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

• URL: http://arxiv.org/abs/2406.14989v3
• Date: Thu, 20 Feb 2025 11:24:31 GMT
• Title: Inhomogeneous adiabatic preparation of a quantum critical ground state in two dimensions
• Authors: Ihor Sokolov, Francis A. Bayocboc Jr., Marek M. Rams, Jacek Dziarmaga,
• Abstract summary: We consider inhomogeneous ramps in two dimensions: initially, the parameter is made critical at the center of a lattice.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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