Crosscap Quenches and Entanglement Evolution

TL;DR

This work introduces crosscap quenches, a protocol to study how highly structured thermal-pure states like entangled antipodal pair (EAP) states relax under unitary dynamics. By formulating crosscap quenches in 2D CFTs, applying the replica trick, and analyzing holographic duals via the $\mathbb{RP}^2$ geon, it uncovers universal entanglement-entropy evolution: single intervals display volume-law entanglement while antipodal double intervals exhibit an area-law initially, followed by linear growth and eventual thermalization to a volume-law spectrum. The holographic results, together with numerical simulations in nonintegrable and integrable spin chains, show concordant qualitative behavior and highlight the role of integrability in late-time dynamics, including oscillations and extensive deviations in the integrable case. Overall, crosscap quenches provide a cohesive framework linking CFT, holography, and lattice models to understand how structured thermal states scramble into typical thermal states under quantum dynamics.

Abstract

Understanding the mechanisms by which complex correlations emerge through the dynamics of quantum many-body systems remains a fundamental challenge in modern physics. To address this, quench dynamics starting from nonthermal states have been extensively studied, leading to significant progress. In this paper, we propose a novel quench protocol, termed the "crosscap quench", to investigate how highly structured thermal pure states relax into typical ones. We begin by analyzing conformal field theories (CFTs) and derive universal features in the time evolution of the entanglement entropy. Furthermore, leveraging the AdS/CFT correspondence, we study holographic CFTs, providing an analytically tractable example in chaotic CFTs. Finally, we validate these findings through numerical simulations in both nonintegrable and integrable quantum spin systems.

Figures (6)

• Figure 1: Entanglement entropy $S_A$ of the time-evolved EAP state $\ket{{\rm EAP}(t)}$ in the critical Heisenberg chain with next-nearest-neighbor interactions as a function of $t$ for total system size $2N=24$ and various subsystem size $l$, with solid lines representing the antipodally located double intervals $A = \{1, 2, \dots, l/2\} \cup \{N+1, N+2, \dots, N+l/2\}$ and dashed lines represent the single intervals $A = \{1, 2, \dots, l\}$.
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• Figure 5: Entanglement entropy $S_A$ of the time-evolved EAP state $\ket{{\rm EAP}(t)}$ in the critical transverse-field Ising chain as a function of $t$ for total system size $2N=24$ and various subsystem size $l$, with solid lines representing the antipodally located double intervals $A = \{1, 2, \dots, l/2\} \cup \{N+1, N+2, \dots, N+l/2\}$ and dashed lines represent the single intervals $A = \{1, 2, \dots, l\}$.
• Figure 6: