Matrix Product Symmetries and Breakdown of Thermalization from Hard Rod Deformations.

We construct families of exotic spin-1/2 chains using a procedure called "hard rod deformation." We treat both integrable and nonintegrable examples. The models possess a large noncommutative symmetry algebra, which is generated by matrix product operators with a fixed small bond dimension.

Sublattice entanglement in an exactly solvable anyonlike spin ladder.

We introduce an integrable spin ladder model and study its exact solution, correlation functions, and entanglement properties. The model supports two particle types (corresponding to the even and odd sublattices), such that the scattering phases are constants: Particles of the same type scatter as free fermions, whereas the interparticle phase shift is a constant tuned by an interaction parameter. Therefore, the spin ladder bears similarities with anyonic models.

Integrable hard-rod deformation of the Heisenberg spin chains.

We present integrable models of interacting spin-1/2 chains which can be interpreted as hard-rod deformations of the XXZ Heisenberg chains. The models support multiple particle types: Dynamical hard rods of length ℓ and particles with lengths ℓ^{'}<ℓ that are immobile except for the interaction with the hard rods. We encounter a remarkable phenomenon in these interacting models: Exact spectral degeneracies across different deformations and volumes.

Integrable spin chains and cellular automata with medium-range interaction.

We study integrable spin chains and quantum and classical cellular automata with interaction range ℓ≥3. This is a family of integrable models for which there was no general theory so far. We develop an algebraic framework for such models, generalizing known methods from nearest-neighbor interacting chains.

Integrable spin chain with Hilbert space fragmentation and solvable real-time dynamics.

We revisit the so-called folded XXZ model, which was treated earlier by two independent research groups. We argue that this spin-1/2 chain is one of the simplest quantum integrable models, yet it has quite remarkable physical properties. The particles have constant scattering lengths, which leads to a simple treatment of the exact spectrum and the dynamics of the system.

Constructing Integrable Lindblad Superoperators.

We develop a new method for the construction of one-dimensional integrable Lindblad systems, which describe quantum many body models in contact with a Markovian environment. We find several new models with interesting features, such as annihilation-diffusion processes, a mixture of coherent and classical particle propagation, and a rectified steady state current. We also find new ways to represent known classical integrable stochastic equations by integrable Lindblad operators.

Algebraic Construction of Current Operators in Integrable Spin Chains.

Generalized hydrodynamics is a recent theory that describes the large scale transport properties of one dimensional integrable models. At the heart of this theory lies an exact quantum-classical correspondence, which states that the flows of the conserved quantities are essentially quasiclassical even in the interacting quantum many body models. We provide the algebraic background to this observation, by embedding the current operators of the integrable spin chains into the canonical framework of Yang-Baxter integrability.