Contributor info: Dr Paul A. McClarty

Kristian Tyn Kai Chung, Rafael Flores-Calderón, Rafael C. Torres, Pedro Ribeiro, Sergej Moroz, Paul McClarty

SciPost Phys. 19, 105 (2025) · published 21 October 2025 | Toggle abstract · pdf

Motivated by recent work connecting Higgs phases to symmetry protected topological (SPT) phases, we investigate the interplay of gauge redundancy and global symmetry in lattice gauge theories with Higgs fields in the presence of a boundary. The core conceptual point is that a global symmetry associated to a Higgs field, which is pure-gauge in a closed system, acts physically at the boundary under boundary conditions which allow electric flux to escape the system. We demonstrate in both Abelian and non-Abelian models that this symmetry is spontaneously broken in the Higgs regime, implying the presence of gapless edge modes. Starting with the U(1) Abelian Higgs model in 4D, we demonstrate a boundary phase transition in the 3D XY universality class separating the bulk Higgs and confining regimes. Varying the boundary coupling while preserving the symmetries shifts the location of the boundary phase transition. We then consider non-Abelian gauge theories with fundamental and group-valued Higgs matter, and identify the analogous non-Abelian global symmetry acting on the boundary generated by the total color charge. For $\mathrm{SU}{N}$ gauge theory with fundamental Higgs matter we argue for a boundary phase transition in the $\mathrm{O}{2N}$ universality class, verified numerically for $N=2,3$. For group-valued Higgs matter, the boundary theory is a principal chiral model exhibiting chiral symmetry breaking. We further demonstrate this mechanism in theories with higher-form Higgs fields. We show how the higher-form matter symmetry acts at the boundary and can spontaneously break, exhibiting a boundary confinement-deconfinement transition. We also study the electric-magnetic dual theory, demonstrating a dual magnetic defect condensation transition at the boundary. We discuss some implications and extensions of these findings and what they may imply for the relation between Higgs and SPT phases.

Hana Schiff, Alberto Corticelli, Afonso Guerreiro, Judit Romhányi, Paul McClarty

SciPost Phys. 18, 109 (2025) · published 24 March 2025 | Toggle abstract · pdf

The spin point groups are finite groups whose elements act on both real space and spin space. Among these groups are the magnetic point groups in the case where the real and spin space operations are locked to one another. The magnetic point groups are central to magnetic crystallography for strong spin-orbit coupled systems and the spin point groups generalize these to the intermediate and weak spin-orbit coupled cases. The spin point groups were introduced in the 1960's in the context of condensed matter physics and enumerated shortly thereafter. In this paper, we complete the theory ofcrystallographic spin point groups by presenting an account of these groups and their representation theory. Our main findings are that the so-called nontrivial spin point groups (numbering $598$ groups) have co-irreps corresponding exactly to the (co-)-irreps of regular or black and white groups and we tabulate this correspondence for each nontrivial group. However a total spin group, comprising the product of a nontrivial group and a spin-only group, has new co-irreps in cases where there is continuous rotational freedom. We provide explicit co-irrep tables for all these instances. We also discuss new forms of spin-only group extending the Litvin-Opechowski classes. To exhibit the usefulness of these groups to physically relevant problems we discuss a number of examples from electronic band structures of altermagnets to magnons.

Dominik Hahn, Paul A. McClarty, David J. Luitz

SciPost Phys. 11, 074 (2021) · published 6 October 2021 | Toggle abstract · pdf

The fully frustrated ladder - a quasi-1D geometrically frustrated spin one half Heisenberg model - is non-integrable with local conserved quantities on rungs of the ladder, inducing the fragmentation of the Hilbert space into sectors composed of singlets and triplets on rungs. We explore the far-from-equilibrium dynamics of this model through the entanglement entropy and out-of-time-ordered correlators (OTOC). The post-quench dynamics of the entanglement entropy is highly anomalous as it shows clear non-damped revivals that emerge from short connected chunks of triplets and whose persistence is therefore a consequence of fragmentation. We find that the maximum value of the entropy follows from a picture where coherences between different fragments co-exist with perfect thermalization within each fragment. This means that the eigenstate thermalization hypothesis holds within all sufficiently large Hilbert space fragments. The OTOC shows short distance oscillations arising from short coupled fragments, which become decoherent at longer distances, and a sub-ballistic spreading and long distance exponential decay stemming from an emergent length scale tied to fragmentation.

Luis Colmenarez, Paul A. McClarty, Masudul Haque, David J. Luitz

SciPost Phys. 7, 064 (2019) · published 21 November 2019 | Toggle abstract · pdf

Ergodic quantum many-body systems satisfy the eigenstate thermalization hypothesis (ETH). However, strong disorder can destroy ergodicity through many-body localization (MBL) -- at least in one dimensional systems -- leading to a clear signal of the MBL transition in the probability distributions of energy eigenstate expectation values of local operators. For a paradigmatic model of MBL, namely the random-field Heisenberg spin chain, we consider the full probability distribution of eigenstate correlation functions across the entire phase diagram. We find gaussian distributions at weak disorder, as predicted by pure ETH. At intermediate disorder -- in the thermal phase -- we find further evidence for anomalous thermalization in the form of heavy tails of the distributions. In the MBL phase, we observe peculiar features of the correlator distributions: a strong asymmetry in $S_i^z S_{i+r}^z$ correlators skewed towards negative values; and a multimodal distribution for spin-flip correlators. A quantitative quasi-degenerate perturbation theory calculation of these correlators yields a surprising agreement of the full distribution with the exact results, revealing, in particular, the origin of the multiple peaks in the spin-flip correlator distribution as arising from the resonant and off-resonant admixture of spin configurations. The distribution of the $S_i^zS_{i+r}^z$ correlator exhibits striking differences between the MBL and Anderson insulator cases.