Numerical renormalization group method for entanglement negativity at finite temperature

Abstract

We develop a numerical method to compute the negativity, an entanglement measure for mixed states, between the impurity and the bath in quantum impurity systems at finite temperature. We construct a thermal density matrix by using the numerical renormalization group (NRG), and evaluate the negativity by implementing the NRG approximation that reduces computational cost exponentially. We apply the method to the single-impurity Kondo model and the single-impurity Anderson model. In the Kondo model, the negativity exhibits a power-law scaling at temperature much lower than the Kondo temperature and a sudden death at high temperature. In the Anderson model, the charge fluctuation of the impurity contribute to the negativity even at zero temperature when the on-site Coulomb repulsion of the impurity is finite, while at low temperature the negativity between the impurity spin and the bath exhibits the same power-law scaling behavior as in the Kondo model.

References in corpus (19)

• Entanglement detection
• The numerical renormalization group method for quantum impurity systems
• Sudden Death of Entanglement
• Quantum entanglement in condensed matter systems
• Real-time dynamics in Quantum Impurity Systems: A Time-dependent Numerical Renormalization Group Approach
• Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group
• A Numerical Renormalization Group approach to Green's Functions for Quantum Impurity Models
• Finite temperature entanglement negativity in conformal field theory
• Entanglement negativity in the harmonic chain out of equilibrium
• On the partial transpose of fermionic Gaussian states
• Thermal state entanglement in harmonic lattices
• Density matrix numerical renormalization group for non-Abelian symmetries
• An order parameter for impurity systems at quantum criticality
• Nonzero temperature Entanglement Negativity of quantum spin models: Area law, Linked Cluster Expansions and Sudden Death
• Scaling of tripartite entanglement at impurity quantum phase transitions
• Macroscopic Quantum Entanglement of a Kondo Cloud at Finite Temperature
• Full density matrix numerical renormalization group calculation of impurity susceptibility and specific heat of the Anderson impurity model
• Detecting Kondo Entanglement by Electron Conductance
• Nonlocal Entanglement of 1D Thermal States Induced by Fermion Exchange Statistics

Cited by in corpus (11)

• Thermometry of Strongly Correlated Fermionic Quantum Systems using Impurity Probes
• Sharp entanglement thresholds in the logarithmic negativity of disjoint blocks in the transverse-field Ising chain
• Universal Thermal Entanglement of Multichannel Kondo Effects
• Hierarchical entanglement shells of multichannel Kondo clouds
• Tracking the variation of entanglement Rényi negativity: a quantum Monte Carlo study
• Quantum entanglement and transport in non-equilibrium interacting double-dot setup: The curious role of degeneracy
• Perturbative expansion of entanglement negativity using patterned matrix calculus
• System-bath entanglement of noninteracting fermionic impurities: Equilibrium, transient, and steady-state regimes
• Quantum entanglement in a pure state of strongly correlated quantum impurity systems
• Nonequilibrium steady states in multi-bath quantum collision models
• Quantum Information Approaches to Quantum Gravity