Description
20 min Talk plus 10 Min Discussion
The rational Calogero-Sutherland-Moser model is originally a system of identical particles scattering on the line with inverse-square potential. There are also trigonometric, hyperbolic and elliptic version of this model. The integrability of the model follows from the presence of a Lax pair.
The Calogero system of type $A$ admits the so-called $R$-matrix Lax pair presentation, the matrix...
The Eigenstate Thermalization Hypothesis (ETH) provides a foundational framework for understanding thermalization in quantum ergodic systems and, with appropriate generalizations, for characterizing equilibration in integrable models. However, numerical verification of ETH has traditionally relied on exact diagonalization (ED), which severely limits accessible system sizes.
In this work, we...
In the first part of the talk we will investigate the finite-volume spectra the nonrelativistic Calogero-Moser quantum systems, which can be solved analytically. We will compare the analytically calculated spectra from the finite-volume Calogero-Moser systems to the wavenumbers obtained from the corresponding Bethe ansatz equations. The eigenstates are also calculated numerically using the...
I will introduce a method to compute the minimal form factors of diagonal integrable field theories perturbed by generalized $T \bar{T}$-perturbations that is going to appear in the next few months in a new paper with O. Castro-Alvaredo and S. Negro. Building on our previous results, these MFFs are constructed in such a way as to not allow for any free parameters, an issue that plagued...
Integrable systems provide a rare opportunity to exactly understand the physics of complex systems, especially in the case of many-body quantum systems, where exponential complexity of simulation severely limits the effectiveness of brute-force approaches. With the recent rapid progress of quantum computers, integrable circuits have increasingly come into focus. While integrability is...
The characterization of ensembles of random states over many qubits and their realization by quantum circuits are important tasks in quantum-information theory. In this work, we study ensembles of states 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...
Classical cellular automata represent a class of explicit discrete spacetime lattice models in which complex large-scale phenomena emerge from simple deterministic rules. We discuss a classification of three-state cellular automata (with a stable ‘vacuum’ state and ‘particles’ with ± charges). The classification is aided by the automata’s different transformation proper- ties under discrete...
A large class of free fermionic spin chain models have been found recently, that are not soluble by a Jordan-Wigner transformation, but by some more complex construction introduced in the original work of Fendley, that rather resembles the methods to solve integrable systems. In the present work we relied on these techniques to calculate the correlation functions of some local operators in...
Integrable systems feature an infinite number of conserved charges and on hydrodynamic scales are described by generalised hydrodynamics (GHD). This description breaks down when the integrability is weakly broken and sufficiently large space-time-scales are probed. The emergent hydrodynamics depends then on the charges conserved by the perturbation.
In my contribution I will focus on...
The Lie symmetries of the Pais-Uhlenbeck Oscillator (PUO) are identified. They are then used to generate the Bi-Hamiltonian structure of this system. We then study how we might leverage this Bi-Hamiltonian
structure to mitigate the pathologies associated with theories where, as in the case of the PUO, the lagrangian admits time derivatives of order two or higher. Theories of this nature are...
In this talk, I will discuss the nonequilibrium dynamics in a quantum Ising chain where the transverse field slowly rotates. The corresponding magnetization oscillations are found to be non-thermalized and can be explained by contributions from different particle excitations in the quantum E_8 integrable model. For the details of the talk, firstly, I will provide a brief introduction to the...
In this talk, I will discuss how to study the probabilities of observing unusually large or small particle currents in the context of the totally asymmetric simple exclusion process (TASEP) on a ring. To do this, we will revisit the large deviation function derived in a seminal paper by Derrida and Lebowitz (Phys.Rev.Lett.80,209(1998). We adapt their approach for the TASEP with accelerated...
The sine-Gordon theory is a paradigmatic integrable field theory, relevant for the description of many 1D gapped systems. Despite its integrable nature, calculating finite temperature physical quantities, such as correlation functions, remains a challenge. The titular method of random surfaces is a Monte Carlo-based numerical algorithm that makes it possible to get non-perturbative results at...
In this talk, I explain the structure of the local consrvetaion law in several interacting integrable systems.
Quantum integrable systems are exactly solvable by the Bethe ansatz.
Behind their exact solvability, there is an infinite number of local conserved quantities $\{Q_{k}\}_{k=2,3,4,\ldots}$.
Although the existence of $Q_{k}$ itself is guaranteed from the quantum inverse scattering...
From a many-body perspective, classical integrable systems fall into two broad categories: fluids and chains. The former are particle-based and their hydrodynamics closely mirrors that of quantum models. Chain systems, on the other hand, behave like integrable wave equations, with their long-time dynamics separating into solitons and dispersive radiation. While soliton gases are relatively...
One of the more recent concepts in condensed matter theory are symmetry-protected topological (SPT) phases. Although the core of the theory exists, particular models as well as models outside the basic paradigm are not studied well yet. Here we study the topological modes protected by the $Z_N^{\otimes 3}$ symmetries in two-dimensional systems. A class of models with massless excitations...
The $J_1$-$J_2$ spin chain is one of the canonical models of quantum magnetism, and has long been known to host a critical antiferromagnetic phase with power-law decay of spin correlations.
Using the matrix product state path integral to capture the effects of entanglement near the saddle points, we argue here that there are, in fact, two distinct critical phases: the 'Affleck-Haldane'...
