Entanglement is a key quantum phenomena and understanding transitions between phases of matter with different entanglement properties are an interesting probe of quantum mechanics. We numerically study a model of a 2D tensor network proposed to have an entanglement entropy transition first considered by Vasseur et al.[Phys. Rev. B 100, 134203 (2019)]. We find that by varying the bond dimension of the tensors in the network we can observe a transition between an area and volume phase with a logarithmic critical point around $D\approx 2$ . We further characterize the critical behavior measuring a critical exponent using entanglement entropy and the tripartite quantum mutual information, observe a crossover from a `nearly pure' to entangled area law phase using the the distributions of the entanglement entropy and find a cubic decay of the pairwise mutual information at the transition. We further consider the dependence of these observables for different Rényi entropy. This work helps further validate and characterize random tensor networks as a paradigmatic examples of an entanglement transition.Entanglement is a key quantum phenomena and understanding transitions between phases of matter with different entanglement properties are an interesting probe of quantum mechanics. We numerically study a model of a 2D tensor network proposed to have an entanglement entropy transition first considered by Vasseur et al.[Phys. Rev. B 100, 134203 (2019)]. We find that by varying the bond dimension of the tensors in the network we can observe a transition between an area and volume phase with a logarithmic critical point around $D\approx 2$. We further characterize the critical behavior measuring a critical exponent using entanglement entropy and the tripartite quantum mutual information, observe a crossover from a `nearly pure' to entangled area law phase using the the distributions of the entanglement entropy and find a cubic decay of the pairwise mutual information at the transition. We further consider the dependence of these observables for different Rényi entropy. This work helps further validate and characterize random tensor networks as a paradigmatic examples of an entanglement transition.

arXiv:2108.02225Aug 4, 20218 citations

Tensor-entanglement renormalization

Zheng‐Cheng Gu

Bulletin of the American Physical SocietyMar 16, 20090 citations

Highly entangled 2D ground states: Tensor network, order parameter and correlation

Olai B. Mykland, Zhao Zhang

We present analytical results on the exact tensor network representations and correlation functions of the first examples of 2D ground states with quantum phase transitions between area law and extensive entanglement entropy. The tensor networks constructed are one dimension higher than the lattices of the physical systems, allowing entangled physical degrees of freedoms to be paired with one another arbitrarily far away. Contraction rules of the internal legs are specified by a simple translationally invariant set of rules in terms of the tesselation of cubes or prisms in 3D space. The networks directly generalize the previous holographic tensor networks for 1D Fredkin and Motzkin chains. We also analyze the correlation in the spin and color sectors from the scaling of the height function of random surfaces, revealing additional characterizations of the exotic phase transitions.We present analytical results on the exact tensor network representations and correlation functions of the first examples of 2D ground states with quantum phase transitions between area law and extensive entanglement entropy. The tensor networks constructed are one dimension higher than the lattices of the physical systems, allowing entangled physical degrees of freedoms to be paired with one another arbitrarily far away. Contraction rules of the internal legs are specified by a simple translationally invariant set of rules in terms of the tesselation of cubes or prisms in 3D space. The networks directly generalize the previous holographic tensor networks for 1D Fredkin and Motzkin chains. We also analyze the correlation in the spin and color sectors from the scaling of the height function of random surfaces, revealing additional characterizations of the exotic phase transitions.

arXiv:2502.20192SciPost PhysicsMay 4, 20261 citation

Highly entangled tensor networks

Yingfei Gu, Daniel Bulmash, Xiao-Liang Qi

Bulletin of the American Physical SocietyMar 14, 20160 citations

Mean-field entanglement transitions in random tree tensor networks

Javier Lopez-Piqueres, Brayden Ware, Romain Vasseur

Entanglement phase transitions in quantum chaotic systems subject to projective measurements and in random tensor networks have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a mean-field theory of such transitions by studying the entanglement properties of random tree tensor networks. As a function of bond dimension, we find a phase transition separating area-law from logarithmic scaling of the entanglement entropy. Using a mapping onto a replica statistical mechanics model defined on a Cayley tree and the cavity method, we analyze the scaling properties of such transitions. Our approach provides a tractable, mean-field-like example of an entanglement transition. We verify our predictions numerically by computing directly the entanglement of random tree tensor network states.Entanglement phase transitions in quantum chaotic systems subject to projective measurements and in random tensor networks have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a mean-field theory of such transitions by studying the entanglement properties of random tree tensor networks. As a function of bond dimension, we find a phase transition separating area-law from logarithmic scaling of the entanglement entropy. Using a mapping onto a replica statistical mechanics model defined on a Cayley tree and the cavity method, we analyze the scaling properties of such transitions. Our approach provides a tractable, mean-field-like example of an entanglement transition. We verify our predictions numerically by computing directly the entanglement of random tree tensor network states.

arXiv:2003.01138Physical review. B./Physical review. BAug 6, 202071 citations

D\approx 2

. We further characterize the critical behavior measuring a critical exponent using entanglement entropy and the tripartite quantum mutual information, observe a crossover from a `nearly pure' to entangled area law phase using the the distributions of the entanglement entropy and find a cubic decay of the pairwise mutual information at the transition. We further consider the dependence of these observables for different Rényi entropy. This work helps further validate and characterize random tensor networks as a paradigmatic examples of an entanglement transition.