arXiv subjects

Bruno de O. Carvalho

Publications and source records attributed to Bruno de O. Carvalho.

3 recordsLinked to original sources

arXiv2026

Pure gapped ground states of spin chains are short-range entangled

We consider spin chains with a finite range Hamiltonian. For reasons of simplicity, the chain is taken to be infinitely long. A ground state is said to be a unique gapped ground state if its GNS Hamiltonian has a unique ground state, separated by a gap from the rest of the spectrum. By combining some powerful techniques developed in the last years, we prove that each unique gapped ground state is short-range entangled: It can be mapped into a product state by a finite time evolution map generated by a Hamiltonian with exponentially quasi-local interaction terms. This claim makes precise the common belief that one-dimensional gapped systems are topologically trivial in the bulk.

math-ph↗

arXiv2026

A complete classification of 2d symmetry protected states with symmetric entanglers

We consider symmetry protected topological states of 2d quantum spin systems, with a finite symmetry group $G$. It has been conjectured that such states are classified by the cohomology group $H^3(G,U(1))$, but the completeness of this classfication is an open problem. We restrict ourselves to symmetry protected topological states that can be prepared from a product state by a symmetric entangler. For this class of states, we prove that the classification by $H^3(G,U(1))$ is complete.

math-ph↗

arXiv2025

Classification of locality preserving symmetries on spin chains

We consider the action of a finite group $G$ by locality preserving automorphisms (quantum cellular automata) on quantum spin chains. We refer to such group actions as ``symmetries''. The natural notion of equivalence for such symmetries is \emph{stable equivalence}, which allows for stacking with factorized group actions. Stacking also endows the set of equivalence classes with a group structure. We prove that the anomaly of such symmetries provides an isomorphism between the group of stable equivalence classes of symmetries with the cohomology group $H^3(G,U(1))$, consistent with previous conjectures. This amounts to a complete classification of locality preserving symmetries on spin chains. We further show that a locality preserving symmetry is stably equivalent to one that can be presented by finite depth quantum circuits with covariant gates if and only if the slant product of its anomaly is trivial in $H^2(G, U(1)[G])$.

quant-ph↗