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.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.

arXiv:2406.14989Physical review. B./Physical review. BAug 6, 20244 citations

Low-temperature expansion for lattice systems with many ground states

Joseph Slawny

Journal of Statistical PhysicsJun 1, 197942 citations

Adiabatic ground state preparation in an expanding lattice

Christopher T. Olund, Maxwell Block, Snir Gazit +2 more

We implement and characterize a numerical algorithm inspired by the $s$ source framework [B. Swingle and J. McGreevy, Phys. Rev. B 93, 045127 (2016)] for building a quantum many-body ground state wave function on a lattice of size $2L$ by applying adiabatic evolution to the corresponding ground state at size $L$ , along with $L$ interleaved ancillae. The procedure can in principle be iterated to repeatedly double the size of the system. We implement the algorithm for several one-dimensional (1D) spin model Hamiltonians, and find that the construction works particularly well when the gap is large and, interestingly, at scale-invariant critical points. We explain this feature as a natural consequence of the lattice expansion procedure. This behavior holds for both the integrable transverse-field Ising model and nonintegrable variations. We also develop an analytic perturbative understanding of the errors deep in either phase of the transverse-field Ising model, and suggest how the circuit could be modified to parametrically reduce errors. In addition to sharpening our perspective on entanglement renormalization in 1D, the algorithm could also potentially be used to build states experimentally, enabling the realization of certain long-range correlated states with low-depth quantum circuits.We implement and characterize a numerical algorithm inspired by the $s$ source framework [B. Swingle and J. McGreevy, Phys. Rev. B 93, 045127 (2016)] for building a quantum many-body ground state wave function on a lattice of size $2L$ by applying adiabatic evolution to the corresponding ground state at size $L$, along with $L$ interleaved ancillae. The procedure can in principle be iterated to repeatedly double the size of the system. We implement the algorithm for several one-dimensional (1D) spin model Hamiltonians, and find that the construction works particularly well when the gap is large and, interestingly, at scale-invariant critical points. We explain this feature as a natural consequence of the lattice expansion procedure. This behavior holds for both the integrable transverse-field Ising model and nonintegrable variations. We also develop an analytic perturbative understanding of the errors deep in either phase of the transverse-field Ising model, and suggest how the circuit could be modified to parametrically reduce errors. In addition to sharpening our perspective on entanglement renormalization in 1D, the algorithm could also potentially be used to build states experimentally, enabling the realization of certain long-range correlated states with low-depth quantum circuits.

arXiv:2002.09592Physical review. B./Physical review. BApr 30, 20202 citations

Adiabatic Preparation of Strongly Correlated Many-body States

Christopher T. Olund, Snir Gazit, John McGreevy +1 more

Bulletin of the American Physical SocietyMay 30, 20180 citations

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.

We implement and characterize a numerical algorithm inspired by the

s

source framework [B. Swingle and J. McGreevy, Phys. Rev. B 93, 045127 (2016)] for building a quantum many-body ground state wave function on a lattice of size

2L

by applying adiabatic evolution to the corresponding ground state at size

L

, along with

L

interleaved ancillae. The procedure can in principle be iterated to repeatedly double the size of the system. We implement the algorithm for several one-dimensional (1D) spin model Hamiltonians, and find that the construction works particularly well when the gap is large and, interestingly, at scale-invariant critical points. We explain this feature as a natural consequence of the lattice expansion procedure. This behavior holds for both the integrable transverse-field Ising model and nonintegrable variations. We also develop an analytic perturbative understanding of the errors deep in either phase of the transverse-field Ising model, and suggest how the circuit could be modified to parametrically reduce errors. In addition to sharpening our perspective on entanglement renormalization in 1D, the algorithm could also potentially be used to build states experimentally, enabling the realization of certain long-range correlated states with low-depth quantum circuits.