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Modern Physics Letters B

BERRY PHASE AND CRITICAL BEHAVIOR OF THE XY SPIN CHAIN WITH THREE-SITE INTERACTION

Han‐li Lian

Published Jul 27, 2012• 2 citations
Publisher

Abstract

By calculating the Berry Phase (BP) of a central spin, the quantum criticality of the surrounding environment described by an XY spin chain with the three-site interaction in a transverse magnetic field is explored. The BP presents anomalous behavior along the critical region. The finite-size scaling behaviors suggest that the BP of the central spin can well capture the critical properties of the XY spin chain with the three-site interaction.

DOI
10.1142/s0217984912501412

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By calculating the Berry Phase (BP) of a central spin, the quantum criticality of the surrounding environment described by an XY spin chain with the three-site interaction in a transverse magnetic field is explored. The BP presents anomalous behavior along the critical region. The finite-size scaling behaviors suggest that the BP of the central spin can well capture the critical properties of the XY spin chain with the three-site interaction.
We study the quantum critical behavior of the XY\mathit{XY}XY spin chain with multisite interaction by means of a fidelity susceptibility (FS) calculation. The key ingredients (e.g., finite-size scaling behavior, universality principle) of the quantum criticality near the critical point are investigated carefully. The results show that the FS calculation is reliable to characterize the quantum critical behavior and that the multisite interaction can induce the redistribution of the criticality region.
We study the Loschmidt echo (LE) of a coupled system consisting of a central spin and its surrounding environment described by a general XYXYXY spin-chain model. The quantum dynamics of the LE is shown to be remarkably influenced by the quantum criticality of the spin chain. In particular, the decaying behavior of the LE is found to be controlled by the anisotropy parameter of the spin chain. Furthermore, we show that due to the coupling to the spin chain, the ground-state Berry phase for the central spin becomes nonanalytical and its derivative with respect to the magnetic parameter $\ensuremath{\lambda}$ in spin chain diverges along the critical line $\ensuremath{\lambda}=1$, which suggests an alternative measurement of the quantum criticality of the spin chain.
We show that the geometric phase of the ground state in the XY model obeys scaling behavior in the vicinity of a quantum phase transition. In particular we find that the geometric phase is nonanalytical and its derivative with respect to the field strength diverges at the critical magnetic field. Furthermore, the universality in the critical properties of the geometric phase in a family of models is verified. In addition, since the quantum phase transition occurs at a level crossing or avoided level crossing and these level structures can be captured by the Berry curvature, the established relation between the geometric phase and quantum phase transitions is not a specific property of the XY model, but a very general result of many-body systems.
We present exact results for the ground-state and thermodynamic properties of the spin-1/2 XX\mathit{XX}XX chain with three-site interactions in a random (Lorentzian) transverse field. We discuss the influence of randomness on the quantum critical behavior known to be present in the nonrandom model. We find that at zero temperature the characteristic features of the quantum phase transition, such as kinks in the magnetization versus field curve, are smeared out by randomness. However, at low but finite temperatures signatures of the quantum critical behavior are preserved if the randomness is not too large. Even the quantum critical region may be slightly enlarged for very weak randomness. In addition to the exact results for Lorentzian randomness we present a more general discussion of an arbitrarily random transverse magnetic field based on the inspection of the moments of the density of states.