We study quantum quench dynamics in ($1+1$)-dimensional critical systems, starting from thermal pure states called crosscap states, and evolving them under spatially inhomogeneous Hamiltonians. The spatial inhomogeneity is introduced through a deformation of the Hamiltonian, expressed as linear combinations of the generators of the ${\mathrm{SL}}^{\left(q\right)}(2,\mathbb{R})$ subalgebra of the Virasoro algebra. We analyze the free massless Dirac fermion theory and holographic conformal field theory as prototypical examples of integrable and nonintegrable dynamics. Consistent with general expectations, “Möbius-type” deformations lead to thermalization in the nonintegrable case, and to periodic revivals in the integrable one. In contrast, “sine-square-type” and “displacement-type” deformations prevent both thermalization and scrambling, instead producing late-time, graphlike entanglement patterns. These patterns emerge from the interplay between the deformed Hamiltonian and the crosscap initial state and appear to be universal: they are determined solely by the deformation profile while remaining largely insensitive to microscopic details. Finally, we perform a holographic calculation in three-dimensional gravity using the ${\text{AdS}}_3/{\text{CFT}}_2$ correspondence, which reproduces the main features of our ($1+1$)-dimensional study.

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• Dynamical phase transitions
• Exotic phases of matter
• Nonequilibrium systems
• Quantum chaotic systems
• Conformal symmetry
• Conformal field theory
• Critical phenomena