Perturbations of ground states in weakly interacting quantum spin systems

DOI10.1063/1.1705718zbMath1071.82519OpenAlexW2001570391MaRDI QIDQ4833414

D. A. Yarotskij

Publication date: 15 December 2004

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.1705718

Mathematics Subject Classification ID

Quantum equilibrium statistical mechanics (general) (82B10) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (10)

Lieb-Robinson bounds, Arveson spectrum and Haag-Ruelle scattering theory for gapped quantum spin systems ⋮ Ground states in relatively bounded quantum perturbations of classical lattice systems ⋮ The adiabatic theorem and linear response theory for extended quantum systems ⋮ Local stability of ground states in locally gapped and weakly interacting quantum spin systems ⋮ A short proof of stability of topological order under local perturbations ⋮ An exponentially local spectral flow for possibly non-self-adjoint perturbations of non-interacting quantum spins, inspired by KAM theory ⋮ Scattering of quasi-particle excitations in weakly coupled stochastic lattice spin systems ⋮ Polynomial-time algorithm for simulation of weakly interacting quantum Spin systems ⋮ Uniqueness of the ground state in weak perturbations of non-interacting gapped quantum lattice systems ⋮ Perturbation theory for parent Hamiltonians of matrix product states

Cites Work

• Uniqueness of the translationally invariant ground state in quantum spin systems
• On the spectrum of the Heisenberg Hamiltonian
• Hidden symmetry breaking and the Haldane phase in \(S=1\) quantum spin chains
• One-particle subspaces in the stochastic \(XY\) model
• Instability of interfaces in the antiferromagnetic \(XXZ\) chain at zero temperature
• Expansions for one quasiparticle states in spin 1/2 systems
• On the spectrum of the generator of an infinite system of interacting diffusions
• Existence of phase transitions for quantum lattice systems
• A link between quantum and classical Potts models
• The one-particle energy spectrum of weakly coupled quantum rotators

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