Fermionic logarithmic negativity in the Krawtchouk chain

Abstract

The entanglement of non-complementary regions is investigated in an inhomogeneous free-fermion chain through the lens of the fermionic logarithmic negativity. Focus is on the Krawtchouk chain, whose relation to the eponymous orthogonal polynomials allows for exact diagonalization and analytical calculations of certain correlation functions. For adjacent regions, the negativity scaling corresponds to that of a conformal field theory with central charge $c=1$, in agreement with previous studies on bipartite entanglement in the Krawtchouk chain. For disjoint regions, we focus on the skeletal regime where each region reduces to a single site. This regime is sufficient to extract the leading behaviour at large distances. In the bulk, the negativity decays as $d^{-4{\Delta }_f}$ with ${\Delta }_f=1/2$, where $d$ is the separation between the regions. This is in agreement with the homogeneous result of free Dirac fermions in one dimension. Surprisingly, when one site is close to the boundary, this exponent changes and depends on the parity of the boundary site $m=0,1,2,\dots$, with ${\Delta }_f^{\text{even}}=3/8$ and ${\Delta }_f^{\text{odd}}=5/8$. The results are supported by numerics and analytical calculations.

21 pages, 8 figures, v2: minor modifications to match the published version, v3: minor typos corrected

References in corpus (46)

• A computable measure of entanglement
• Entanglement Entropy and Quantum Field Theory
• Area laws for the entanglement entropy - a review
• Entanglement in quantum critical phenomena
• Scaling of Entanglement close to a Quantum Phase Transitions
• The logarithmic negativity: A full entanglement monotone that is not convex
• Entanglement in a simple quantum phase transition
• Calculation of reduced density matrices from correlation functions
• An Area Law for One Dimensional Quantum Systems
• Quantum entanglement in condensed matter systems
• Reduced density matrices and entanglement entropy in free lattice models
• Area laws in quantum systems: mutual information and correlations
• Entanglement entropy in free quantum field theory
• Entanglement negativity in quantum field theory
• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• Bipartite Fluctuations as a Probe of Many-Body Entanglement
• Entanglement negativity in extended systems: A field theoretical approach
• Conformal Field Theory for Inhomogeneous One-dimensional Quantum Systems: the Example of Non-Interacting Fermi Gases
• Entanglement entropy of two disjoint blocks in XY chains
• Partial time-reversal transformation and entanglement negativity in fermionic systems
• Entanglement in fermionic systems
• Symmetry resolved entanglement in free fermionic systems
• Quasiparticle dynamics of symmetry resolved entanglement after a quench: the examples of conformal field theories and free fermions
• Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
• Entanglement negativity of fermions: monotonicity, separability criterion, and classification of few-mode states
• Entanglement negativity bounds for fermionic Gaussian states
• Symmetry decomposition of negativity of massless free fermions
• Twisted and untwisted negativity spectrum of free fermions
• Analytical results for the entanglement Hamiltonian of a free-fermion chain
• Entanglement entropy of integer Quantum Hall states
• Entanglement in spin chains with gradients
• Finite-temperature entanglement negativity of free fermions
• Free-fermion entanglement and spheroidal functions
• Free-Fermion entanglement and orthogonal polynomials
• Entanglement negativity between separated regions in quantum critical systems
• Sharp entanglement thresholds in the logarithmic negativity of disjoint blocks in the transverse-field Ising chain
• Entanglement in Fermionic Chains and Bispectrality
• Entanglement of inhomogeneous free fermions on hyperplane lattices
• Inhomogeneous XX spin chains and quasi-exactly solvable models
• Entanglement of Free Fermions on Johnson Graphs
• Multipartite information of free fermions on Hamming graphs
• Entanglement entropy of inhomogeneous XX spin chains with algebraic interactions
• Entanglement of Free Fermions on Hadamard Graphs
• Absence of logarithmic enhancement in the entanglement scaling of free fermions on folded cubes
• Computation of entanglement entropy in inhomogeneous free fermions chains by algebraic Bethe ansatz
• Currents in non-equilibrium steady states of open inhomogeneous $XX$-spin chains

Cited by in corpus (3)

• Entanglement of Inhomogeneous Free Bosons and Orthogonal Polynomials
• Multi-indexed Orthogonal Polynomials of a Discrete Variable and Exactly Solvable Birth and Death Processes
• Local fermion density in inhomogeneous free-fermion chains: a discrete WKB approach