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Lie–Schwinger Block-Diagonalization and Gapped Quantum Chains

Jürg Martin Fröhlich, Alessandro Pizzo

Communications in Mathematical PhysicsMar 20, 202020 citations

Lie-Schwinger block-diagonalization and gapped quantum chains: Analyticity of the ground-state energy

Simone Del Vecchio, Jürg Martin Fröhlich, Alessandro Pizzo +1 more

arXiv:1908.07486Journal of Functional AnalysisJul 9, 20206 citations

Block-diagonalization of infinite-volume lattice Hamiltonians with unbounded interactions

Simone Del Vecchio, Jürg Martin Fröhlich, Alessandro Pizzo

arXiv:2108.13907Journal of Functional AnalysisOct 5, 20222 citations

Lie-Schwinger block-diagonalization and gapped quantum chains

Froehlich, Juerg, Alessandro Pizzo

We study quantum chains whose Hamiltonians are perturbations by bounded interactions of short range of a Hamiltonian that does not couple the degrees of freedom located at different sites of the chain and has a strictly positive energy gap above its ground-state energy. We prove that, for small values of a coupling constant, the spectral gap of the perturbed Hamiltonian above its ground-state energy is bounded from below by a positive constant uniformly in the length of the chain. In our proof we use a novel method based on local Lie-Schwinger conjugations of the Hamiltonians associated with connected subsets of the chain.We study quantum chains whose Hamiltonians are perturbations by bounded interactions of short range of a Hamiltonian that does not couple the degrees of freedom located at different sites of the chain and has a strictly positive energy gap above its ground-state energy. We prove that, for small values of a coupling constant, the spectral gap of the perturbed Hamiltonian above its ground-state energy is bounded from below by a positive constant uniformly in the length of the chain. In our proof we use a novel method based on local Lie-Schwinger conjugations of the Hamiltonians associated with connected subsets of the chain.

arXiv:1812.02457Dec 6, 20181 citation

Boundary effects and the stability of the low energy spectrum of the AKLT model

Simone Del Vecchio, Jürg Martin Fröhlich, Alessandro Pizzo +1 more

In this paper we study the low-lying spectrum of the AKLT model perturbed by small, finite-range potentials and with open boundary conditions imposed at the edges of the chain. Our analysis is based on the \emph{local, iterative Lie Schwinger block-diagonalization method} which allows us to control small interaction terms localized near the boundary of the chain that are responsible for the possible splitting of the ground-state energy of the AKLT Hamiltonian into energy levels separated by small gaps. This improves earlier results concerning the persistence of the so called \emph{bulk} gap in these models, besides illustrating the power of our general methods in a non-trivial application.In this paper we study the low-lying spectrum of the AKLT model perturbed by small, finite-range potentials and with open boundary conditions imposed at the edges of the chain. Our analysis is based on the \emph{local, iterative Lie Schwinger block-diagonalization method} which allows us to control small interaction terms localized near the boundary of the chain that are responsible for the possible splitting of the ground-state energy of the AKLT Hamiltonian into energy levels separated by small gaps. This improves earlier results concerning the persistence of the so called \emph{bulk} gap in these models, besides illustrating the power of our general methods in a non-trivial application.

arXiv:2308.02811Aug 5, 20230 citations

A Class of Asymmetric Gapped Hamiltonians on Quantum Spin Chains and its Characterization II

Yoshiko Ogata

arXiv:1510.07751Communications in Mathematical PhysicsJun 29, 201613 citations

Lie–Schwinger Block-Diagonalization and Gapped Quantum Chains with Unbounded Interactions

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