Area law for fixed points of rapidly mixing dissipative quantum systems

DOI10.1063/1.4932612zbMath1325.81009arXiv1505.02776OpenAlexW3103705471WikidataQ59451004 ScholiaQ59451004MaRDI QIDQ3450542

David Pérez-García, Spyridon Michalakis, Fernando G. S. L. Brandão, Angelo Lucia, Toby S. Cubitt

Publication date: 6 November 2015

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

Full work available at URL: https://arxiv.org/abs/1505.02776

Mathematics Subject Classification ID

Many-body theory; quantum Hall effect (81V70) Measures of information, entropy (94A17) Quantum coherence, entanglement, quantum correlations (81P40) Open systems, reduced dynamics, master equations, decoherence (81S22)

Related Items (7)

Matrix product operator algebras. II: Phases of matter for 1D mixed states ⋮ An exponentially local spectral flow for possibly non-self-adjoint perturbations of non-interacting quantum spins, inspired by KAM theory ⋮ Quasi-locality bounds for quantum lattice systems. I. Lieb-Robinson bounds, quasi-local maps, and spectral flow automorphisms ⋮ Lieb-Robinson bounds, the spectral flow, and stability of the spectral gap for lattice fermion systems ⋮ On the modified logarithmic Sobolev inequality for the heat-bath dynamics for 1D systems ⋮ Hypercontractivity and logarithmic Sobolev inequality for non-primitive quantum Markov semigroups and estimation of decoherence rates ⋮ Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1  +  1d

Cites Work

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• Stability of frustration-free Hamiltonians
• On the generators of quantum dynamical semigroups
• For 2-D lattice spin systems weak mixing implies strong mixing
• Cutoff for the Ising model on the lattice
• Stability of local quantum dissipative systems
• A continuity property of the entropy density for spin lattice systems
• Spectral convergence bounds for classical and quantum Markov processes
• Exponential decay of correlations implies area law
• Statistical mechanics of quantum spin systems. II
• Quantum Gibbs samplers: the commuting case
• Lieb-Robinson Bounds and Existence of the Thermodynamic Limit for a Class of Irreversible Quantum Dynamics
• Quantum Computation and Quantum Information
• Area Laws in Quantum Systems: Mutual Information and Correlations
• A cutoff phenomenon for quantum Markov chains
• Logarithmic Sobolev Inequalities
• Continuity of quantum conditional information
• Completely positive dynamical semigroups of N-level systems
• An area law for one-dimensional quantum systems
• A sharp continuity estimate for the von Neumann entropy
• Mixed-state entanglement and quantum error correction
• Quantum logarithmic Sobolev inequalities and rapid mixing
• Rapid mixing implies exponential decay of correlations
• The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice

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