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Inhomogeneous adiabatic preparation of a quantum critical ground state in two dimensions
- Source :
- Phys. Rev. B 110, 054410 (2024)
- Publication Year :
- 2024
-
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.<br />Comment: 12 pages, 9 figures; Updated with changes made for publication in Physical Review B
- Subjects :
- Quantum Physics
Condensed Matter - Statistical Mechanics
Subjects
Details
- Database :
- arXiv
- Journal :
- Phys. Rev. B 110, 054410 (2024)
- Publication Type :
- Report
- Accession number :
- edsarx.2406.14989
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevB.110.054410