Inhomogeneous adiabatic preparation of a quantum critical ground state in two dimensions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915162121830400 |
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| author | Sokolov, Ihor Bayocboc Jr., Francis A. Rams, Marek M. Dziarmaga, Jacek |
| author_facet | Sokolov, Ihor Bayocboc Jr., Francis A. Rams, Marek M. Dziarmaga, Jacek |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_14989 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inhomogeneous adiabatic preparation of a quantum critical ground state in two dimensions Sokolov, Ihor Bayocboc Jr., Francis A. Rams, Marek M. Dziarmaga, Jacek Quantum Physics Statistical Mechanics 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. |
| title | Inhomogeneous adiabatic preparation of a quantum critical ground state in two dimensions |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2406.14989 |