Mean-field approach to Mid-spectrum Eigenstates of long-range interacting Quantum Systems

• URL: http://arxiv.org/abs/2310.09803v1
• Date: Sun, 15 Oct 2023 11:20:35 GMT
• Title: Mean-field approach to Mid-spectrum Eigenstates of long-range interacting Quantum Systems
• Abstract summary: We study the equilibrium properties of the spin-$1/2$ XY chain with an infinite-range transverse interaction. We show that the two gapless points of the XY model behave in fundamentally different ways.
• Score: 0.5874142059884521
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the equilibrium properties of the spin-$1/2$ XY chain with an infinite-range transverse interaction. At zero temperature, competition between the XY- and the $z$-ordered phases induced by the infinite-range interactions gives rise to a first-order transition upon increasing the transverse coupling. We show that the two gapless points of the XY model behave in fundamentally different ways: isotropic spin chains experience a first-order transition at finite coupling; maximal anisotropic chains overcome a non-algebraic phase transition at zero coupling strength. The phase diagram depicts a first-order reentrant transition that turns second-order along a tricritical line separating a paramagnetic phase from an ordered one at finite temperature. The mean-field approach captures the local properties of the eigenstates and reveals the appearance of a magnetization gap in the spectrum. Global properties, e.g., entanglement entropy, are well approximated only at spectral boundaries. The mean entanglement entropy and the level-spacing ratio deviate from the Gaussian results, revealing the interacting nature of the problem.

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