Entanglement distribution in fermion model with long-range interaction

Abstract

How two-party entanglement (TPE) is distributed in the many-body systems? This is a fundamental issue because the total TPE between one party with all the other parties, ${\mathcal{C}}^N$, is upper bounded by the Coffman, Kundu and Wootters (CKW) monogamy inequality, from which ${\mathcal{C}}^N\le \sqrt{N-1}$ can be proved by the geometric inequality. Here we explore the total entanglement ${\mathcal{C}}^{\infty }$ and the associated total tangle ${\tau }^{\infty }$ in a $p$-wave free fermion model with long-range interaction, showing that ${\mathcal{C}}^{\infty }\sim \mathcal{O}(1)$ and ${\tau }^{\infty }$ may become vanishing small with the increasing of long-range interaction. However, we always find ${\mathcal{C}}^{\infty }\sim 2\xi {\tau }^{\infty }$, where $\xi$ is the truncation length of entanglement, beyond which the TPE is quickly vanished, hence ${\tau }^{\infty }\sim 1/\xi$. This relation is a direct consequence of the exponential decay of the TPE induced by the long-range interaction. These results unify the results in the Lipkin-Meshkov-Glick (LMG) model and Dicke model and generalize the Koashi, Buzek and Imono bound to the quantum many-body models, with much broader applicability.

References in corpus (49)

• Quantum Cryptography
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Experimental quantum teleportation
• Separability Criterion for Density Matrices
• Unpaired Majorana fermions in quantum wires
• Separability of Mixed States: Necessary and Sufficient Conditions
• Three qubits can be entangled in two inequivalent ways
• New directions in the pursuit of Majorana fermions in solid state systems
• Entanglement of a Pair of Quantum Bits
• Entanglement in quantum critical phenomena
• Distributed Entanglement
• Scaling of Entanglement close to a Quantum Phase Transitions
• Search for Majorana fermions in superconductors
• Entanglement in a simple quantum phase transition
• Chaos and the Quantum Phase Transition in the Dicke Model
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Quantum Chaos Triggered by Precursors of a Quantum Phase Transition: The Dicke Model
• Research on Hidden Variable Theories: a review of recent progresses
• Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
• A geometric theory of non-local two-qubit operations
• Majorana Fermions and Topology in Superconductors
• Entanglement Certification $-$ From Theory to Experiment
• A practical scheme for quantum computation with any two-qubit entangling gate
• Monogamy Inequality in terms of Negativity for Three-Qubit States
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
• Continuous variable tangle, monogamy inequality, and entanglement sharing in Gaussian states of continuous variable systems
• Entangled three-qubit states without concurrence and three-tangle
• Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
• Long-distance entanglement in spin systems
• Dynamical quantum phase transitions in the dissipative Lipkin-Meshkov-Glick model and proposed realization in optical cavity QED
• Monogamy inequality for distributed Gaussian entanglement
• Entangled webs: Tight bound for symmetric sharing of entanglement
• Long-distance entanglement and quantum teleportation in XX spin chains
• Monogamy and polygamy for multi-qubit entanglement using Rényi entropy
• The ground state entanglement in the $XXZ$ model
• The 1D Ising model and topological order in the Kitaev chain
• Pairwise entanglement in symmetric multi-qubit systems
• Long-distance entanglement in many-body atomic and optical systems
• Experimental entanglement redistribution under decoherence channels
• Essential singularity in the Renyi entanglement entropy of the one-dimensional XYZ spin-1/2 chain
• Entanglement crossover close to a quantum critical point
• Probing quantum criticality and symmetry breaking at the microscopic level
• Experimental investigation of dynamical invariants in bipartite entanglement
• Exact dimer phase with anisotropic interaction for one dimensional magnets
• Spin squeezing and concurrence
• Realization of the tradeoff between internal and external entanglement
• From Ising model to Kitaev Chain -- An introduction to topological phase transitions
• Scaling of finite size effect of $\alpha$-Rényi entropy in disjointed intervals under dilation

Cited by in corpus (1)

• Long-range bipartite entanglement in XXZ spin chains with the exponential and power-law long-range interactions