Mutual information for fermionic systems

Abstract

We study the behavior of the mutual information (MI) in various quadratic fermionic chains, with and without pairing terms and both with short- and long-range hoppings. The models considered include the short-range limit and long-range versions of the Kitaev model as well, and also cases in which the area law for the entanglement entropy is - logarithmically or non-logarithmically - violated. In all cases surveyed, when the area law is violated at most logarithmically, the MI is a monotonically increasing function of the conformal four-point ratio x. Where non-logarithmic violations of the area law are present, non-monotonic features can be observed in the MI and the four-point ratio, as well as other natural combinations of the parameters, is found not to be sufficient to capture the whole structure of the MI with a collapse onto a single curve. We interpret this behavior as a sign that the structure of peaks is related to a non-universal spatial configuration of Bell pairs. For the model exhibiting a perfect volume law, the MI vanishes identically. For the Kitaev model the MI is vanishing for x -> 0 and it remains zero up to a finite x in the gapped case. In general, a larger range of the pairing corresponds to a reduction of the MI at small x. A discussion of the comparison with the results obtained by the AdS/CFT correspondence in the strong coupling limit is presented.

References in corpus (13)

• General Monogamy Inequality for Bipartite Qubit Entanglement
• Area laws in quantum systems: mutual information and correlations
• Kitaev chains with long-range pairing
• Multipartite entanglement in topological quantum phases
• Quantum Mutual Information as a Probe for Many-Body Localization
• Finite Size Scaling of Mutual Information: A Scalable Simulation
• Finite Temperature Critical Behavior of Mutual Information
• Information scrambling vs. decoherence -- two competing sinks for entropy
• Information theoretic aspects of the two-dimensional Ising model
• Explicit Hamiltonians Inducing Volume Law for Entanglement Entropy in Fermionic Lattices
• Universal behavior of the Shannon and Rényi mutual information of quantum critical chains
• Anisotropic Long-Range Spin Systems
• Entanglement entropy of the long-range Dyson hierarchical model

Cited by in corpus (7)

• Many-body magic via Pauli-Markov chains -- from criticality to gauge theories
• Logarithmic, Fractal and Volume-Law Entanglement in a Kitaev chain with long-range hopping and pairing
• Universal structure of measurement-induced information in many-body ground states
• Machine Learning the Operator Content of the Critical Self-Dual Ising-Higgs Gauge Model
• Universality in the tripartite information after global quenches: (generalised) quantum XY models
• Signatures of quantum phases in a dissipative system
• Entanglement transition in unitary system-bath dynamics