The gap of the area-weighted Motzkin spin chain is exponentially small

DOI10.1088/1751-8121/aa6cc4zbMath1377.82018arXiv1611.03147OpenAlexW3106527847MaRDI QIDQ5348000

Ramis Movassagh, Lionel Levine

Publication date: 11 August 2017

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

Full work available at URL: https://arxiv.org/abs/1611.03147

zbMATH Keywords

gapMarkov chainsrandom walksprobabilityentanglementquantum spin-chainviolation of the area law

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Stochastic methods applied to problems in equilibrium statistical mechanics (82B31) Quantum coherence, entanglement, quantum correlations (81P40)

Related Items (5)

Finite-size gap, magnetization, and entanglement of deformed Fredkin spin chain ⋮ Entropy, gap and a multi-parameter deformation of the Fredkin spin chain ⋮ Spectral gaps of frustration-free spin systems with boundary ⋮ Unusual area-law violation in random inhomogeneous systems ⋮ Dynamics and correlations in Motzkin and Fredkin spin chains

Cites Work

• Unnamed Item
• The gap of Fredkin quantum spin chain is polynomially small
• Entanglement and correlation functions of the quantum Motzkin spin-chain
• Complexity of Stoquastic Frustration-Free Hamiltonians
• Novel quantum phase transition from bounded to extensive entanglement
• Supercritical entanglement in local systems: Counterexample to the area law for quantum matter
• An area law for one-dimensional quantum systems

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