Fast Preparation of Critical Ground States Using Superluminal Fronts

Area of Science:

• Quantum Many-Body Physics
• Condensed Matter Theory
• High-Energy Physics

Background:

• Preparing ground states of gapless quantum models is crucial for understanding emergent phenomena.
• Adiabatic state preparation is often too slow for practical applications, especially in large systems.

Purpose of the Study:

• To introduce a novel spatiotemporal quench protocol for rapid ground state preparation.
• To demonstrate the efficiency of this protocol compared to traditional adiabatic methods.

Main Methods:

• A superluminally moving mass-quenching front is employed.
• The protocol is analyzed using concepts of relativistic rarefaction of excitations.
• Exact solutions for free bosons and fermions are derived.
• Numerical simulations on the quantum Heisenberg spin chain are performed.

Main Results:

• The protocol rapidly prepares states arbitrarily close to the ground state of gapless models.
• The quench protocol scales as O(L) in time for a system of size ~L^d, significantly faster than the O(L^2) of adiabatic methods.
• The method is validated for free boson and fermion systems and illustrated for interacting spin chains.

Conclusions:

• The proposed spatiotemporal quench protocol offers a significantly faster route to ground state preparation in gapless systems.
• This method provides a powerful tool for exploring quantum many-body physics and condensed matter systems.
• The protocol's efficiency and applicability are demonstrated across various theoretical models and numerical simulations.