Anomalous behavior of the energy gap in the one-dimensional quantum XY model

Abstract

We re-examine the well-studied one dimensional spin-1/2 $XY$ model to reveal its nontrivial energy spectrum, in particular the energy gap between the ground state and the first excited state. In the case of the isotropic $XY$ model -- the $XX$ model -- the gap behaves very irregularly as a function of the system size at a second order transition point. This is in stark contrast to the usual power-law decay of the gap and is reminiscent of the similar behavior at the first order phase transition in the infinite-range quantum $XY$ model. The gap also shows nontrivial oscillatory behavior for the phase transitions in the anisotropic model in the incommensurate phase. We observe a close relation between this anomalous behavior of the gap and the correlation functions. These results, those for the isotropic case in particular, are important from the viewpoint of quantum annealing where the efficiency of computation is strongly affected by the size dependence of the energy gap.

25 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:1501.02926

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• Longitudinal magnetization dynamics in the quantum Ising ring: A Pfaffian method based on correspondence between momentum space and real space
• Exact thermal properties of free-fermionic spin chains
• Exponentially improved efficient machine learning for quantum many-body states with provable guarantees
• Scaling of the Formation Probabilities and Universal Boundary Entropies in the Quantum XY Spin Chain
• Uhlmann Fidelity and Fidelity Susceptibility for Integrable Spin Chains at Finite Temperature: Exact Results
• Effects of dynamical paths on the energy gap and the corrections to free energy in path integrals of mean-field quantum spin systems
• Ballistic propagation of a local impact in the one-dimensional $XY$ model