The entanglement membrane in exactly solvable lattice models

Abstract

Entanglement membrane theory is an effective coarse-grained description of entanglement dynamics and operator growth in chaotic quantum many-body systems. The fundamental quantity characterizing the membrane is the entanglement line tension. However, determining the entanglement line tension for microscopic models is in general exponentially difficult. We compute the entanglement line tension in a recently introduced class of exactly solvable yet chaotic unitary circuits, so-called generalized dual-unitary circuits, obtaining a non-trivial form that gives rise to a hierarchy of velocity scales with $v_E<v_B$. For the lowest level of the hierarchy, ${\bar{\mathcal{L}}}_2$ circuits, the entanglement line tension can be computed entirely, while for the higher levels the solvability is reduced to certain regions in spacetime. This partial solvability enables us to place bounds on the entanglement velocity. We find that ${\bar{\mathcal{L}}}_2$ circuits saturate certain bounds on entanglement growth that are also saturated in holographic models. Furthermore, we relate the entanglement line tension to temporal entanglement and correlation functions. We also develop new methods of constructing generalized dual-unitary gates, including constructions based on complex Hadamard matrices that exhibit additional solvability properties and constructions that display behavior unique to local dimension greater than or equal to three. Our results shed light on entanglement membrane theory in microscopic Floquet lattice models and enable us to perform non-trivial checks on the validity of its predictions by comparison to exact and numerical calculations. Moreover, they demonstrate that generalized dual-unitary circuits display a more generic form of information dynamics than dual-unitary circuits.

22 pages, 13 figures, 2 tables + 6 pages, 1 figure appendix; Added material: pedagogical introduction to entanglement membrane theory, extended bounds on $v_E$ in higher levels of the hierarchy, constructions of generalized dual-unitary gates based on complex Hadamard matrices, tensor product constructions

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• Black holes as mirrors: quantum information in random subsystems
• Scrambling in Random Unitary Circuits: Exact Results
• Exact quench dynamics of the Floquet quantum East model at the deterministic point
• Quantum information spreading in generalised dual-unitary circuits
• All unitaries having operator Schmidt rank 2 are controlled unitaries
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Cited by in corpus (12)

• Fock-space delocalization and the emergence of the Porter-Thomas distribution from dual-unitary dynamics
• Operator dynamics and entanglement in space-time dual Hadamard lattices
• Exactly solvable many-body dynamics from space-time duality
• Temporal Entanglement Barriers in Dual-Unitary Clifford Circuits with Measurements
• Fundamental charges for dual-unitary circuits
• Entanglement in dual unitary quantum circuits with impurities
• More on the Operator Space Entanglement (OSE): Rényi OSE, revivals, and integrability breaking
• Solvable Quantum Circuits in Tree+1 Dimensions
• Geometric constructions of generalized dual-unitary circuits from biunitarity
• Entanglement dynamics from universal low-lying modes
• Roughening Transition in Quantum Circuits
• Entanglement structure for finite system under dual-unitary dynamics