Entanglement Pattern Transition of Quantum States from Directed Percolation

• URL: http://arxiv.org/abs/2605.26219v1
• Date: Mon, 25 May 2026 18:00:04 GMT
• Title: Entanglement Pattern Transition of Quantum States from Directed Percolation
• Abstract summary: Changes in the entanglement structure and critical phenomena are hallmarks of quantum phase transitions.<n>We show how they appear in transitions between classes of states with distinct entanglement patterns beyond the paradigm of stable equilibrium phases of matter.<n>Our results demonstrate how the correspondence between isoTNS and classical evolution can be used to probe the space structure beyond stable ground state.
• Score: 0.007496778384043148
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Changes in the entanglement structure and critical phenomena are hallmarks of quantum phase transitions. Here, we discuss how they appear in transitions between classes of states with distinct entanglement patterns beyond the paradigm of stable equilibrium phases of matter. Using a mapping between stochastic automata and isometric Tensor Network States (isoTNS), we construct a two-dimensional quantum state from the Domany-Kinzel automaton, which is a (1+1)D process with an absorbing phase transition in the directed percolation class. At the critical point of the automaton, the corresponding isoTNS hosts algebraic correlations in all spatial directions. The continuous parent Hamiltonian of this state has a degenerate ground state manifold. It consists of a product state (the absorbing state) and a second state that undergoes a transition from pairwise entanglement between distant regions, similarly to the W state, to a state with trivial entanglement. Our results demonstrate how the correspondence between isoTNS and classical stochastic evolution can be used to probe the Hilbert space structure beyond stable ground state manifolds.

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