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arXiv:2104.12791 · Physical review. B./Physical review. B

Higher-order topology and corner triplon excitations in two-dimensional quantum spin-dimer models

Arijit Haldar, Geremia Massarelli, Arun Paramekanti

Published Nov 2, 2021• 6 citations
arXivHTMLPDF

Abstract

The concept of free fermion topology has been generalized to $d$-dimensional phases that exhibit $(d\ensuremath{-}n)$-dimensional boundary modes, such as zero-dimensional (0D) corner excitations. Motivated by recent extensions of these ideas to magnetic systems, we consider 2D quantum paramagnets formed by interacting spin dimers with dispersive triplet excitations. We propose two examples of such dimer models, where the spin-gapped bosonic triplon excitations are shown to host bands with nontrivial higher-order topology. We demonstrate this using real-space Bogoliubov--de Gennes calculations that reveal the existence of near-mid band gap corner triplon modes as a signature of higher-order bulk topology. We provide an understanding of the higher-order topology in these systems via computation of bulk topological invariants as well as the construction of edge theories and study their phase transitions as we tune parameters in the model Hamiltonians. We also discuss possible experimental approaches for detecting the emergent corner triplon modes.

DOI
10.1103/physrevb.104.184403

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The concept of free fermion topology has been generalized to ddd-dimensional phases that exhibit (d\ensuremath−n)(d\ensuremath{-}n)(d\ensuremath−n)-dimensional boundary modes, such as zero-dimensional (0D) corner excitations. Motivated by recent extensions of these ideas to magnetic systems, we consider 2D quantum paramagnets formed by interacting spin dimers with dispersive triplet excitations. We propose two examples of such dimer models, where the spin-gapped bosonic triplon excitations are shown to host bands with nontrivial higher-order topology. We demonstrate this using real-space Bogoliubov--de Gennes calculations that reveal the existence of near-mid band gap corner triplon modes as a signature of higher-order bulk topology. We provide an understanding of the higher-order topology in these systems via computation of bulk topological invariants as well as the construction of edge theories and study their phase transitions as we tune parameters in the model Hamiltonians. We also discuss possible experimental approaches for detecting the emergent corner triplon modes.
The concept of free fermion topology has been generalized to ddd-dimensional phases that exhibit (d−n)(d-n)(d−n)-dimensional boundary modes, such as zero-dimensional (0D) corner excitations. Motivated by recent extensions of these ideas to magnetic systems, we consider 2D quantum paramagnets formed by interacting spin dimers with dispersive triplet excitations. We propose two examples of such dimer models, where the spin-gapped bosonic triplon excitations are shown to host bands with nontrivial higher-order topology. We demonstrate this using real-space Bogoliubov--de Gennes calculations that reveal the existence of mid-bandgap corner triplon modes as a signature of higher-order bulk topology. We provide an understanding of the higher-order topology in these systems via a computation of bulk topological invariants as well as the construction of edge theories, and study their phase transitions as we tune parameters in the model Hamiltonians. We also discuss possible experimental approaches for detecting the emergent corner triplon modes.
It has recently been found that bosonic excitations of ordered media, such as phonons or spinons, can exhibit topologically nontrivial band structures. Of particular interest are magnon and triplon excitations in quantum magnets, as they can easily be manipulated by an applied field. Here, we study triplon excitations in an S=1/2S=1/2S=1/2 quantum spin ladder and show that they exhibit nontrivial topology, even in the quantum-disordered paramagnetic phase. Our analysis reveals that the paramagnetic phase actually consists of two separate regions with topologically distinct triplon excitations. We demonstrate that the topological transition between these two regions can be tuned by an external magnetic field. The winding number that characterizes the topology of the triplons is derived and evaluated. By bulk-boundary correspondence, we find that the nonzero winding number implies the presence of localized triplon end states. Experimental signatures and possible physical realizations of the topological paramagnetic phase are discussed.
Many magnetic materials are predicted to exhibit bosonic topological edge modes in their excitation spectra, because of the nontrivial topology of their magnon, triplon, or other quasiparticle band structures. However, there is a discrepancy between theory prediction and experimental observation, which suggests some underlying mechanism that intrinsically suppresses the expected experimental signatures, like the thermal Hall current. Many-body interactions that are not accounted for in the noninteracting quasiparticle picture are most often identified as the reason for the absence of the topological edge modes. Here we report persistent bosonic edge modes at the boundaries of a ladder quantum paramagnet with gapped triplon excitations in the presence of the full many-body interaction. We use tensor network methods to resolve topological edge modes in the time-dependent spin-spin correlations and the dynamical structure factor, which is directly accessible experimentally. We further show that signatures of these edge modes survive even when the noninteracting quasiparticle theory breaks down; we discuss the topological phase diagram of the model, demonstrate the fractionalization of its low-lying excitations, and propose potential material candidates.
We discuss an extension of higher-order topological phases to include bosonic systems. We present two spin models for a second-order topological phase protected by a global ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ symmetry. One model is built from layers of an exactly solvable cluster model for a one-dimensional ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ topological phase, while the other is built from more conventional spin couplings (XY or Heisenberg). These models host gapped, symmetry-protected topological phases on their edges, and corner modes that fall into a projective representation of the symmetry. Using Jordan-Wigner transformations we show that both our models are related to a bilayer of free Majorana fermions that form a fermionic second-order topological phase. We also discuss how our models can be extended to three dimensions to form a third-order topological phase.
We study the higher-order topological spin phases based on a spin analogue of Benalcazar-Bernevig-Hughes model in two dimensions using large-scale quantum Monte Carlo simulations. A continuous Néel-valence bond solid quantum phase transition is revealed by tuning the ratio between dimerized spin couplings, namely, the weak and strong exchange couplings. Through the finite-size scaling analysis, we identify the phase critical points, and consequently, map out the full phase diagrams in related parameter spaces. Particularly, we find that the valence bond solid phase can be a higher-order topological spin phase, which has a gap for spin excitations in the bulk while demonstrates characteristic gapless spin modes at corners of open lattices. We further discuss the connection between the higher-order topological spin phases and the electronic correlated higher-order phases, and find both of them possess gapless spin corner modes that are protected by higher-order topology. Our result exemplifies higher-order physics in the correlated spin systems and will contribute to further understandings of the many-body higher-order topological phenomena.
We present an experimental feasible proposal for synthesizing second-order topological superfluids that support Majorana corner modes in spin-orbit coupled Fermi gases. For this purpose, we consider the staggered spin-orbit coupling introduced in one direction. This results in a system consisted of two sublattices, providing extra degree of freedom for the emergent higher-order topological state. We find the topological trivial superfluids, first-order topological superfluids and boundary-obstructed second-order topological superfluids, as well as different topological phase transitions among them with respect to the the experimental tunable parameters. At the weak interaction regime, the phase transition is characterized by the Chern number accompanied by the bulk gap closing and reopening. However, at the strong interaction regime, we find the system can support the boundary-obstructed topological superfluids with Majorana corner modes, but topological phase transition dose not undergo the gap-closing of bulk bands. Instead the transition is refined by the quadrupole moment and signaled out by the gap-closing of edge-state. The proposal is simply based on the sss-wave interaction and readily feasible via existing experimental techniques, which suggests new possibilities in interacting spin-orbit coupled systems by unifying both first- and higher-order topological superfluids in a simple but realistic microscopic model.