TY - JOUR

T1 - Fast Preparation of Critical Ground States Using Superluminal Fronts

AU - Agarwal, Kartiek

AU - Bhatt, R. N.

AU - Sondhi, S. L.

N1 - Funding Information:
We thank Eugene Demler, Emanuele G. Dalla Torre, and Joerg Schmiedmayer for insightful comments on this work and for previous related collaborations. We also thank Ivar Martin, Anatoli Polkovnikov, and Alexander M. Polyakov for discussions. We acknowledge support from DOE-BES Grant No. DE-SC0002140 (R. N. B.), DOE Grant No. DE-SC/0016244 (S. L. S.) and the U.K. foundation (K. A.).

PY - 2018/5/22

Y1 - 2018/5/22

N2 - We propose a spatiotemporal quench protocol that allows for the fast preparation of ground states of gapless models with Lorentz invariance. Assuming the system initially resides in the ground state of a corresponding massive model, we show that a superluminally moving "front" that locally quenches the mass, leaves behind it (in space) a state arbitrarily close to the ground state of the gapless model. Importantly, our protocol takes time O(L) to produce the ground state of a system of size ∼Ld (d spatial dimensions), while a fully adiabatic protocol requires time ∼O(L2) to produce a state with exponential accuracy in L. The physics of the dynamical problem can be understood in terms of relativistic rarefaction of excitations generated by the mass front. We provide proof of concept by solving the proposed quench exactly for a system of free bosons in arbitrary dimensions, and for free fermions in d=1. We discuss the role of interactions and UV effects on the free-theory idealization, before numerically illustrating the usefulness of the approach via simulations on the quantum Heisenberg spin chain.

AB - We propose a spatiotemporal quench protocol that allows for the fast preparation of ground states of gapless models with Lorentz invariance. Assuming the system initially resides in the ground state of a corresponding massive model, we show that a superluminally moving "front" that locally quenches the mass, leaves behind it (in space) a state arbitrarily close to the ground state of the gapless model. Importantly, our protocol takes time O(L) to produce the ground state of a system of size ∼Ld (d spatial dimensions), while a fully adiabatic protocol requires time ∼O(L2) to produce a state with exponential accuracy in L. The physics of the dynamical problem can be understood in terms of relativistic rarefaction of excitations generated by the mass front. We provide proof of concept by solving the proposed quench exactly for a system of free bosons in arbitrary dimensions, and for free fermions in d=1. We discuss the role of interactions and UV effects on the free-theory idealization, before numerically illustrating the usefulness of the approach via simulations on the quantum Heisenberg spin chain.

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U2 - 10.1103/PhysRevLett.120.210604

DO - 10.1103/PhysRevLett.120.210604

M3 - Article

C2 - 29883141

AN - SCOPUS:85047616725

VL - 120

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 21

M1 - 210604

ER -