A mini-workshop on timely entanglement
SCHEDULE
10:30 – meets and greets, coffee + cookies
10:45 – Talk 1: Bruno Bertini “Temporal entanglement in chaotic quantum circuits”
11:30 – Lunch/food provided (BYOD) and discussion
12:30 – Talk 2: Katja Klobas “Entanglement negativity and mutual information after a quantum quench: Exact link from space-time duality”
1:15 – followup discussions
Talk 1 Title: Temporal Entanglement in Chaotic Quantum Circuits
Abstract: The concept of space-evolution (or space-time duality) has emerged as a promising approach for studying quantum dynamics. The basic idea involves exchanging the roles of space and time, evolving the system using a space transfer matrix rather than the time evolution operator. The infinite-volume limit is then described by the fixed points of the latter transfer matrix, also known as influence matrices. To establish the potential of this method as a bona fide computational scheme, it is important to understand whether the influence matrices can be efficiently encoded in a classical computer. In this talk I will present a systematic characterisation of their entanglement -- dubbed temporal entanglement -- in chaotic quantum systems with special focus on dual-unitary circuits. Specifically, I will show that, although Rényi entropies with index larger than one are sub-linear in time, the von Neumann entanglement entropy grows linearly.
Talk 2 Title: Entanglement negativity and mutual information after a quantum quench: Exact link from space-time duality
Abstract: I will present recent results on the growth of entanglement between two adjacent regions in a tripartite, one-dimensional many-body system after a quantum quench. Combining a replica trick with a space-time duality transformation a universal relation between the entanglement negativity and Renyi-1/2 mutual information can be derived, which holds at times shorter than the sizes of all subsystems. The proof is directly applicable to any local quantum circuit, i.e., any lattice system in discrete time characterised by local interactions, irrespective of the nature of its dynamics. The derivation indicates that such a relation can be directly extended to any system where information spreads with a finite maximal velocity. The talk is based on [1].
[1] B. Bertini, K. Klobac, T.-C. Lu, Phys. Rev. Lett. 129, 140503 (2022).
ORGANIZERS
Vadim Oganesyan, ITS, CUNY Graduate Center