Related papers: $U_{\mathfrak{q}}(\mathfrak{sl}_3)$ web models: Lo…
We continue our work on lattice models of webs, which generalise the well-known loop models to allow for various kinds of bifurcations [arXiv:2101.00282, arXiv:2107.10106]. Here we define new web models corresponding to each of the rank-two…
This is the first in a series of papers devoted to generalisations of statistical loop models. We define a lattice model of $U_q(\mathfrak{sl}_n)$ webs on the honeycomb lattice, for $n \ge 2$. It is a statistical model of closed, cubic…
Quantum loop and dimer models are archetypal examples of correlated systems with local constraints. Obtaining generic solutions for these models is difficult due to the lack of controlled methods to solve them in the thermodynamic limit.…
Given a semisimple Lie algebra $\mathfrak{g}$, we can represent invariants of tensor products of fundamental representations of the quantum enveloping algebra $U_q(\mathfrak{g})$ using particular directed graphs called webs. In particular…
The sl_3 spider is a diagrammatic category used to study the representation theory of the quantum group U_q(sl_3). The morphisms in this category are generated by a basis of non-elliptic webs. Khovanov- Kuperberg observed that non-elliptic…
A lattice model of critical dense polymers is solved exactly on a cylinder with finite circumference. The model is the first member LM(1,2) of the Yang-Baxter integrable series of logarithmic minimal models. The cylinder topology allows for…
Generalized symmetries often appear in the form of emergent symmetries in low energy effective descriptions of quantum many-body systems. Non-invertible symmetries are a particularly exotic class of generalized symmetries, in that they are…
Webs are a kind of planar, directed, edge-labeled graph that encode invariant vectors for quantum representations of $\mathfrak{sl}_n$. The theory of webs developed organically for $\mathfrak{sl}_2$, where they are also known as noncrossing…
The three-site model has been offered as a benchmark for studying the collider phenomenology of Higgsless models. In this paper we analyze how well the three-site model performs as a general exemplar of Higgsless models in describing W_L…
We study the $S>1/2$ antiferromagnetic Heisenberg model on the 1/5-depleted square lattice as a function of the ratio of the intra-plaquette coupling to the inter-plaquette coupling. Using stochastic series expansion quantum Monte Carlo…
We consider the spherical model on a spider-web graph. This graph is effectively infinite-dimensional, similar to the Bethe lattice, but has loops. We show that these lead to non-trivial corrections to the simple mean-field behavior. We…
We present geometric methods for uniformly discretizing the continuous N-qubit Hilbert space. When considered as the vertices of a geometrical figure, the resulting states form the equivalent of a Platonic solid. The discretization…
We consider some classical and frustrated lattice spin models with global O(3) spin symmetry. There is no general analytical method to find a ground-state if the spin dependence of the Hamiltonian is more than quadratic (i.e. beyond the…
A lattice model of critical spanning webs is considered for the finite cylinder geometry. Due to the presence of cycles, the model is a generalization of the known spanning tree model which belongs to the class of logarithmic theories with…
A model describing the three-dimensional folding of the triangular lattice on the face-centered cubic lattice is generalized allowing the presence of defects corresponding to cuts in the two-dimensional network. The model can be expressed…
We study a model of dilute oriented loops on the square lattice, where each loop is compatible with a fixed, alternating orientation of the lattice edges. This implies that loop strands are not allowed to go straight at vertices, and…
We describe the $\mathfrak sl_3$ non-elliptic webs in terms of convex sets in the affine building. Kuperberg defined the non-elliptic web basis in his work on rank-$2$ spider categories. Fontaine, Kamnitzer, Kuperberg showed that the…
We introduce a variational wave function based on Neural-Network Quantum States (NQS) to study lattice systems whose local Hilbert space contains both spin and fermionic degrees of freedom. Our approach is based on the use of the…
The spin network quantum simulator relies on the su(2) representation ring (or its q-deformed counterpart at q= root of unity) and its basic features naturally include (multipartite) entanglement and braiding. In particular, q-deformed spin…
We study phase-space properties of critical, parity symmetric, $N$-quDit systems undergoing a quantum phase transition (QPT) in the thermodynamic $N\to\infty$ limit. The $D=3$ level (qutrit) Lipkin-Meshkov-Glick (LMG) model is eventually…