Inhomogeneous adiabatic preparation of a quantum critical ground state in two dimensions

TL;DR

This paper demonstrates that inhomogeneous, subsonic ramps can adiabatically prepare critical ground states in two-dimensional quantum systems more efficiently than uniform ramps, by exploiting the finite velocity of the critical region expansion.

Contribution

It introduces a method of inhomogeneous adiabatic ramps in 2D quantum systems that achieve faster critical state preparation than uniform ramps, leveraging the critical region's expansion velocity.

Findings

Inhomogeneous ramps become adiabatic with subsonic velocities.

Critical state can be prepared faster than with uniform ramps.

The method applies to models with anisotropic critical dispersion.

Abstract

Adiabatic preparation of a critical ground state is hampered by the closing of its energy gap as the system size increases. However, this gap is directly relevant only for a uniform ramp, where a control parameter in the Hamiltonian is tuned uniformly in space towards the quantum critical point. Here, we consider inhomogeneous ramps in two dimensions: initially, the parameter is made critical at the center of a lattice, from where the critical region expands at a fixed velocity. In the 1D and 2D quantum Ising models, which have a well-defined speed of sound at the critical point, the ramp becomes adiabatic with a subsonic velocity. This subsonic ramp can prepare the critical state faster than a uniform one. Moreover, in both a model of $p$-wave paired 2D fermions and the Kitaev model, the critical dispersion is anisotropic -- linear with a nonzero velocity in one direction and quadratic in the other -- but the gap is still inversely proportional to the linear size of the critical region, with a coefficient proportional to the nonzero velocity. This suffices to make the inhomogeneous ramp adiabatic below a finite crossover velocity and superior to the homogeneous one.