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Peculiar properties of many classical and quantum systems can be related to, or derived from those of a free particle. In this way we explain the appearance and peculiarities of the exotic nonlinear Poincar\'e supersymmetry in…
We demonstrate the existence of a novel set of discrete symmetries in the context of N = 2 supersymmetric (SUSY) quantum mechanical model with a potential function f(x) that is a generalization of the potential of the 1D SUSY harmonic…
The asymmetrically forced, damped Duffing oscillator is introduced as a prototype model for analyzing the homoclinic tangle of symmetric dissipative systems with \textit{symmetry breaking} disturbances. Even a slight fixed asymmetry in the…
By analyzing the characteristics of hardware-native Ising Models and their performance on current and next generation quantum annealers, we provide a framework for determining the prospect of advantage utilizing adiabatic evolution compared…
In this letter we explore different representations of the SU(2) principal chiral model on the lattice. We couple chemical potentials to two of the conserved charges to induce finite density. This leads to a complex action such that the…
We present a new duality between the F-terms of supersymmetric field theories defined in two- and four-dimensions respectively. The duality relates N=2 supersymmetric gauge theories in four dimensions, deformed by an Omega-background in one…
The Wegner $Z_2$ gauge theory-$Z_2$ Ising spin model duality in $(2+1)$ dimensions is revisited and derived through a series of canonical transformations. The Kramers-Wannier duality is similarly obtained. The Wegner $Z_2$ gauge-spin…
Conformal defects -- extended objects in conformal field theories -- carry localised excitations inherited from symmetry currents, known as the displacements and tilts. They capture the linear response of the defect to deformations of its…
We briefly review the Ising model with uncorrelated, quenched random-site or random-bond disorder, which has been controversial in both two and four dimensions. In these dimensions, the leading exponent alpha, which characterizes the…
Lieb-Schultz-Mattis (LSM) theorems impose non-perturbative constraints on the zero-temperature phase diagrams of quantum lattice Hamiltonians (always assumed to be local in this paper). LSM theorems have recently been interpreted as the…
Deformations of quantum field theories which preserve Poincar\'e covariance and localization in wedges are a novel tool in the analysis and construction of model theories. Here a general scenario for such deformations is discussed, and an…
Integrable trotterization provides a method to evolve a continuous time integrable many-body system in discrete time, such that it retains its conserved quantities. Here we explicitly show that the first order trotterization of the critical…
I derive a formulation of the 2-dimensional critical Ising model on non-uniform simplicial lattices. Surprisingly, the derivation leads to a set of geometric constraints that a lattice must satisfy in order for the model to have a…
In recent years, the concept of global symmetry has generalized considerably. Two dramatic examples of this generalization are the exotic symmetries that govern theories with fractons and non-invertible symmetries, which do not fuse…
A family of completely integrable nonlinear deformations of systems of N harmonic oscillators are constructed from the non-standard quantum deformation of the sl(2,R) algebra. Explicit expressions for all the associated integrals of motion…
The construction of a statistical model for eigenfunctions of the Ising model in transverse and longitudinal fields is discussed in detail for the chaotic case. When the number of spins is large, each wave function coefficient has the…
We study generalized Kahler structures on N = (2, 2) supersymmetric Wess-Zumino-Witten models; we use the well known case of SU(2) x U(1) as a toy model and develop tools that allow us to construct the superspace action and uncover the…
We discuss various dualities, relating integrable systems and show that these dualities are explained in the framework of Hamiltonian and Poisson reductions. The dualities we study shed some light on the known integrable systems as well as…
We study Energy Correlators as probes of strongly-coupled nearly-conformal field theories within their holographically dual descriptions, focusing on the important features that appear in realistic theories going beyond the standard model.…
The self-duality of the transverse-field Ising model is an archetype for dualities that, alongside symmetry and topology, are used as an organizing principle throughout modern physics. This duality, however, is not exact. The original and…