Entanglement Entropy in the Two-Dimensional Random Transverse Field Ising Model

Abstract

The scaling behavior of the entanglement entropy in the two-dimensional random transverse field Ising model is studied numerically through the strong disordered renormalization group method. We find that the leading term of the entanglement entropy always scales linearly with the block size. However, besides this \emph{area law} contribution, we find a subleading logarithmic correction at the quantum critical point. This correction is discussed from the point of view of an underlying percolation transition, both at finite and at zero temperature.

4.3 pages, 4 figures

References in corpus (26)

• Entanglement Entropy and Quantum Field Theory
• Entanglement in quantum critical phenomena
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Violation of the entropic area law for Fermions
• Entropy, entanglement, and area: analytical results for harmonic lattice systems
• Strong disorder RG approach of random systems
• Entanglement entropy of random quantum critical points in one dimension
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Infinite-randomness quantum Ising critical fixed points
• An entanglement-area law for general bosonic harmonic lattice systems
• Entanglement scaling in critical two-dimensional fermionic and bosonic systems
• Scaling of Entanglement Entropy in the Random Singlet Phase
• Critical Behavior and Griffiths-McCoy Singularities in the Two-Dimensional Random Quantum Ising Ferromagnet
• Scaling Behavior of Entanglement in Two- and Three-Dimensional Free Fermions
• Statistics dependence of the entanglement entropy
• Entanglement entropy at infinite randomness fixed points in higher dimensions
• Infinite-Randomness Fixed Points for Chains of Non-Abelian Quasiparticles
• Conformal boundary loop models
• Entanglement entropy of aperiodic quantum spin chains
• Numerical renormalization group study of random transverse Ising models in one and two space dimensions
• Random quantum magnets with broad disorder distribution
• Entanglement entropy of the random spin-1 Heisenberg chain
• Entanglement Entropy in Random Quantum Spin-S Chains
• Entanglement in bosonic systems

Cited by in corpus (65)

• Area laws for the entanglement entropy - a review
• Quantum entanglement in condensed matter systems
• Classical Correlation and Quantum Discord in Critical Systems
• Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
• A short review on entanglement in quantum spin systems
• The entanglement negativity in random spin chains
• Renormalization group study of the two-dimensional random transverse-field Ising model
• Entanglement equipartition in critical random spin chains
• Entanglement Entropy of the Two-Dimensional Heisenberg Antiferromagnet
• Strong Disorder RG approach - a short review of recent developments
• Criticality and entanglement in random quantum systems
• Scaling of entanglement entropy at deconfined quantum criticality
• Infinite disorder scaling of random quantum magnets in three and higher dimensions
• Entanglement entropy dynamics of disordered quantum spin chains
• Entanglement entropies in free fermion gases for arbitrary dimension
• Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations
• Renormalization group study of random quantum magnets
• Finite-size scaling of the entanglement entropy of the quantum Ising chain with homogeneous, periodically modulated and random couplings
• Topological order in paired states of fermions in two-dimensions with breaking of parity and time-reversal symmetries
• Critical behavior and entanglement of the random transverse-field Ising model between one and two dimensions
• Random transverse-field Ising chain with long-range interactions
• Universal logarithmic terms in the entanglement entropy of 2d, 3d and 4d random transverse-field Ising models
• Entanglement Scaling of Fractional Quantum Hall states through Geometric Deformations
• Many-Body Localization : construction of the emergent local conserved operators via block real-space renormalization
• Negativity Spectrum in the Random Singlet Phase
• Edge Mode Combinations in the Entanglement Spectra of Non-Abelian Fractional Quantum Hall States on the Torus
• Disorder overtakes Order in Information Concentration over Quantum Networks
• Subarea law of entanglement in nodal fermionic systems
• Long-range random transverse-field Ising model in three dimensions
• The cavity method for quantum disordered systems: from transverse random field ferromagnets to directed polymers in random media
• Adaptive-weighted tree tensor networks for disordered quantum many-body systems
• Random Transverse Field Ising Model in dimension $d>1$ : scaling analysis in the disordered phase from the Directed Polymer model
• Corner contribution to percolation cluster numbers
• Probability distribution of the entanglement across a cut at an infinite-randomness fixed point
• Complex quantum network models from spin clusters
• Corner contribution to cluster numbers in the Potts model
• Dyson Hierarchical Long-Ranged Quantum Spin-Glass via real-space renormalization
• Quantum criticality in the 2d quasiperiodic Potts model
• Reentrant Random Quantum Ising Antiferromagnet
• Random Transverse Field Ising Model in dimension $d=2,3$ : Infinite Disorder scaling via a non-linear transfer approach
• The scaling of entanglement entropy in a honeycomb lattice on a torus
• Holographic Approach to Entanglement Entropy in Disordered Systems
• Random Transverse Field Spin-Glass Model on the Cayley tree : phase transition between the two Many-Body-Localized Phases
• Periodically driven random quantum spin chains : Real-Space Renormalization for Floquet localized phases
• One-dimensional Ising spin-glass with power-law interaction : real-space renormalization at zero temperature
• Corner contribution to percolation cluster numbers in three dimensions
• Strong Disorder RG principles within a fixed cell-size real space renormalization : application to the Random Transverse Field Ising model on various fractal lattices
• Block Renormalization for quantum Ising models in dimension $d=2$ : applications to the pure and random ferromagnet, and to the spin-glass
• Random Transverse Field Ising model in $d=2$ : analysis via Boundary Strong Disorder Renormalization
• Extreme statistics of the excitations in the random transverse Ising chain
• Logarithmic entanglement growth in two-dimensional disordered fermionic systems
• Entanglement entropy and localization in disordered quantum chains
• Random Transverse Field Ising model on the Cayley Tree : analysis via Boundary Strong Disorder Renormalization
• Healing of Defects in Random Antiferromagnetic Spin Chains
• Quantum-critical properties of the one- and two-dimensional random transverse-field Ising model from large-scale quantum Monte Carlo simulations
• Transverse-spin correlations of the random transverse-field Ising model
• Cluster tomography in percolation
• Random quantum Ising model with three-spin couplings
• Random Ising chain in transverse and longitudinal fields: Strong disorder RG study
• Finite-size scaling analysis of the two-dimensional random transverse-field Ising ferromagnet
• Boundary critical phenomena of the random transverse Ising model in D>=2 dimensions
• Entanglement Entropy of $(2+1)$D Quantum Critical Points with Quenched Disorder: Dimensional Reduction Approach
• The expected number of critical percolation clusters intersecting a line segment
• Random transverse and longitudinal field Ising chains
• Geometry of rare regions behind Griffiths singularities in random quantum magnets