Universal Behavior of Entanglement in 2D Quantum Critical Dimer Models

Abstract

We examine the scaling behavior of the entanglement entropy for the 2D quantum dimer model (QDM) at criticality and derive the universal finite sub-leading correction ${\gamma }_{QCP}$. We compute the value of ${\gamma }_{QCP}$ without approximation working directly with the wave function of a generalized 2D QDM at the Rokhsar-Kivelson QCP in the continuum limit. Using the replica approach, we construct the conformal boundary state corresponding to the cyclic identification of $n$-copies along the boundary of the observed region. We find that the universal finite term is ${\gamma }_{QCP}=\ln R-1/2$ where $R$ is the compactification radius of the bose field theory quantum Lifshitz model, the effective field theory of the 2D QDM at quantum criticality. We also demonstrated that the entanglement spectrum of the critical wave function on a large but finite region is described by the characters of the underlying conformal field theory. It is shown that this is formally related to the problems of quantum Brownian motion on $n$-dimensional lattices or equivalently a system of strings interacting with a brane containing a background electromagnetic field and can be written as an expectation value of a vertex operator.

v2. Corrected the glueing condition for the boundary state, published version

References in corpus (38)

• Entanglement Entropy and Quantum Field Theory
• Entanglement in quantum critical phenomena
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Entropy and Area
• Geometric and Renormalized Entropy in Conformal Field Theory
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• String-net condensation: A physical mechanism for topological phases
• On Geometric Entropy
• Entanglement and correlation functions following a local quench: a conformal field theory approach
• Topological Order and Conformal Quantum Critical Points
• Quantum Noise as an Entanglement Meter
• Short-ranged RVB physics, quantum dimer models and Ising gauge theories
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Boundary conformal field theory approach to the two-dimensional critical Ising model with a defect line
• A Class of $P,T$-Invariant Topological Phases of Interacting Electrons
• Topological Entanglement Entropy in Chern-Simons Theories and Quantum Hall Fluids
• Shannon and entanglement entropies of one- and two-dimensional critical wave functions
• Entanglement Entropy in the O(N) model
• Relaxation time for a dimer covering with height representation
• Junctions of three quantum wires
• General Relation between Entanglement and Fluctuations in One Dimension
• Topological Entanglement Entropy in the Quantum Dimer Model on the Triangular Lattice
• Unusual Corrections to Scaling in Entanglement Entropy
• Universal entanglement entropy in 2D conformal quantum critical points
• From quantum mechanics to classical statistical physics: generalized Rokhsar-Kivelson Hamiltonians and the "Stochastic Matrix Form" decomposition
• Interacting classical dimers on the square lattice
• Criticality and entanglement in random quantum systems
• Quantum brownian motion on a triangular lattice and c=2 boundary conformal field theory
• Quantum noise and entanglement generated by a local quantum quench
• Topological order from quantum loops and nets
• Phase Diagram of the Dissipative Hofstadter Model
• Scaling of Entanglement Entropy at 2D quantum Lifshitz fixed points and topological fluids
• Quantum Impurity Problems in Condensed Matter Physics
• Loop models and their critical points
• Magnetic Fields and Fractional Statistics in Boundary Conformal Field Theory
• Boundary Conformal Field Theory and Entanglement Entropy in Two-Dimensional Quantum Lifshitz Critical Point
• Scaling of von Neumann entropy at the Anderson transition

Cited by in corpus (24)

• Bipartite Fluctuations as a Probe of Many-Body Entanglement
• Quantifying nonstabilizerness of matrix product states
• Phase transition in the Rényi-Shannon entropy of Luttinger liquids
• Logarithmic terms in entanglement entropies of 2D quantum critical points and Shannon entropies of spin chains
• Entanglement spectrum of random-singlet quantum critical points
• Entanglement scaling in two-dimensional gapless systems
• Entanglement entropy of the large $N$ Wilson-Fisher conformal field theory
• Entanglement entropy between two coupled Tomonaga-Luttinger liquids
• Entanglement entropy of integer Quantum Hall states in polygonal domains
• Rényi entanglement entropies in quantum dimer models : from criticality to topological order
• The Renyi Entropy and the Multifractal Spectrum of Systems Near the Localization Transition
• Logarithmic Negativity in Quantum Lifshitz Theories
• On the reconstruction of Lifshitz spacetimes
• Entanglement Entropy in Generalised Quantum Lifshitz Models
• Boundary Conformal Field Theory and Entanglement Entropy in Two-Dimensional Quantum Lifshitz Critical Point
• System-environment entanglement phase transitions
• Many-body Localization Transition in Rokhsar-Kivelson-type wave functions
• Particle partition entanglement of bosonic Luttinger liquids
• Cornering gapless quantum states via their torus entanglement
• Dynamical stability of the quantum Lifshitz theory in 2+1 Dimensions
• The classical mutual information in mean-field spin glass models
• Stabilizer Rényi Entropy and Conformal Field Theory
• Entanglement Entropy of Excited States in the Quantum Lifshitz Model
• Universal Renyi mutual information in classical systems: the case of kagome ice