Entanglement Barriers in Dual-Unitary Circuits

Abstract

After quantum quenches in many-body systems, finite subsystems evolve non-trivially in time, eventually approaching a stationary state. In typical situations, the reduced density matrix of a given subsystem begins and ends this endeavour as a low-entangled vector in the space of operators. This means that if its operator space entanglement initially grows (which is generically the case), it must eventually decrease, describing a barrier-shaped curve. Understanding the shape of this "entanglement barrier" is interesting for three main reasons: (i) it quantifies the dynamics of entanglement in the (open) subsystem; (ii) it gives information on the approximability of the reduced density matrix by means of matrix product operators; (iii) it shows qualitative differences depending on the type of dynamics undergone by the system, signalling quantum chaos. Here we compute exactly the shape of the entanglement barriers described by different Rényi entropies after quantum quenches in dual-unitary circuits initialised in a class of solvable matrix product states (MPS)s. We show that, for free (SWAP-like) circuits, the entanglement entropy behaves as in rational CFTs. On the other hand, for completely chaotic dual-unitary circuits it behaves as in holographic CFTs, exhibiting a longer entanglement barrier that drops rapidly when the subsystem thermalises. Interestingly, the entanglement spectrum is non-trivial in the completely chaotic case. Higher Rényi entropies behave in an increasingly similar way to rational CFTs, such that the free and completely chaotic barriers are identical in the limit of infinite replicas (i.e. for the so called min-entropy). We also show that, upon increasing the bond dimension of the MPSs, the barrier maintains the same shape. It simply shifts to the left to accommodate for the larger initial entanglement.

27 pages, 4 figures; v2 as appears in the journal

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• Entanglement Negativity and Mutual Information after a Quantum Quench: Exact Link from Space-Time Duality
• Construction and the ergodicity properties of dual unitary quantum circuits
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• From observations to complexity of quantum states via unsupervised learning
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• Exactly solvable many-body dynamics from space-time duality
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• Temporal Entanglement Barriers in Dual-Unitary Clifford Circuits with Measurements
• Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor
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• Structural Stability Hypothesis of Dual Unitary Quantum Chaos
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