Dipole-dipole interaction induced phases in Hydrogen-bonded squaric acid crystal

TL;DR

This study analyzes the finite-temperature phase diagram of proton ordering in squaric acid crystal, revealing two phases influenced by dipole interactions and quantum fluctuations, using advanced Monte Carlo simulations.

Contribution

It introduces a detailed quantum Monte Carlo analysis of dipole interactions in squaric acid, highlighting the impact on phase transitions and the role of quantum and thermal fluctuations.

Findings

Identification of ferroelectric and quantum liquid-like phases.

Small specific heat peak indicating transition influenced by dipole interactions.

Larger dipole strength needed for ferroelectric phase in four-spin models.

Abstract

We study analytically the finite-temperature phase diagram of proton ordering of a quasi-two dimensional hydrogen-bonded system, namely the squaric acid crystal($\text{H}_2\text{C}_4\text{O}_4$). We take into account the four-spin interaction model at the zeroth order. Using an improvised loop algorithm within the Stochastic series expansion quantum monte carlo method, we find two distinct phases as we increase the temperature and magnetic-field. One of the phase is the $\Pi_f$, the phase with long range ferroelectric order and the other being an intermediate state with strong local correlations, i.e, a quantum liquid-like state $\Pi_{ql}$. The transition to $\Pi_{f}$ shows a very small anomalous peak in the specific heat with strong dependence of critical temperature on the strength of dipole-dipole interaction. The presence of the small peak is attributed to the absence of macroscopic degeneracy in the presence of dipole-dipole interaction and re-entrance of such degeneracy to some extent at small temperature. Though the degenerate ground state manifold is identical for a four-spin interaction or appropriate two-spin interaction model at zeroth order, we find that for the former case, the required strength of dipole-dipole interaction is quite larger to induce a ferroelectric phase. The work also presents an intricate connection of quantum fluctuation and thermal fluctuation in the presence of competing interaction with entropic effects.