies puts strong constraints on the RG group flow from perturbed UV fixed 2D CFT.
I will then focus on the specific case of...
We consider the six-vertex model on the N x N lattice, with domain
wall boundary conditions, and at ice-point, $\Delta=1/2$. We focus on
the Emptiness Formation Probability (EFP), for which we build an
explicit and exact (although still conjectural) expression, as the
Fredholm determinant of some linear integral operator. We study the
asymptotic behaviour of the obtained representation at...
We apply CFT and gauge theory inspired techniques to the study of gravitational scattering and collisions of binary systems in the extreme mass-ratio regime.
Recently a family of quantum spin chains was discovered, which can be solved by hidden free fermionic structures. It was proven that these structures are not equivalent to the Jordan-Wigner transformation or any direct generalization thereof. In this talk we discuss recent results in this topic, including different families of such models, the computation of real time dynamics in them, and...
We present recent applications of the Modified Algebraic Bethe Ansatz (MABA) to two-dimensional vertex models and one-dimensional spin chains.
First, we address the eigenvalue problem and scalar products within the MABA framework. In particular, we exploit the SLโ invariance of the underlying R-matrix and introduce a modified representation theory that generalizes the conventional...
The renormalized angular momentum appearing in the time-honored ManoโSuzukiโTakasugi (MST) method, which is useful for solving the confluent Heun equation as an infinite expansion of hypergeometric functions, is a fundamental quantity that arises in almost every black hole perturbation theory context, such as quasi-normal mode computations, tidal Love numbers, and waveforms. The appearance of...
We want to discuss aspects of ODE/IM correspondence for WN algebras, with particular focus on the relevant symmetries of the family (in particular the triality symmetry) and the associated geometric structures.
We develop a systematic procedure for calculating the expressions for local higher spin charges in terms of solutions of Bethe ansatz equations of BLZ type (we write these equations...
In this talk, we present an analytic method for performing exact computations of one-loop effective actions in black hole backgrounds. The method is based on a generalization of the Gelfand-Yaglom formalism to second-order linear ordinary differential equations, where the resulting expressions are governed by the connection coefficients of equations belonging to the Heun class.
As an...
Since the early days of Bose-Einstein condensation in ultracold gas experiments the momentum distribution of the atoms has been a pivotal experimental observable. Measured via time-of-flight imaging, the momentum distribution has allowed to observe and characterize a wide range of phenomena in a wide range of systems. It also contributed to the development of theories describing...
In this talk, we discuss some aspects of the connection between the one-dimensional XXZ chain and two-dimensional conformal field theories. Namely, we consider the XXZ spin chain in the scaling limit in the Matsubara direction. Our approach is based on the fermionic basis construction developed in [1, 2, 3, 4]. The main feature of the fermionic basis is the factorization of the algebraic and...
I will revise recent developments in the calculation of conformal blocks and its relation to black hole perturbations, especially the calculation of quasinormal modes for generic black hole solutions. A number of conformal operators are related to the black hole in asymptotically flat and anti-de Sitter spacetimes, including primary and Whittaker operators. An alternative view in terms of...
We study the ODE/IM correspondence between two-dimensional Wg-type conformal field theories and the higher-order ordinary differential equations
(ODEs) obtained from the affine Toda field theories associated with g-type
affine Lie algebras. We calculate the period integrals of the WKB solution to the
ODE along the Pochhammer contour, where the WKB expansions correspond to
the classical...
We discuss unconventional transport phenomena in a spin-1 model that supports a tower of quantum many-body scars. In quantum many-body systems, the late-time dynamics of local observables are typically governed by conserved operators with local densities, such as energy and magnetization. In the model under investigation, however, there is an additional dynamical symmetry restricted to the...
I will give an overview of the integrability properties of ยฝ BPS Nahm pole defects in N=4 SYM paying special attention to the case of Gukov-Witten surface defects which have only very recently been studied in the integrability context. Furthermore, I will discuss how localization results for one-point functions in these set-ups imply an intriguing structure of perturbation theory that might...
We investigate non-local charges for perturbations of two-dimensional conformal field theories that arise as perturbations of conformal defects. We find solutions for a wide range of perturbations including the well-known (1,2), (1,3) and (1,5) integrable perturbations of Virasoro minimal models (with associated local conserved charges), but we also find solutions for other bulk perturbations,...
We developed a variational approach to study a two-dimensional non-integrable quantum field theories through the lenses of integrable ones. We focus on the ฯ4 Landau- Ginzburg theory and compare it with the integrable Sinh-Gordon. We employ exact Vacuum Expectation Values and Form Factors of local operators of the Sinh-Gordon model for getting the best variational estimates of several...
Parisi-Sourlas (PS) supersymmetry is known to emerge in some models with random field type of disorder. When PS SUSY is present, the $d$-dimensional theory allows for a $dโ2$-dimensional description. In this talk I focus on the reversed question and provide new indications that any given CFT$_{dโ2}$ can be uplifted to a PS SUSY CFT$_d$. I show that any scalar four-point function of a...
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...
In the last few years, quantifying the complexity of quantum states has found applications in many fields, including quantum information and computing, quantum dynamics in many-body systems, and black hole physics. Among these measures, the spread complexity roughly quantifies the size of the space of states visited along quantum dynamics. It is obtained through Krylov space methods, which...
