Related papers: Structure of the conservation laws in integrable s…
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.…
We develop a numerical algorithm for identifying approximately conserved quantities in models perturbed away from integrability. In the long-time regime, these quantities fully determine correlation functions of local observables. Applying…
We propose a Lax equation for the non-linear sigma model which leads directly to the conserved local charges of the system. We show that the system has two infinite sets of such conserved charges following from the Lax equation, much like…
The subject under study is an open subsystem of a larger linear and conservative system and the way in which it is coupled to the rest of system. Examples are a model of crystalline solid as a lattice of coupled oscillators with a finite…
In these lecture notes we aim for a pedagogical introduction to both classical and quantum integrability. Starting from Liouville integrability and passing through Lax pair and r-matrix we discuss the construction of the conserved charges…
In this work, with focus on the energy transport properties in quantum, low dimensional, graded materials, we address the investigation of the energy (and spin) current in XXZ open chains with graded inner structures and driven out of…
We derive an explicit mapping between the spectra of conserved local operators of integrable quantum lattice models and the density distributions of their thermodynamic particle content. This is presented explicitly for the Heisenberg XXZ…
We study the role of coherence in closed and open quantum batteries. We obtain upper bounds to the work performed or energy exchanged by both closed and open quantum batteries in terms of coherence. Specifically, we show that the energy…
We propose a theoretical framework to describe the ladder systems. The N-chain Hubbard model has been studied within the Composite Operator Method. In this scheme of calculations the single-particle Green's function for any number of…
We study the structure of the spectrum of the infinite XXZ quantum spin chain, an anisotropic version of the Heisenberg model. The XXZ chain Hamiltonian preserves the number of down spins (or particle number), allowing to represent it as a…
We study the lowest order conservation laws in one-dimensional (1D) integrable quantum many-body models (IQM) as the Heisenberg spin 1/2 chain, the Hubbard and t-J model. We show that the energy current is closely related to the first…
A continuous family of quasilocal exact conservation laws is constructed in the anisotropic Heisenberg (XXZ) spin-1/2 chain for periodic (or twisted) boundary conditions and for a set of commensurate anisotropies densely covering the entire…
For quantum integrable systems the currents averaged with respect to a generalized Gibbs ensemble are revisited. An exact formula is known, which we call "collision rate ansatz". While there is considerable work to confirm this ansatz in…
This work is based on the author's PhD thesis. The main result of the thesis is the use of the boost operator to develop a systematic method to construct new integrable spin chains with nearest-neighbour interaction and characterized by an…
We study the $S=\frac{1}{2}$ quantum spin system on the $d$-dimensional hypercubic lattice with $d\ge2$ with uniform nearest-neighbor interaction of the XY or XYZ type and arbitrary uniform magnetic field. By extending the method recently…
We show how the tracer motion of tagged, distinguishable particles can effectively describe transport in various homogeneous quantum many-body systems with constraints. We consider systems of spinful particles on a one-dimensional lattice…
Through an $\hbar$-expansion of the confined Calogero model with spin exchange interactions, we extract a generating function for the involutive conserved charges of the Frahm-Polychronakos spin chain. The resulting conservation laws…
The conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces are derived. For discrete models the conserved charges are constructed explicitly. The applications of the general…
Conservation laws can constrain entanglement dynamics in isolated quantum systems, manifest in a slowdown of higher R\'enyi entropies. Here, we explore this phenomenon in a class of long-range random Clifford circuits with U$(1)$ symmetry…
Sutherland showed that the XYZ quantum spin-chain Hamiltonian commutes with the eight-vertex model transfer matrix, so that Baxter's subsequent tour de force proves the integrability of both. The proof requires parametrising the Boltzmann…