Finite Temperature Critical Behavior of Mutual Information
arXiv:1101.0430 · doi:10.1103/PhysRevLett.106.135701
Abstract
We study mutual information for Renyi entropy of arbitrary index n, in interacting quantum systems at finite-temperature critical points, using high-temperature expansion, quantum Monte Carlo simulations and scaling theory. We find that for n>1, the critical behavior is manifest at two temperatures T_c and n*T_c. For the XXZ model with Ising anisotropy, the coefficient of the area-law has a t*ln(t) singularity, whereas the subleading correction from corners has a logarithmic divergence, with a coefficient related to the exact results of Cardy and Peschel. For T<n*T_c there is a constant term associated with broken symmetries that jumps at both T_c and n*T_c, which can be understood in terms of a scaling function analogous to the boundary entropy of Affleck and Ludwig.
4 pages, 3 figures, 1 table. To appear in Phys. Rev. Lett
References in corpus (8)
- Entanglement Entropy and Quantum Field Theory
- Holographic Entanglement Entropy: An Overview
- Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
- Interacting anyons in topological quantum liquids: The golden chain
- Universal terms for the entanglement entropy in 2+1 dimensions
- Finite Size Scaling of Mutual Information: A Scalable Simulation
- Statistics dependence of the entanglement entropy
- Valence Bond and von Neumann Entanglement Entropy in Heisenberg Ladders
Cited by in corpus (57)
- Does a single eigenstate encode the full Hamiltonian?
- Genuine quantum correlations in quantum many-body systems: a review of recent progress
- Anomalies in the Entanglement Properties of the Square Lattice Heisenberg Model
- Quantum Monte Carlo calculation of entanglement Renyi entropies for generic quantum systems
- Quantum Mutual Information as a Probe for Many-Body Localization
- Many-body magic via Pauli-Markov chains -- from criticality to gauge theories
- Holographic Mutual Information at Finite Temperature
- Boundary-locality and perturbative structure of entanglement spectra in gapped systems
- Entanglement entropies in free fermion gases for arbitrary dimension
- Entanglement negativity via replica trick: a Quantum Monte Carlo approach
- Finite-temperature mutual information in a simple phase transition
- Nonzero temperature Entanglement Negativity of quantum spin models: Area law, Linked Cluster Expansions and Sudden Death
- Entanglement negativity and conformal field theory: a Monte Carlo study
- Entanglement in ground and excited states of gapped fermion systems and their relationship with fermi surface and thermodynamic equilibrium properties
- Area law violation for the mutual information in a nonequilibrium steady state
- Detecting Classical Phase Transitions with Renyi Mutual Information
- Thermodynamic singularities in the entanglement entropy at a 2D quantum critical point
- Renyi Entanglement Entropy of Interacting Fermions Calculated Using Continuous-Time Quantum Monte Carlo Method
- Entanglement entropy and mutual information across the Mott transition in the two-dimensional Hubbard model
- A Wang-Landau method for calculating Renyi entropies in finite-temperature quantum Monte Carlo simulations
- A path integral Monte Carlo method for Rényi entanglement entropies
- Out-of-equilibrium protocol for Rényi entropies via the Jarzynski equality
- Quantum Virtual Cooling
- Thermodynamic and information-theoretic description of the Mott transition in the two-dimensional Hubbard model
- Particle entanglement in continuum many-body systems via quantum Monte Carlo
- Temperature driven quenches in the Ising model: appearance of negative Rényi mutual information
- Entanglement in gapless resonating valence bond states
- A hybrid Monte Carlo approach to the entanglement entropy of interacting fermions
- Geometric mutual information at classical critical points
- Quantifying non-Gaussianity of quantum-state correlation
- Entanglement and classical fluctuations at finite-temperature critical points
- Entanglement, noise, and the cumulant expansion
- Computable Rényi mutual information: Area laws and correlations
- Rényi Mutual Information in Quantum Field Theory
- Unusual Corrections to Scaling and Convergence of Universal Renyi Properties at Quantum Critical Points
- Local master equations may fail to describe dissipative critical behavior
- Quantum Critical Universality and Singular Corner Entanglement Entropy of Bilayer Heisenberg-Ising model
- Entanglement and classical correlations at the doping-driven Mott transition in the two-dimensional Hubbard model
- On the entanglement across a cubic interface in 3+1 dimensions
- Entanglement properties of the antiferromagnetic-singlet transition in the Hubbard model on bilayer square lattices
- Entanglement Entropy of Coupled Conformal Field Theories and Fermi Liquids
- Entanglement entropy, dualities, and deconfinement in gauge theories
- Entanglement Rényi Negativity of Interacting Fermions from Quantum Monte Carlo Simulations
- Mutual information for fermionic systems
- Critical scaling of the mutual information in two-dimensional disordered Ising models
- Entanglement measures and the quantum to classical mapping
- A Path Integral Ground State Monte Carlo Algorithm for Entanglement of Lattice Bosons
- Geometrical mutual information at the tricritical point of the two-dimensional Blume-Capel model
- Dynamical mean-field theory for Rényi entanglement entropy and mutual Information in Hubbard Model
- Quantum Rényi entropy by optimal thermodynamic integration paths
- Rényi Information flow in the Ising model with single-spin dynamics
- Construction of spin models displaying quantum criticality from quantum field theory
- Entanglement of Free Fermions and Bosons at Finite Temperature
- Rényi entropy of quantum anharmonic chain at non-zero temperature
- Critical exponents of block-block mutual information in one-dimensional infinite lattice systems
- Mutual information in interacting spin systems
- Spin Squeezing, Macrorealism and the Heisenberg uncertainty principle