Topological aspects and deconfinement of quantum critical points in 2 + 1 dimension antiferromagnets

Zaira Nazario, David Santiago

Matthew S. Block, Ribhu K. Kaul

Max A. Metlitski

This thesis is devoted to the study of strongly correlated electron systems in two spatial dimensions. The main perspective used in this work is that of scaling, implemented by the renormalization group formalism. This thesis can be divided into three main parts. The first part, comprised of chapters 2-5, investigates various aspects of two dimensional insulating quantum antiferromagnets. In particular, chapters 2-4 deal with the phase transition between an ordered antiferromagnet and a valence bond solid on a square lattice. This transition falls outside the conventional Landau-Ginzburg-Wilson paradigm and is described by a so-called “deconfined ” quantum critical point. In chapter 2, we present an elegant calculation of the scaling dimension of the valence bond solid order parameter at this quantum critical point. Chapters 3 and 4 investigate signatures of deconfined criticality in the response of an antiferromagnet to non-magnetic impurities. Chapter 5 describes the edge response of a conventional ordered square-lattice antiferromagnet. The second part of this thesis, comprised of chapters 6 and 7, studies the subject

Zaira Nazario, David Santiago

Chen Peng, Long Zhang, Zhong-Yi Lu

A higher-order (HO) symmetry-protected topological (SPT) state can be realized in a plaquette-modulated square lattice antiferromagnet, which hosts a spin-$1/2$ degenerate mode on each corner of the lattice with open boundaries. In this work, we show with the field-theoretic analysis and quantum Monte Carlo simulations that the plaquette modulation can drive a direct topological quantum phase transition from the HOSPT to a trivial disordered phase across the deconfined quantum critical point (DQCP) between the antiferromagnetic (AF) order and the valence bond solid (VBS) order, thus the DQCP is a multicritical point bridging both the AF-VBS transition and the topological transition of the HOSPT phase. Our work thus reveals the ubiquitous duality between topological transitions of SPT phases and DQCPs.

Chao‐Ming Jian, Alex Thomson, Alex Rasmussen +2 more

In this work we propose a theory for the deconfined quantum critical point (DQCP) for spin-1/2 systems on a triangular lattice, which is a direct unfine-tuned quantum phase transition between the standard ``$\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$'' noncollinear antiferromagnetic order (or the so-called ${120}^{\ensuremath{\circ}}$ state) and the ``$\sqrt{12}\ifmmode\times\else\texttimes\fi{}\sqrt{12}$'' valence solid bond (VBS) order, both of which are very standard ordered phases often observed in numerical simulations. This transition is beyond the standard Landau-Ginzburg paradigm and is also fundamentally different from the original DQCP theory on the square lattice due to the very different structures of both the magnetic and VBS order on frustrated lattices. We first propose a topological term in the effective-field theory that captures the ``intertwinement'' between the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ antiferromagnetic order and the $\sqrt{12}\ifmmode\times\else\texttimes\fi{}\sqrt{12}$ VBS order. Then using a controlled renormalization-group calculation, we demonstrate that an unfine-tuned direct continuous DQCP exists between the two ordered phases mentioned above. This DQCP is described by the ${N}_{f}=4$ quantum electrodynamics (QED) with an emergent PSU(4)=SU(4)/${Z}_{4}$ symmetry only at the critical point. The aforementioned topological term is also naturally derived from the ${N}_{f}=4$ QED. We also point out that physics around this DQCP is analogous to the boundary of a $3d$ bosonic symmetry- protected topological state with only on-site symmetries.