Scaling of Entanglement Entropy at 2D quantum Lifshitz fixed points and topological fluids

Abstract

The entanglement entropy of a pure quantum state of a bipartite system is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. Critical ground states of local Hamiltonians in one dimension have an entanglement entropy that diverges logarithmically in the subsystem size, with a universal coefficient that is is related to the central charge of the associated conformal field theory. Here I will discuss recent extensions of these ideas to a class of quantum critical points with dynamic critical exponent $z=2$ in two space dimensions and to 2D systems in a topological phase. The application of these ideas to quantum dimer models and fractional quantum Hall states will be discussed.

34 pages, 8 figures. Review paper to appear in a special issue of J. Phys. A on Entanglement Entropy

References in corpus (30)

• Non-Abelian Anyons and Topological Quantum Computation
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement entropy and conformal field theory
• Holographic Entanglement Entropy: An Overview
• High Resolution Polar Kerr Effect Measurements of Sr2RuO4: Evidence for Broken Time Reversal Symmetry in the Superconducting State
• Quantum Noise as an Entanglement Meter
• Topological Order and Conformal Quantum Critical Points
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Entanglement entropy in fermionic Laughlin states
• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• Shannon and entanglement entropies of one- and two-dimensional critical wave functions
• Entanglement Entropy in the O(N) model
• Universal entanglement entropy in 2D conformal quantum critical points
• Bipartite entanglement entropy in fractional quantum Hall states
• A quantum topological phase transition at the microscopic level
• Criticality and entanglement in random quantum systems
• On bipartite Rokhsar-Kivelson points and Cantor deconfinement
• Topological Entanglement Entropy from the Holographic Partition Function
• Quantum criticality, lines of fixed points, and phase separation in doped two-dimensional quantum dimer models
• Quantum noise and entanglement generated by a local quantum quench
• Universal and measurable entanglement entropy in the spin-boson model
• An extended Hubbard model with ring exchange: a route to a non-Abelian topological phase
• Entanglement entropy and multifractality at localization transitions
• Topological order from quantum loops and nets
• Entanglement signatures of quantum Hall phase transitions
• Topological phases and topological entropy of two-dimensional systems with finite correlation length
• Entanglement entropy of the random spin-1 Heisenberg chain
• Quantum Hall States at $\nu =\frac{2}{k+2}$
• Replacing energy by von Neumann entropy in quantum phase transitions
• Zero-temperature Kosterlitz-Thouless transition in a two-dimensional quantum system

Cited by in corpus (33)

• Entanglement entropy and conformal field theory
• Holographic Entanglement Entropy: An Overview
• Entanglement entropy in free quantum field theory
• An analytic Lifshitz black hole
• Negativity and topological order in the toric code
• Criticality and entanglement in random quantum systems
• Entanglement spectrum of random-singlet quantum critical points
• Entanglement entropies in free fermion gases for arbitrary dimension
• Quantum noise and entanglement generated by a local quantum quench
• Entanglement Entropy in Lifshitz Theories
• Entanglement entropy of integer Quantum Hall states in polygonal domains
• Scaling of entanglement entropy across Lifshitz transitions
• Entanglement entropy and the complex plane of replicas
• Universal Behavior of Entanglement in 2D Quantum Critical Dimer Models
• Universal Boundary Entropies in Conformal Field Theory: A Quantum Monte Carlo Study
• Lifshitz entanglement entropy from holographic cMERA
• Lifshitz fermionic theories with z=2 anisotropic scaling
• Massless Lifshitz Field Theory for Arbitrary $z$
• Distilling topological entropy from single entanglement measures on projected systems
• Incommensurability Effects in Odd Length J_1-J_2 Quantum Spin Chains: On-site magnetization and Entanglement
• Entanglement Entropy at Generalized Rokhsar-Kivelson Points of Quantum Dimer Models
• The classical mutual information in mean-field spin glass models
• Identifying topological order in the Shastry-Sutherland model via entanglement entropy
• Entanglement Entropy in Excited States of the Quantum Lifshitz Model
• Entanglement Entropy Near Kondo-Destruction Quantum Critical Points
• Evidence of quantum phase transition in real-space vacuum entanglement of higher derivative scalar quantum field theories
• Aspects of quantum information in finite density field theory
• Entanglement Entropy with Lifshitz Fermions
• Correlations, Dynamics, and Interferometry of Anyons in the Lowest Landau Level
• Field Space Entanglement Entropy, Zero Modes and Lifshitz Models
• 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