Universal behavior of the Shannon and Rényi mutual information of quantum critical chains

Abstract

We study the Shannon and Rényi mutual information (MI) in the ground state (GS) of different critical quantum spin chains. Despite the apparent basis dependence of these quantities we show the existence of some particular basis (we will call them conformal basis) whose finite-size scaling function is related to the central charge $c$ of the underlying conformal field theory of the model. In particular, we verified that for large index $n$, the MI of a subsystem of size $\ell$ in a periodic chain with $L$ sites behaves as $\frac{c}{4}\frac{n}{n-1}\ln\Big{(}\frac{L}π\sin(\frac{π\ell}{L})\Big{)}$, when the ground-state wavefunction is expressed in these special conformal basis. This is in agreement with recent predictions. For generic local basis we will show that, although in some cases $b_n\ln\Big{(}\frac{L}π\sin(\frac{π\ell}{L})\Big{)}$ is a good fit to our numerical data, in general there is no direct relation between $b_n$ and the central charge of the system. We will support our findings with detailed numerical calculations for the transverse field Ising model, $Q=3,4$ quantum Potts chain, quantum Ashkin-Teller chain and the XXZ quantum chain. We will also present some additional results of the Shannon mutual information ($n=1$), for the parafermionic $Z_Q$ quantum chains with $Q=5,6,7$ and $8$.

arXiv comment11 Pages, 12 figures, v2: a new figure added and some other minor additions

References in corpus (20)

• The density-matrix renormalization group
• Geometric and Renormalized Entropy in Conformal Field Theory
• Entanglement entropy and conformal field theory
• The classical-quantum boundary for correlations: discord and related measures
• Area laws in quantum systems: mutual information and correlations
• Topological Order and Conformal Quantum Critical Points
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Shannon and entanglement entropies of one- and two-dimensional critical wave functions
• Universal entanglement entropy in 2D conformal quantum critical points
• Universal behavior beyond multifractality in quantum many-body systems
• Exact Correlation Amplitude for the S=1/2 Heisenberg Antiferromagnetic Chain
• Phase transition in the Rényi-Shannon entropy of Luttinger liquids
• Rényi entropy of a line in two-dimensional Ising models
• Shannon and Rényi mutual information in quantum critical spin chains
• Universal behavior of the Shannon mutual information of critical quantum chains
• Area law violation for the mutual information in a nonequilibrium steady state
• Shannon-Rényi entropies and participation spectra across 3d $O(3)$ criticality
• Information theoretic aspects of the two-dimensional Ising model
• Emptiness formation probability, Toeplitz determinants, and conformal field theory
• Entanglement versus mutual information in quantum spin chains

Cited by in corpus (35)

• Quantum entanglement in condensed matter systems
• Genuine quantum correlations in quantum many-body systems: a review of recent progress
• Random matrices and entanglement entropy of trapped Fermi gases
• Critical behaviors of non-stabilizerness in quantum spin chains
• Post measurement bipartite entanglement entropy in conformal field theories
• Entanglement entropy after a partial projective measurement in $1+1$ dimensional conformal field theories: exact results
• Entanglement properties of correlated random spin chains and similarities with conformal invariant systems
• Many-Body-Localization Transition : strong multifractality spectrum for matrix elements of local operators
• Temperature driven quenches in the Ising model: appearance of negative Rényi mutual information
• Generalized mutual informations of quantum critical chains
• Formation probabilities and Shannon information and their time evolution after quantum quench in transverse-field XY-chain
• Computable Rényi mutual information: Area laws and correlations
• Rényi Mutual Information in Quantum Field Theory
• Formation probabilities and statistics of observables as defect problems in the free fermions and the quantum spin chains
• Statistical properties of the Green function in finite size for Anderson Localization models with multifractal eigenvectors
• Entanglement entropy after selective measurements in quantum chains
• Universal behavior of the Shannon mutual information in non-integrable self-dual quantum chains
• Formation probabilities in quantum critical chains and Casimir effect
• Magic transition in measurement-only circuits
• Stabilizer Rényi Entropy and Conformal Field Theory
• Mutual information for fermionic systems
• Finite size corrections to scaling of the formation probabilities and the Casimir effect in the conformal field theories
• Universal logarithmic correction to Rényi (Shannon) entropy in generic systems of critical quadratic fermions
• Pure and Random Quantum Ising Chain : Shannon and Renyi entropies of the ground state via real space renormalization
• A Rényi entropy perspective on topological order in classical toric code models
• Star junctions and watermelons of pure or random quantum Ising chains : finite-size properties of the energy gap at criticality
• Area law and universality in the statistics of subsystem energy
• Explicit Pfaffian Formula for Amplitudes of Fermionic Gaussian Pure States in Arbitrary Pauli Bases
• Efficient Representation of Gaussian Fermionic Pure States in Non-Computational Bases
• Construction of Many-Body-Localized Models where all the eigenstates are Matrix-Product-States
• Shannon entropy in quasiparticle states of quantum chains
• On the simplest scale invariant Tree-Tensor-States preserving the quantum symmetries of the antiferromagnetic XXZ chain
• Critical exponents of block-block mutual information in one-dimensional infinite lattice systems
• Explicit properties of the simplest inhomogeneous Matrix-Product-State including the Riemann metric of the MPS manifold
• Equivalence of Stabilizer and Shannon Rényi Entropies: Exact Results for Quantum Critical Chains