6 papers
Deformations of the Boundary Theory of the Square Lattice AKLT Model
John Martyn, Kohtaro Kato, Angelo Lucia
The 1D AKLT model is a paradigm of antiferromagnetism, and its ground state exhibits symmetry-protected topological order. On a 2D lattice, the AKLT model has recently gained atten…
A class of two-dimensional AKLT models with a gap
Houssam Abdul-Rahman, Marius Lemm, Angelo Lucia +2
The AKLT spin chain is the prototypical example of a frustration-free quantum spin system with a spectral gap above its ground state. Affleck, Kennedy, Lieb, and Tasaki also conjec…
Undecidability of the Spectral Gap in One Dimension
Johannes Bausch, Toby Cubitt, Angelo Lucia +1
The spectral gap problem - determining whether the energy spectrum of a system has an energy gap above ground state, or if there is a continuous range of low-energy excitations - p…
Tensor network representations from the geometry of entangled states
Matthias Christandl, Angelo Lucia, Péter Vrana +1
Tensor network states provide successful descriptions of strongly correlated quantum systems with applications ranging from condensed matter physics to cosmology. Any family of ten…
Quantum conditional relative entropy and quasi-factorization of the relative entropy
Angela Capel, Angelo Lucia, David Pérez-García
The existence of a positive log-Sobolev constant implies a bound on the mixing time of a quantum dissipative evolution under the Markov approximation. For classical spin systems, s…
Stability and area law for rapidly mixing quantum dissipative systems
Angelo Lucia
In this thesis we study properties of open quantum dissipative evolutions of spin systems on lattices described by Lindblad generators, in a particular regime that we denote rapid…