Critical Behavior of Mutual Information

The critical behaviors of the mutual information in the one-dimensional spin-1 bilinear biquadratic model are studied. It is found that all the quantum phase transition points including the order-disorder ones and the infinite-order ones in the system can be quantified from the singularity analysis of the mutual information of two sites with the longest distance, because the mutual information captures the correlation properties about the critical fluctuations. More interestingly, the special structure of the wavefunction and the special symmetric property of the system can be indicated by the entropy correlation behaviors. The finite size scaling laws of the mutual information and its derivative are also studied.The critical behaviors of the mutual information in the one-dimensional spin-1 bilinear biquadratic model are studied. It is found that all the quantum phase transition points including the order-disorder ones and the infinite-order ones in the system can be quantified from the singularity analysis of the mutual information of two sites with the longest distance, because the mutual information captures the correlation properties about the critical fluctuations. More interestingly, the special structure of the wavefunction and the special symmetric property of the system can be indicated by the entropy correlation behaviors. The finite size scaling laws of the mutual information and its derivative are also studied.

Journal of Physics A Mathematical and TheoreticalApr 28, 20089 citations

Information Theory

Eduardo Jose Bayro-Corrochano

Springer eBooksJan 1, 20240 citations

Holographic mutual information and critical exponents of the strongly coupled plasma

Hajar Ebrahim, Gol-Mohammad Nafisi

This paper contains discussions on the entanglement entropy and mutual information of a strongly coupled field theory with a critical point which has a holographic dual. We investigate analytically, in the specific regimes of parameters, how these nonlocal operators behave near the critical point. Interestingly, we observe that although the mutual information is constant at the critical point, its slope shows a power-law divergence in the vicinity of the critical point. We show that the leading behavior of mutual information at and near the critical point could yield a set of critical exponents if we regard it as an order parameter. Our result for this set of static critical exponents is $(1/2,1/2,1/2,2)$ which is identical to the one calculated via the thermodynamic quantities. Hence it suggests that beside the numerous merits of mutual information, this quantity also captures the critical behavior of the underlying field theory and it could be used as a proper measure to probe the phase structure associated with the strongly coupled systems.This paper contains discussions on the entanglement entropy and mutual information of a strongly coupled field theory with a critical point which has a holographic dual. We investigate analytically, in the specific regimes of parameters, how these nonlocal operators behave near the critical point. Interestingly, we observe that although the mutual information is constant at the critical point, its slope shows a power-law divergence in the vicinity of the critical point. We show that the leading behavior of mutual information at and near the critical point could yield a set of critical exponents if we regard it as an order parameter. Our result for this set of static critical exponents is $(1/2,1/2,1/2,2)$ which is identical to the one calculated via the thermodynamic quantities. Hence it suggests that beside the numerous merits of mutual information, this quantity also captures the critical behavior of the underlying field theory and it could be used as a proper measure to probe the phase structure associated with the strongly coupled systems.

arXiv:2002.09993Physical review. D/Physical review. D.Nov 6, 202021 citations

Information and Interaction

Ian T. Durham, Dean P. Rickles

The frontiers collectionDec 10, 201622 citations

Universal Behavior of the Shannon Mutual Information of Critical Quantum Chains

Francisco Castilho Alcaraz, M. A. Rajabpour

We consider the Shannon mutual information of subsystems of critical quantum chains in their ground states. Our results indicate a universal leading behavior for large subsystem sizes. Moreover, as happens with the entanglement entropy, its finite-size behavior yields the conformal anomaly c of the underlying conformal field theory governing the long-distance physics of the quantum chain. We study analytically a chain of coupled harmonic oscillators and numerically the Q-state Potts models (Q=2, 3, and 4), the XXZ quantum chain, and the spin-1 Fateev-Zamolodchikov model. The Shannon mutual information is a quantity easily computed, and our results indicate that for relatively small lattice sizes, its finite-size behavior already detects the universality class of quantum critical behavior.We consider the Shannon mutual information of subsystems of critical quantum chains in their ground states. Our results indicate a universal leading behavior for large subsystem sizes. Moreover, as happens with the entanglement entropy, its finite-size behavior yields the conformal anomaly c of the underlying conformal field theory governing the long-distance physics of the quantum chain. We study analytically a chain of coupled harmonic oscillators and numerically the Q-state Potts models (Q=2, 3, and 4), the XXZ quantum chain, and the spin-1 Fateev-Zamolodchikov model. The Shannon mutual information is a quantity easily computed, and our results indicate that for relatively small lattice sizes, its finite-size behavior already detects the universality class of quantum critical behavior.

arXiv:1305.1239Physical Review LettersJul 2, 201370 citations

(1/2,1/2,1/2,2)

which is identical to the one calculated via the thermodynamic quantities. Hence it suggests that beside the numerous merits of mutual information, this quantity also captures the critical behavior of the underlying field theory and it could be used as a proper measure to probe the phase structure associated with the strongly coupled systems.