The 1D quantum XY model exact solution requires careful application of the Bogoliubov transformation.
the verdict
INSUFFICIENT LEANING
refutedsupported
the weight of evidence
2 sources for · 0 against
The retrieved literature discusses the exact solution and simulation of 1D spin models and related exact methods like the Jordan-Wigner transformation, but none of the items provide full, direct coverage establishing that the exact solution of the 1D quantum XY model specifically requires the Bogoliubov transformation.
Abstract The anisotropic XY-model in a transverse field ( s= 1 2 ) on the one-dimensional alternating superlattice (closed chain) is considered. The solution of the model is obtained by introducing a generalized Jordan–Wigner transformation which maps the system onto a non-interacting fermion gas. The exact excitation spectrum is determined by reducing the problem to a diagonalization of a block matrix, and it is shown that it is numerically identical to the one obtained by using the approximate transfer matrix method. The induced magnetization and the susceptibility χ zz are determined as a function of the transverse field, and it is shown that, at T =0, the susceptibility presents multiple singularities. It is also shown, as expected, that this critical behaviour driven by transverse field belongs to the same universality class of the model on the alternating chain.
The field of quantum computing has grown fast in recent years, both in theoretical advancements and the practical construction of quantum computers. These computers were initially proposed, among other reasons, to efficiently simulate and comprehend the complexities of quantum physics. In this paper, we present a comprehensive scheme for the exact simulation of the 1-D XY model on a quantum computer. We successfully diagonalize the proposed Hamiltonian, enabling access to the complete energy spectrum. Furthermore, we propose a novel approach to design a quantum circuit to perform exact time evolution. Among all the possibilities this opens, we compute the ground and excited state energies for the symmetric XY model with spin chains of
n=4
n
=
4
and
n=8
n
=
8
spins. Further, we calculate the expected value of transverse magnetization for the ground state in the transverse Ising model. Both studies allow the observation of a quantum phase transition from an antiferromagnetic to a paramagnetic state. Additionally, we have simulated the time evolution of the state all spins up in the transverse Ising model. The scalability and high performance of our algorithm make it an ideal candidate for benchmarking purposes, while also laying the foundation for simulating other integrable models on quantum computers.
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