Finite Size Corrections to Entanglement in Quantum Critical Systems

Abstract

We analyze the finite size corrections to entanglement in quantum critical systems. By using conformal symmetry and density functional theory, we discuss the structure of the finite size contributions to a general measure of ground state entanglement, which are ruled by the central charge of the underlying conformal field theory. More generally, we show that all conformal towers formed by an infinite number of excited states (as the size of the system $L\to \infty$) exhibit a unique pattern of entanglement, which differ only at leading order $(1/L{)}^2$. In this case, entanglement is also shown to obey a universal structure, given by the anomalous dimensions of the primary operators of the theory. As an illustration, we discuss the behavior of pairwise entanglement for the eigenspectrum of the spin-1/2 XXZ chain with an arbitrary length $L$ for both periodic and twisted boundary conditions.

9 pages, 2 figures. v2: References updated. Published version

References in corpus (20)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• A computable measure of entanglement
• Entanglement in quantum critical phenomena
• Scaling of Entanglement close to a Quantum Phase Transitions
• Entanglement in a simple quantum phase transition
• Quantum Phase Transitions and Bipartite Entanglement
• Universality of Entropy Scaling in 1D Gap-less Models
• Entanglement entropy of random quantum critical points in one dimension
• Boundary effects in the critical scaling of entanglement entropy in 1D systems
• Entanglement and Quantum Phase Transition Revisited
• Entanglement in Quantum Spin Chains, Symmetry Classes of Random Matrices, and Conformal Field Theory
• Nonuniqueness of the Potentials of Spin-Density-Functional Theory
• Linking entanglement and quantum phase transitions via density functional theory
• Entanglement and Criticality in Quantum Impurity Systems
• Macroscopic entanglement jumps in model spin systems
• Entanglement entropy at infinite randomness fixed points in higher dimensions
• Entanglement in spatially inhomogeneous many-fermion systems
• Entanglement and Quantum Phases in the Anisotropic Ferromagnetic Heisenberg Chain in the Presence of Domain Walls
• Quantum Communication Through a Spin-Ring with Twisted Boundary Conditions
• Entanglement Entropy in Random Quantum Spin-S Chains

Cited by in corpus (14)

• Entanglement of low-energy excitations in Conformal Field Theory
• Entanglement entropy of excited states
• Entanglement of excited states in critical spin chians
• Excited state entanglement in homogeneous fermionic chains
• The entanglement entropy of 1D systems in continuous and homogenous space
• Renyi Entropy and Parity Oscillations of the Anisotropic Spin-s Heisenberg Chains in a Magnetic Field
• Precise Determination of Quantum Critical Points by the Violation of the Entropic Area Law
• Two particle excited states entanglement entropy in a one-dimensional ring
• Entanglement of several blocks in fermionic chains
• Entanglement Entropies of the quarter filled Hubbard model
• Entanglement and local extremes at an infinite-order quantum phase transition
• Entanglement Entropy of the Low-Lying Excited States and Critical Properties of an Exactly Solvable Two-Leg Spin Ladder with Three-Spin Interactions
• Entanglement entropy of low-lying excitation in localized interacting system: Signature of Fock space delocalization
• Entanglement Entropy of Excited States in the Quantum Lifshitz Model