Entanglement Entropy with Lifshitz Fermions

Abstract

We investigate fermions with Lifshitz scaling symmetry and study their entanglement entropy in 1+1 dimensions as a function of the scaling exponent $z$. Remarkably, in the ground state the entanglement entropy vanishes for even values of $z$, whereas for odd values it is independent of $z$ and equal to the relativistic case with $z=1$. We show this using the correlation method on the lattice, and also using a holographic cMERA approach. The entanglement entropy in a thermal state is a more detailed function of $z$ and $T$ which we plot using the lattice correlation method. The dependence on the even- or oddness of $z$ still shows for small temperatures, but is washed out for large temperatures or large values of $z$.

arXiv comment19 pages, 4 figures

References in corpus (38)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Entanglement Entropy and Quantum Field Theory
• Entanglement in quantum critical phenomena
• Aspects of Holographic Entanglement Entropy
• Entropy and Area
• Geometric and Renormalized Entropy in Conformal Field Theory
• Entanglement entropy and conformal field theory
• Lectures on holographic methods for condensed matter physics
• Entanglement renormalization
• Calculation of reduced density matrices from correlation functions
• Entanglement Renormalization and Holography
• Entanglement entropy in free quantum field theory
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories
• Entanglement renormalization for quantum fields
• Holographic Geometry of Entanglement Renormalization in Quantum Field Theories
• Spatial structures and localization of vacuum entanglement in the linear harmonic chain
• Universal entanglement entropy in 2D conformal quantum critical points
• Field Theory on Newton-Cartan Backgrounds and Symmetries of the Lifshitz Vacuum
• Asymptotically free four-fermi theory in 4 dimensions at the z=3 Lifshitz-like fixed point
• Strong coupling theory of heavy fermion criticality
• Scaling of Entanglement Entropy at 2D quantum Lifshitz fixed points and topological fluids
• Entanglement Evolution in Lifshitz-type Scalar Theories
• Entanglement Entropy in Lifshitz Theories
• Two-cylinder entanglement entropy under a twist
• Correlation functions in theories with Lifshitz scaling
• Axial anomalies of Lifshitz fermions
• Logarithmic Negativity in Quantum Lifshitz Theories
• Lifshitz entanglement entropy from holographic cMERA
• Entanglement Entropy in Generalised Quantum Lifshitz Models
• Entanglement Entropy and Mutual Information of Circular Entangling Surfaces in 2 + 1-dimensional Quantum Lifshitz Model
• On higher-order corrections in a four-fermion Lifshitz model
• Lifshitz fermionic theories with z=2 anisotropic scaling
• More on axial anomalies of Lifshitz fermions
• Entanglement Entropy of Excited States in the Quantum Lifshitz Model
• Entanglement Entropy in Excited States of the Quantum Lifshitz Model
• Emergent geometry and path integral optimization for a Lifshitz action
• Entanglement after Quantum Quenches in Lifshitz Scalar Theories

Cited by in corpus (6)

• Krylov Complexity in Lifshitz-type Scalar Field Theories
• Finite Temperature Entanglement Negativity of Fermionic Symmetry Protected Topological Phases and Quantum Critical Points in One Dimension
• Krylov Complexity in Lifshitz-type Dirac Field Theories
• Entanglement in Lifshitz Fermion Theories
• Entanglement entropies of an interval in the free Schrödinger field theory on the half line
• Entanglement entropies of an interval in the free Schrödinger field theory at finite density