Universality of Critical Dynamics with Finite Entanglement

Area of Science:

• Quantum physics
• Condensed matter theory
• Computational physics

Background:

• The quantum Kibble-Zurek mechanism predicts universal behavior when crossing quantum critical points.
• This mechanism is applied in quantum computing and simulations, often compared with matrix product state (MPS) studies.
• However, limitations in capturing entanglement entropy can modify the mechanism's predictions.

Purpose of the Study:

• To investigate how finite entanglement affects the low-energy dynamics of quantum systems near criticality.
• To provide a theoretical framework for understanding these modifications using MPS-described critical points.
• To establish the role of entanglement in time-dependent critical phenomena.

Main Methods:

• Derivation of a scaling function for finite entanglement effects on the Kibble-Zurek process.
• Numerical simulations using matrix product states (MPS) with finite bond dimension (χ).
• Testing the derived scaling function on the transverse field Ising model and the three-state Potts model.

Main Results:

• The effect of finite entanglement on the Kibble-Zurek process is described by a dimensionless scaling function.
• This function depends on the ratio of dynamic and entanglement-determined length scales.
• Numerical results confirm the scaling collapses for different models and show algorithm independence at finite bond dimension.
• The dynamics at finite bond dimension χ are independent of the chosen algorithm.

Conclusions:

• Finite entanglement plays a precise role in time-dependent critical phenomena.
• The derived scaling function offers a way to account for entanglement limitations in quantum simulations and experiments.
• This work has direct implications for quantum state preparation and the classical simulation of quantum states.