Related papers: Hofstadter-Toda spectral duality and quantum group…
We discuss a discretization of the quantum Toda field theory associated with a semisimple finite-dimensional Lie algebra or a tamely-laced infinite-dimensional Kac-Moody algebra $G$, generalizing the previous construction of discrete…
One fruitful motivating principle of much research on the family of integrable systems known as ``Toda lattices'' has been the heuristic assumption that the periodic Toda lattice in an affine Lie algebra is directly analogous to the…
We explore a technique for probing energy spectra in synthetic lattices that is analogous to scanning tunneling microscopy. Using one-dimensional synthetic lattices of coupled atomic momentum states, we explore this spectroscopic technique…
By exhibiting the corresponding Lax pair representations we propose a wide class of integrable two-dimensional (2D) fermionic Toda lattice (TL) hierarchies which includes the 2D N=(2|2) and N=(0|2) supersymmetric TL hierarchies as…
Topological states of matter, such as fractional quantum Hall states, are an active field of research due to their exotic excitations. In particular, ultracold atoms in optical lattices provide a highly controllable and adaptable platform…
We propose an energy-scale correspondence between the Mott physics and the Kondo lattice physics and construct a tentative phase diagram of their correlated electrons with two characteristic energy scales $\omega^*$ and $\Omega$ marking the…
We demonstrate the experimental implementation of an optical lattice that allows for the generation of large homogeneous and tunable artificial magnetic fields with ultracold atoms. Using laser-assisted tunneling in a tilted optical…
Bose-Hubbard models are simple paradigmatic lattice models used to study dynamics and phases of quantum bosonic matter. We combine the extended Bose-Hubbard model in the hard-core regime with ring-exchange hoppings. By investigating the…
To explore superfluidity in flat-band systems, we consider a Bose-Hubbard model on a cross-linked ladder with $\pi$ flux, which has a flat band with a gap between the other band for noninteracting particles, where we study the effect of the…
We consider two lattice models for strongly correlated electrons which are exactly-solvable in one dimension. Along with the Hubbard model and the su(2|2) spin chain, these are the only parity-invariant models that can be obtained from…
Despite a long history of studies of vortex crystals in rotating superfluids, their melting due to quantum fluctuations is poorly understood. Here we develop a fracton-elasticity duality to investigate a two-dimensional vortex lattice…
We argue that the combination of strong repulsive interactions and high magnetic fields can generate electron pairing and superconductivity. Inspired by the large lattice constants of moir\'e materials, which make large flux per unit cell…
New integrable lattice systems are introduced, their different integrable discretization are obtained. B\"acklund transformations between these new systems and the relativistic Toda lattice (in the both continuous and discrete time…
The Hofstadter model, well-known for its fractal butterfly spectrum, describes two-dimensional electrons under a perpendicular magnetic field, which gives rise to the integer quantum hall effect. Inspired by the real-space building blocks…
Hamiltonian tridiagonal matrices characterized by multi-fractal spectral measures in the family of Iterated Function Systems can be constructed by a recursive technique here described. We prove that these Hamiltonians are almost-periodic.…
The studies of quantum states and optics in n- and p-type heterojunctions with lateral surface quantum dot (antidots) superlattice and in the presence of perpendicular magnetic field are performed. The Azbel' - Hofstadter problem is solved…
First, we define a generalization of the standard quantum Toda chain inspired by a construction of quantum cohomology of partial flags spaces GL(\ell+1)/P, P a parabolic subgroup. Common eigenfunctions of the parabolic quantum Toda chains…
We introduce a random matrix framework for studying statistical-mechanical lattice systems through spectral observables. Equilibrium configurations sampled from a Boltzmann measure are mapped to matrix ensembles whose covariance structure…
The quantization of Hall conductance in a p-type heterojunction with lateral surface quantum dot superlattice is investigated. The topological properties of the four-component hole wavefunction are studied both in r- and k-spaces. New…
An alternative derivation of the known action-angle map of the standard open Toda lattice is presented based on its identification as the natural map between two gauge slices in the relevant symplectic reduction of the cotangent bundle of…