Classical origins of Landau-incompatible transitions

Abstract

Continuous phase transitions where symmetry is spontaneously broken are ubiquitous in physics and often found between `Landau-compatible' phases where residual symmetries of one phase are a subset of the other. However, continuous `deconfined quantum critical' transitions between Landau-incompatible symmetry-breaking phases are known to exist in certain quantum systems, often with anomalous microscopic symmetries. In this Letter, we investigate the need for such special conditions. We show that Landau-incompatible transitions can be found in a family of well-known classical statistical mechanical models with anomaly-free symmetries, introduced by José, Kadanoff, Kirkpatrick and Nelson (Phys. Rev. B 16, 1217). The models are anisotropic deformations of the classical 2d XY model labelled by a positive integer $Q$. For a range of temperatures, even $Q$ models exhibit two Landau-incompatible partial symmetry-breaking phases and a direct transition between them for $Q\ge 4$. Characteristic features of deconfined quantum criticality, such as enhanced symmetries and melting of charged defects are easily seen in a classical setting. For odd $Q$, and corresponding temperature ranges, two regions of a single partial symmetry-breaking phase appear, split by a stable `unnecessary critical' line. We discuss experimental systems that realize these transitions and present anomaly-free quantum models that also exhibit similar phase diagrams.

9 (Main + End matter) + 8 (Supplemental) = 17 pages, 5 (Main + End matter) + 7 (Supplemental) = 12 figures. v2: Improved presentation and expanded discussion to include (a) realization in experiments (main text), (b) explicit paths avoiding unnecessary criticality (end matter) and (c) comments on anomalies in classical systems (supplemental materials). Close to the published version

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Cited by in corpus (7)

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• Unconventional criticality in $O(D)$-invariant loop-constrained Landau theory
• Two-dimensional $J_1$-$J_2$ clock model: Enhanced symmetries, emergent orders, and Landau-incompatible transitions
• Phase transitions and crtical exponents in the six-vertex model on kagome lattices
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice