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arXiv:2311.07457 · Physical review. B./Physical review. B

Scalar susceptibility of a diluted classical XY model

Reece Beattie-Hauser, Thomas Vojta

Published May 1, 2024• 2 citations
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Abstract

We analyze the amplitude fluctuations in a diluted 3D classical XY model near the magnetic phase transition, motivated by the unusual localization properties of the amplitude (Higgs) mode recently found at the disordered superfluid-Mott glass quantum phase transition. We calculate the amplitude correlation function and the corresponding scalar susceptibility by means of Monte Carlo simulations. In contrast to the quantum case, in which the scalar susceptibility was found to violate naive scaling, we find that the scalar susceptibility of the classical system fulfills naive scaling (employing the clean critical exponents, as expected from the Harris criterion) as the temperature is varied across the phase transition for several dilutions. We discuss possible reasons for this discrepancy as well as the generality of our findings.

DOI
10.1103/physrevb.109.184202

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The amplitude (Higgs) mode near the two-dimensional superfluid--Mott glass quantum phase transition is studied. We map the Bose-Hubbard Hamiltonian of disordered interacting bosons onto an equivalent classical XY\mathit{XY}XY model in (2+12+12+1) dimensions and compute the scalar susceptibility of the order parameter amplitude via Monte Carlo simulation. Analytic continuation of the scalar susceptibilities from imaginary to real frequency to obtain the spectral densities is performed by a modified maximum entropy technique. Our results show that the introduction of disorder into the system leads to unconventional dynamical behavior of the Higgs mode that violates naive scaling, despite the underlying thermodynamics of the transition being of the conventional power-law type. The computed spectral densities exhibit a broad, noncritical response for all energies, and a momentum-independent dispersion for long wavelengths, indicating strong evidence for the localization of the Higgs mode for all dilutions.
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