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arXiv:2004.04169 · Proceedings of the National Academy of Sciences

Glide symmetry breaking and Ising criticality in the quasi-1D magnet CoNb 2 O 6

Michele Fava, R. Coldea, S. A. Parameswaran

Published Sep 25, 2020• 44 citations
arXivHTMLPDF

Abstract

We construct a microscopic spin-exchange Hamiltonian for the quasi-one-dimensional (1D) Ising magnet [Formula: see text] that captures detailed and hitherto-unexplained aspects of its dynamic spin structure factor. We perform a symmetry analysis that recalls that an individual Ising chain in this material is buckled, with two sites in each unit cell related by a glide symmetry. Combining this with numerical simulations benchmarked against neutron scattering experiments, we argue that the single-chain Hamiltonian contains a staggered spin-exchange term. We further argue that the transverse-field-tuned quantum critical point in [Formula: see text] corresponds to breaking this glide symmetry, rather than an on-site Ising symmetry as previously believed. This gives a unified microscopic explanation of the dispersion of confined states in the ordered phase and quasiparticle breakdown in the polarized phase at high transverse field.

DOI
10.1073/pnas.2007986117

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We construct a microscopic spin-exchange Hamiltonian for the quasi-one-dimensional (1D) Ising magnet [Formula: see text] that captures detailed and hitherto-unexplained aspects of its dynamic spin structure factor. We perform a symmetry analysis that recalls that an individual Ising chain in this material is buckled, with two sites in each unit cell related by a glide symmetry. Combining this with numerical simulations benchmarked against neutron scattering experiments, we argue that the single-chain Hamiltonian contains a staggered spin-exchange term. We further argue that the transverse-field-tuned quantum critical point in [Formula: see text] corresponds to breaking this glide symmetry, rather than an on-site Ising symmetry as previously believed. This gives a unified microscopic explanation of the dispersion of confined states in the ordered phase and quasiparticle breakdown in the polarized phase at high transverse field.
We present experimental and theoretical evidence that an interesting quantum many-body effect---quasiparticle breakdown---occurs in the quasi-one-dimensional spin-12\frac{1}{2}21​ Ising-like ferromagnet CoNb2O6{\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}CoNb2​O6​ in its paramagnetic phase at high transverse field as a result of explicit breaking of spin inversion symmetry. We propose a quantum spin Hamiltonian capturing the essential one-dimensional physics of CoNb2O6{\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}CoNb2​O6​ and determine the exchange parameters of this model by fitting the calculated single-particle dispersion to the one observed experimentally in applied transverse magnetic fields [1]. We present high-resolution inelastic neutron scattering measurements of the single-particle dispersion which observe ``anomalous broadening'' effects over a narrow energy range at intermediate energies. We propose that this effect originates from the decay of the one particle mode into two-particle states. This decay arises from (i) a finite overlap between the one-particle dispersion and the two-particle continuum in a narrow energy-momentum range and (ii) a small misalignment of the applied field away from the direction perpendicular to the Ising axis in the experiments, which allows for nonzero matrix elements for decay by breaking the Z2{\mathbb{Z}}_{2}Z2​ spin inversion symmetry of the Hamiltonian.
We present experimental and theoretical evidence of novel bound state formation in the low transverse field ordered phase of the quasi-one-dimensional Ising-like material CoNb2O6{\text{CoNb}}_{2}{\text{O}}_{6}CoNb2​O6​. High-resolution single-crystal inelastic neutron scattering measurements observe that small transverse fields lead to a breakup of the spectrum into three parts, each evolving very differently upon increasing field. This can be naturally understood starting from the excitations of the ordered phase of the transverse field Ising model, domain wall quasiparticles (solitons). Here, the transverse field and a staggered off-diagonal exchange create one-soliton hopping terms with opposite signs. We show that this leads to a rich spectrum and a special field, when the strengths of the off-diagonal exchange and transverse field match, at which solitons become localized; the highest field investigated is very close to this special regime. We solve this case analytically and find three two-soliton continua, along with three novel bound states. Perturbing away from this novel localized limit, we find very good qualitative agreement with the experimental data. We also present calculations using exact diagonalization of a recently refined Hamiltonian model for CoNb2O6{\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}CoNb2​O6​ and using diagonalization of the two-soliton subspace, both of which provide a quantitative agreement with the observed spectrum. The theoretical models qualitatively and quantitatively capture a variety of nontrivial features in the observed spectrum, providing insight into the underlying physics of bound state formation.
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Exceptional E8_88​ symmetry in spin dynamics of quasi-one-dimensional antiferromagnet BaCo2_22​V2_22​O8_88​
Exotic excitations can emerge in the vicinity of a quantum phase transition. When the quantum critical point of the one-dimensional (1D) transverse field Ising model is perturbed by a longitudinal magnetic field, it was predicted that its massive excitations are precisely described by the exceptional E8_88​ Lie algebra. Here we show an unambiguous experimental realization of the massive E8_88​ phase in the quasi-1D antiferromagnetic material BaCo2_22​V2_22​O8_88​, via nuclear magnetic resonance and inelastic neutron scattering measurements, and detailed theoretical analysis. The large separation between the masked 1D and 3D quantum critical points of the system allows us to identify, for the first time, the full 8 single-particle E8_88​ excitations as well as various multi-particle states in the spin excitation spectrum. Our results open new experimental route for exploring the dynamics of quantum integrable systems and physics beyond integrability, and thus bridge key physics in condensed matter and statistical field theory.
We argue that ground states of 1D spin chains can spontaneously break U(1) ``easy-plane'' spin rotation symmetry, via true long-range order of (Sx,Sy)(S^x, S^y)(Sx,Sy), at the phase transition between two quasi-long-range-ordered phases. The critical point can be reached by tuning a single parameter in a Hamiltonian with the same symmetry as the XXZ model, without further fine-tuning. Equivalently, it can arise in systems of bosons with particle-hole symmetry, as a long-range-ordered transition point between two quasi-long-range-ordered superfluids. Our approach is to start with the continuum field theory of the isotropic Heisenberg ferromagnet and consider generic perturbations that respect easy-plane symmetry. We argue for a renormalization-group flow to a critical point where long-range order in (Sx,Sy)(S^x, S^y)(Sx,Sy) is enabled by coexisting critical fluctuations of SzS^zSz. (We also discuss multicritical points where further parameters are tuned to zero.) These results show that it is much easier to break continuous symmetries in 1D than standard lore would suggest. The failure of standard intuition for 1D chains (based on the quantum--classical correspondence) can be attributed to Berry phases, which prevent the 1+1D system from mapping to a classical 2D spin model. The present theory also gives an example of an ordered state whose Goldstone mode is interacting even in the infra-red, rather than becoming a free field.