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arXiv:1705.06764 · Physical review. B./Physical review. B

Topological quantum paramagnet in a quantum spin ladder

Darshan G. Joshi, Andreas P. Schnyder

Published Dec 20, 2017• 22 citations
arXivHTMLPDF

Abstract

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 $S=1/2$ 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.

DOI
10.1103/physrevb.96.220405

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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.
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.
The concept of free fermion topology has been generalized to ddd-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.
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.
Topological quantum paramagnets are exotic states of matter, whose magnetic excitations have a topological band structure, while the ground state is topologically trivial. Here we show that a simple model of quantum spins on a honeycomb bilayer hosts a time-reversal-symmetry protected Z2{\mathbb{Z}}_{2}Z2​ topological quantum paramagnet (topological triplon insulator) in the presence of spin-orbit coupling. The excitation spectrum of this quantum paramagnet consists of three triplon bands, two of which carry a nontrivial Z2{\mathbb{Z}}_{2}Z2​ index. As a consequence, there appear two counterpropagating triplon excitation modes at the edge of the system. We compute the triplon edge state spectrum and the Z2{\mathbb{Z}}_{2}Z2​ index for various parameter choices. We further show that upon making one of the Heisenberg couplings stronger, the system undergoes a topological quantum phase transition, where the Z2{\mathbb{Z}}_{2}Z2​ index vanishes, to a different topological quantum paramagnet. In this case the counterpopagating triplon edge modes are disconnected from the bulk excitations and are protected by a chiral and a unitary symmetry. We discuss possible realizations of our model in real materials, in particular d4{d}^{4}d4 Mott insulators, and their potential applications.
Topological quantum paramagnets are exotic states of matter, whose magnetic excitations have a topological band structure, while the ground state is topologically trivial. Here we show that a simple model of quantum spins on a honeycomb bilayer hosts a time-reversal-symmetry protected Z2{\mathbb{Z}}_{2}Z2​ topological quantum paramagnet (topological triplon insulator) in the presence of spin-orbit coupling. The excitation spectrum of this quantum paramagnet consists of three triplon bands, two of which carry a nontrivial Z2{\mathbb{Z}}_{2}Z2​ index. As a consequence, there appear two counterpropagating triplon excitation modes at the edge of the system. We compute the triplon edge state spectrum and the Z2{\mathbb{Z}}_{2}Z2​ index for various parameter choices. We further show that upon making one of the Heisenberg couplings stronger, the system undergoes a topological quantum phase transition, where the Z2{\mathbb{Z}}_{2}Z2​ index vanishes, to a different topological quantum paramagnet. In this case the counterpopagating triplon edge modes are disconnected from the bulk excitations and are protected by a chiral and a unitary symmetry. We discuss possible realizations of our model in real materials, in particular d4{d}^{4}d4 Mott insulators, and their potential applications.
We study a generalized quantum spin ladder with staggered long range interactions that decay as a power-law with exponent \alpha α . Using large scale quantum Monte Carlo (QMC) and density matrix renormalization group (DMRG) simulations, we show that this model undergoes a transition from a rung-dimer phase characterized by a non-local string order parameter, to a symmetry broken N'eel phase. We find evidence that the transition is second order. In the magnetically ordered phase, the spectrum exhibits gapless modes, while excitations in the gapped phase are well described in terms of triplons – bound states of spinons across the legs. We obtain the momentum resolved spin dynamic structure factor numerically and find a well defined triplon band that evolves into a gapless magnon dispersion across the transition. We further discuss the possibility of deconfined criticality in this model.