Finite Temperature Critical Behavior of Mutual Information

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 (4)

• 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
• Valence Bond and von Neumann Entanglement Entropy in Heisenberg Ladders

Cited by in corpus (23)

• Quantum Mutual Information as a Probe for Many-Body Localization
• Many-body magic via Pauli-Markov chains -- from criticality to gauge theories
• 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
• 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
• Quantifying non-Gaussianity of quantum-state correlation
• Rényi Mutual Information in Quantum Field Theory
• Computable Rényi mutual information: Area laws and correlations
• Local master equations may fail to describe dissipative critical behavior
• Quantum Critical Universality and Singular Corner Entanglement Entropy of Bilayer Heisenberg-Ising model
• Entanglement properties of the antiferromagnetic-singlet transition in the Hubbard model on bilayer square lattices
• On the entanglement across a cubic interface in 3+1 dimensions
• Entanglement Rényi Negativity of Interacting Fermions from Quantum Monte Carlo Simulations
• Mutual information for fermionic systems
• Entanglement measures and the quantum to classical mapping
• A Path Integral Ground State Monte Carlo Algorithm for Entanglement of Lattice Bosons
• 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
• Rényi entropy of quantum anharmonic chain at non-zero temperature
• Mutual information in interacting spin systems