Related papers: Integrability of rank-two web models
We devise a generic recipe for constructing $D$-dimensional lattice models whose $d$-dimensional boundary states, located on surfaces, hinges, corners, and so forth, can be obtained exactly. The solvability is rooted in the underlying…
In this paper we formulate a new N-state spin integrable model on a three-dimensional lattice with spins interacting round each elementary cube of the lattice. This model can be also reformulated as a vertex type model. Weight functions of…
Inspired by classical results in integrable boundary quantum field theory, we propose a definition of integrable initial states for quantum quenches in lattice models. They are defined as the states which are annihilated by all local…
We study two families of quantum models which have been used previously to investigate the effect of topological symmetries in one-dimensional correlated matter. Various striking similarities are observed between certain $\mathbf{Z}_n$…
An exact mechanism is written down to guarantee extensive residual ground state entropy and spin liquidity in spin-1/2 lattice models with bond-dependent couplings. It is based on the presence of extensively large and mutually non-commuting…
We study transitions between phases of matter with topological order. By studying these transitions in exactly solvable lattice models we show how universality classes may be identified and critical properties described. As a familiar…
We study the integrable two-site states of the quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing $\mathfrak{gl}(N)$-invariant R-matrix. We investigate the overlaps between the integrable two-site states…
Exploiting the quantum integrability condition we construct an ancestor model associated with a new underlying quadratic algebra. This ancestor model represents an exactly integrable quantum lattice inhomogeneous anisotropic model and at…
Despite rapid progress in understanding gapped topological states, much less is known about gapless topological phases of matter, especially in strongly correlated electrons. In this work we discuss a large class of robust gapless quantum…
We study the ground-state properties of a family of frustrated spin-1/2 Heisenberg models on two- and three-dimensional decorated lattices composed of connected star-shaped units. Each star is built from edge-sharing triangles with an…
We study Rokhsar-Kivelson (RK) dimer and spin ice models realizing $U(1)$-lattice gauge theories in a wide class of quasi-one-dimensional settings, which define a setup for the study of few quantum strings (closed electric field lines)…
This thesis addresses whether it is possible to build a robust memory device for quantum information. A three-dimensional gapped lattice spin model is found which demonstrates for the first time that a reliable quantum memory at finite…
The power of machine learning algorithms to automatically classify different phases of matter and detect quantum phase transitions without necessity to characterize phases by various quantities like local order parameters or topological…
We give a fermionic Fock space description of embedded entangled qubits. Within this framework the problem of classification of pure state entanglement boils down to the problem of classifying spinors. The usual notion of separable states…
We construct a class of coherent spin-network states that capture proprieties of curved space-times of the Friedmann-Lama\^itre-Robertson-Walker type on which they are peaked. The data coded by a coherent state are associated to a cellular…
We theoretically address spin chain analogs of the Kitaev quantum spin model on the honeycomb lattice. The emergent quantum spin liquid phases or Anderson resonating valence bond (RVB) states can be understood, as an effective model, in…
A gauge invariant Hamiltonian representation for SU(2) in terms of a spin network basis is introduced. The vectors of the spin network basis are independent and the electric part of the Hamiltonian is diagonal in this representation. The…
We introduce novel polynomial deformations of the Lie algebra $sl(2)$. We construct their finite-dimensional irreducible representations and the corresponding differential operator realizations. We apply our results to a class of spin…
We establish an intriguing connection between quantum phase transitions and bifurcations in the reduced fidelity between two different reduced density matrices for quantum lattice many-body systems with symmetry-breaking orders. Our finding…
We review and analyze the hybrid quantum-classical NMR computing methodology referred to as Type-II quantum computing. We show that all such algorithms considered so far within this paradigm are equivalent to some classical…