Zobrazeno 1 - 10
of 14 549
pro vyhledávání: '"A. Verstraete"'
Autor:
Verstraete, Jacques, Wilson, Chase
Ajtai, Koml\'{o}s, Pintz, Spencer and Szemer\'{e}di proved that every $(r + 1)$-uniform ``locally sparse'' hypergraph $H$ of average degree $d \geq 1$ has an independent set of size \[ \Omega_r\Bigl(\frac{\log d}{d}\Bigr)^{\frac{1}{r}} \cdot |V(H)| \
Externí odkaz:
http://arxiv.org/abs/2409.19908
For a $k$-uniform hypergraph $F$ and a positive integer $n$, the Ramsey number $r(F,n)$ denotes the minimum $N$ such that every $N$-vertex $F$-free $k$-uniform hypergraph contains an independent set of $n$ vertices. A hypergraph is $\textit{slowly gr
Externí odkaz:
http://arxiv.org/abs/2409.01442
We leverage the interplay between gapped phases and dualities of symmetric one-dimensional quantum lattice models to demonstrate that every phase is efficiently characterised by the maximal breaking of the dual (genereralised) symmetry whose structur
Externí odkaz:
http://arxiv.org/abs/2408.06334
Autor:
Mubayi, Dhruv, Verstraete, Jacques
Let $f_{F,G}(n)$ be the largest size of an induced $F$-free subgraph that every $n$-vertex $G$-free graph is guaranteed to contain. We prove that for any triangle-free graph $F$, \[ f_{F,K_3}(n) = f_{K_2,K_3}(n)^{1 + o(1)} = n^{\frac{1}{2} + o(1)}.\]
Externí odkaz:
http://arxiv.org/abs/2407.03121
Autor:
Haegeman, Jutho, Lootens, Laurens, Mortier, Quinten, Stottmeister, Alexander, Ueda, Atsushi, Verstraete, Frank
We develop a Hamiltonian formalism for simulating interacting chiral fermions on the lattice while preserving unitarity and locality and without breaking the chiral symmetry. The fermion doubling problem is circumvented by constructing a Fock space e
Externí odkaz:
http://arxiv.org/abs/2405.10285
Let $ES_{\ell}(n)$ be the minimum $N$ such that every $N$-element point set in the plane contains either $\ell$ collinear members or $n$ points in convex position. We prove that there is a constant $C>0$ such that, for each $\ell, n \ge 3$, $$ (3\ell
Externí odkaz:
http://arxiv.org/abs/2405.03455
Van der Waals heterostructures of two-dimensional transition metal dichalcogenides provide a unique platform to engineer optoelectronic devices tuning their optical properties via stacking, twisting, or straining. Using ab initio Many-Body Perturbati
Externí odkaz:
http://arxiv.org/abs/2404.17182
Autor:
Conlon, David, Fox, Jacob, He, Xiaoyu, Mubayi, Dhruv, Pham, Huy Tuan, Suk, Andrew, Verstraëte, Jacques
Answering a question of Erd\H{o}s and Graham, we show that for each fixed positive rational number $x$ the number of ways to write $x$ as a sum of reciprocals of distinct positive integers each at most $n$ is $2^{(c_x + o(1))n}$ for an explicit const
Externí odkaz:
http://arxiv.org/abs/2404.16016
Autor:
Mortier, Quinten, Devos, Lukas, Burgelman, Lander, Vanhecke, Bram, Bultinck, Nick, Verstraete, Frank, Haegeman, Jutho, Vanderstraeten, Laurens
We show how fermionic statistics can be naturally incorporated in tensor networks on arbitrary graphs through the use of graded Hilbert spaces. This formalism allows to use tensor network methods for fermionic lattice systems in a local way, avoiding
Externí odkaz:
http://arxiv.org/abs/2404.14611
We present a locality preserving unitary mapping from fermions to qubits on a 2D torus whilst accounting for the mapping of topological sectors. Extending the work of Shukla et al. [Phys. Rev. B 101, 155105], an explicit intertwiner is constructed in
Externí odkaz:
http://arxiv.org/abs/2404.07727