Shallow Global Quenches in Critical Spin Chains

Universal behavior emerges near continuous phase transitions, such as a quantum critical point. Quantum simulation experiments, such as Rydberg atom arrays and trapped ion chains, have successfully extracted critical exponents by preparing the critical ground state or by performing a Kibble-Zurek sweep through the phase transition [1,2]. Calabrese and Cardy introduced another possible route for probing criticality via global quenches to 1+1d conformal field theories (CFTs), where critical exponents are encoded in the relaxation rates of local observables [3]. We study the Calabrese-Cardy quench protocol on the lattice, where we examine the nonequilibrium dynamics of local observables after a shallow global quench. We determine experimentally feasible initial states for which the CFT predictions should apply, and bound their regime of validity using free-fermion analytics and matrix product state simulations for interacting models.

[1] Haghshenas et al., arXiv:2305.01650

[2] Keesling et al., Nature 2019

[3] Calabrese and Cardy, J. Stat. Mech., 2016