60 citations · 394 across the 23 of their papers we have counts for
23 papers
Instability of the undecidable behavior of the spectral gap in 1D
Laura Castilla-Castellano, Angelo Lucia
The problem of determining the existence of a spectral gap in a lattice quantum spin system was previously shown to be undecidable for one [J. Bausch et al., "Undecidability of the…
Undecidability of the spectral gap in rotationally symmetric Hamiltonians
Laura Castilla-Castellano, Angelo Lucia
The problem of determining the existence of a spectral gap in a lattice quantum spin system was previously shown to be undecidable for one [J. Bausch et al., "Undecidability of the…
On the critical finite-size gap scaling for frustration-free Hamiltonians
Marius Lemm, Angelo Lucia
We prove that the critical finite-size gap scaling for frustration-free Hamiltonians is of inverse-square type. The result covers general graphs embedded in and gener…
A Nonvanishing Spectral Gap for AKLT Models on Generalized Decorated Graphs
Angelo Lucia, Amanda Young
We consider the spectral gap question for AKLT models defined on decorated versions of simple, connected graphs G. This class of decorated graphs, which are defined by replacing al…
Stability of the spectral gap and ground state indistinguishability for a decorated AKLT model
Angelo Lucia, Alvin Moon, Amanda Young
We use cluster expansions to establish local indistiguishability of the finite-volume ground states for the AKLT model on decorated hexagonal lattices with decoration parameter at…
Rapid thermalization of spin chain commuting Hamiltonians
Ivan Bardet, Ángela Capel, Li Gao +3
We prove that spin chains weakly coupled to a large heat bath thermalize rapidly at any temperature for finite-range, translation-invariant commuting Hamiltonians, reaching equilib…
Entropy decay for Davies semigroups of a one dimensional quantum lattice
Ivan Bardet, Ángela Capel, Li Gao +3
Given a finite-range, translation-invariant commuting system Hamiltonians on a spin chain, we show that the Davies semigroup describing the reduced dynamics resulting from the join…
Thermalization in Kitaev's quantum double models via Tensor Network techniques
Angelo Lucia, David Pérez-García, Antonio Pérez-Hernández
We show that the Davies generator associated to any 2D Kitaev's quantum double model has a non-vanishing spectral gap in the thermodynamic limit. This validates rigorously the exte…
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…
On the modified logarithmic Sobolev inequality for the heat-bath dynamics for 1D systems
Ivan Bardet, Angela Capel, Angelo Lucia +2
The mixing time of Markovian dissipative evolutions of open quantum many-body systems can be bounded using optimal constants of certain quantum functional inequalities, such as the…
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…
Recursion relations for chromatic coefficients for graphs and hypergraphs
Bergfinnur Durhuus, Angelo Lucia
We establish a set of recursion relations for the coefficients in the chromatic polynomial of a graph or a hypergraph. As an application we provide a generalization of Whitney's br…
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…
Locality at the boundary implies gap in the bulk for 2D PEPS
Michael J. Kastoryano, Angelo Lucia, David Perez-Garcia
Proving that the parent Hamiltonian of a Projected Entangled Pair State (PEPS) is gapped remains an important open problem. We take a step forward in solving this problem by showin…
Divide and conquer method for proving gaps of frustration free Hamiltonians
Michael J. Kastoryano, Angelo Lucia
Providing system-size independent lower bounds on the spectral gap of local Hamiltonian is in general a hard problem. For the case of finite-range, frustration free Hamiltonians on…
Superadditivity of quantum relative entropy for general states
Angela Capel, Angelo Lucia, David Pérez-García
The property of superadditivity of the quantum relative entropy states that, in a bipartite system , for every density operato…
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…
Size-Driven Quantum Phase Transitions
Johannes Bausch, Toby S. Cubitt, Angelo Lucia +2
Can the properties of the thermodynamic limit of a many-body quantum system be extrapolated by analysing a sequence of finite-size cases? We present a model for which such an appro…
Area law for fixed points of rapidly mixing dissipative quantum systems
Fernando G. S. L. Brandao, Toby S. Cubitt, Angelo Lucia +2
We prove an area law with a logarithmic correction for the mutual information for fixed points of local dissipative quantum system satisfying a rapid mixing condition, under either…
Rapid mixing and stability of quantum dissipative systems
Angelo Lucia, Toby S. Cubitt, Spyridon Michalakis +1
The physics of many materials is modeled by quantum many-body systems with local interactions. If the model of the system is sensitive to noise from the environment, or small pertu…
Stability of local quantum dissipative systems
Toby S. Cubitt, Angelo Lucia, Spyridon Michalakis +1
Open quantum systems weakly coupled to the environment are modeled by completely positive, trace preserving semigroups of linear maps. The generators of such evolutions are called…