Related papers: Algebraic structure of Fock-state lattices
We introduce Liouville Fock state lattices (LFSLs) as a framework for visualizing open quantum systems through matrix representations of the Lindblad master equation (LME). By vectorizing the LME, the state evolves in a doubled Hilbert…
Fock-state lattices (FSLs), composed of photon number states with infinite Hilbert space, have emerged as a promising platform for simulating high-dimensional physics due to their potential to extend into arbitrarily high dimensions. Here,…
A 2D Fock-state lattice (FSL is constructed from the many-body states of two interacting two-mode quantum gases. By periodically driving the interspecies interactions and pulsing the tunneling between the two modes of each gas, a synthetic…
The $K=4$ fractional superstring Fock space is constructed in terms of $\bZ_4$ parafermions and free bosons. The bosonization of the $\bZ_4$ parafermion theory and the generalized commutation relations satisfied by the modes of various…
We construct lattice gauge field theory based on a quantum group on a lattice of dimension 1. Innovations include a coalgebra structure on the connections, and an investigation of connections that are not distinguishable by observables. We…
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams…
We study elliptic fibrations by analyzing suitable deformations of the fibrations and vanishing cycles. We introduce geometric string junctions and describe some of their properties. We show how the structure of the geometric string…
Fracton theories possess exponentially degenerate ground states, excitations with restricted mobility, and nontopological higher-form symmetries. This paper shows that such theories can be defined on arbitrary spatial lattices in three…
We consider a realistic model, i.e., ultracold atoms in a driven optical lattice, to realize phase space crystals [Phys. Rev. Lett. 111, 205303 (2013)]. The corresponding lattice structure in phase space is more complex and contains rich…
Within the C*-algebraic framework of the resolvent algebra for canonical quantum systems, the structure of oscillating lattice systems with bounded nearest neighbor interactions is studied in any number of dimensions. The global dynamics of…
We introduce and investigate the solvable graph $\Gamma_\mathfrak{S}(L)$ of a finite-dimensional Lie algebra $L$ over a field $F$. The vertices are the elements outside the solvabilizer $\sol(L)$, and two vertices are adjacent whenever they…
Fock-state lattices (FSLs) are becoming an emerging research hotspot in quantum physics, not only because the FSLs provide a new perspective for studying atom-field interactions, but also because they build the connection between quantum…
Every Lie algebra over a field $E$ gives rise to new Lie algebras over any subfield $F \subseteq E$ by restricting the scalar multiplication. This paper studies the structure of these underlying Lie algebra in relation to the structure of…
Emergence of fundamental forces from gauge symmetry is among our most profound insights about the physical universe. In nature, such symmetries remain hidden in the space of internal degrees of freedom of subatomic particles. Here we…
The interaction of a Lie algebra $\LL,$ having a weight space decomposition with respect to a nonzero toral subalgebra, with its corresponding root system forms a powerful tool in the study of the structure of $\LL.$ This, in particular,…
We study locally conformal symplectic (LCS) structures of the second kind on a Lie algebra. We show a method to build new examples of Lie algebras admitting LCS structures of the second kind starting with a lower dimensional Lie algebra…
Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are noncommutative spaces that inherit a well defined mathematical structure from the quantum group symmetry. In turn such quantum spaces can be…
Model wave functions are essential for studying fractional quantum Hall phases, yet lattice model states have so far been limited to bosonic systems with on-site interactions. In this work, by combining analytical and numerical methods, we…
We construct generalized Hofstadter models that possess "color-entangled" flat bands and study interacting many-body states in such bands. For a system with periodic boundary conditions and appropriate interactions, there exist gapped…
We investigate topological features in the synthetic Fock-state lattice (FSL) of a single-atom system described by the quantum Rabi model. By diagonalizing the Hamiltonian, we identify a zero-energy defect state localized at a domain wall…