Entanglement entropy and boundary renormalization group flow - exact results in the Ising universality class

Abstract

The entanglement entropy in one dimensional critical systems with boundaries has been associated with the noninteger ground state degeneracy. This quantity, being a characteristic of boundary fixed points, decreases under renormalization group flow, as predicted by the g-theorem. Here, using conformal field theory methods, we exactly calculate the entanglement entropy in the boundary Ising universality class. Our expression can be separated into the well known bulk term and a boundary entanglement term, displaying a universal flow between two boundary conditions, in accordance with the g-theorem. These results are obtained within the replica trick approach, where we show that the associated twist field, a central object generating the geometry of an $n$-sheeted Riemann surface, can be bosonized, giving simple analytic access to multiple quantities of interest. We argue that our result applies to other models falling into the same universality class. This includes the vicinity of the quantum critical point of the two-channel Kondo model, allowing to track in real space the presence of a region containing one half of a qubit with entropy $\frac{1}{2}\log (2)$, associated with a free local Majorana fermion.

13 pages, 4 figures

References in corpus (14)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Quantum entanglement in condensed matter systems
• Entanglement negativity in quantum field theory
• Entanglement entropy of two disjoint intervals in conformal field theory II
• Entanglement of low-energy excitations in Conformal Field Theory
• Finite temperature entanglement negativity in conformal field theory
• The g-theorem and quantum information theory
• Entanglement negativity and entropy in non-equilibrium conformal field theory
• Universal low-temperature crossover in two-channel Kondo models
• Entanglement Entropy in a Holographic Kondo Model
• Macroscopic Quantum Entanglement of a Kondo Cloud at Finite Temperature
• Renyi entanglement entropies of descendant states in critical systems with boundaries: conformal field theory and spin chains
• Impurity entanglement entropy in Kondo systems from conformal field theory
• Corrections to scaling in entanglement entropy from boundary perturbations

Cited by in corpus (13)

• Symmetry-resolved entanglement in many-body systems
• Entanglement and symmetry resolution in two dimensional free quantum field theories
• Imbalance Entanglement: Symmetry Decomposition of Negativity
• Measuring Fermionic Entanglement: Entropy, Negativity, and Spin Structure
• U(1) symmetry resolved entanglement in free 1+1 dimensional field theories via form factor bootstrap
• Boundary effects on symmetry resolved entanglement
• Universal Thermal Entanglement of Multichannel Kondo Effects
• Hierarchical entanglement shells of multichannel Kondo clouds
• Universal finite size scaling around tricriticality between topologically ordered, SPT, and trivial phases
• Stabilizer Rényi Entropy Encodes Fusion Rules of Topological Defects and Boundaries
• Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models
• Rényi entropies for one-dimensional quantum systems with mixed boundary conditions
• $2$-Rényi CCNR Negativity of Compact Boson for multiple disjoint intervals