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arXiv:2001.02339 · Physical review. B./Physical review. B

Anomalous thermal broadening from an infrared catastrophe in two-dimensional quantum antiferromagnets

Matthew C. O'Brien, Oleg P. Sushkov

Published Feb 28, 2020• 2 citations
arXivHTMLPDF

Abstract

The nature of quasiparticles in two-dimensional quantum antiferromagnets at finite temperature remains an open question despite decades of theoretical work. In particular, it is not fully understood how long wavelength excitations contribute to significant broadening of the experimentally observable spectrum. Motivated by this problem, we consider the $XY$ model of easy-plane antiferromagnets, and compute the dynamic structure factor by direct summation of diagrams. In doing so, we find that noninteracting quasiparticles with infinite lifetimes can still lead to a broad response. This forms the basis for a new paradigm describing the interaction of experimental probes with a physical system, where broadening is due neither to the lifetime, nor to the emergence of fractional quasiparticles. Instead, strong fluctuations drive the probe to absorb and radiate an infinite number of arbitrarily low energy quasiparticles, leading us to draw parallels with the infrared catastrophe in quantum electrodynamics.

DOI
10.1103/physrevb.101.064431

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The nature of quasiparticles in two-dimensional quantum antiferromagnets at finite temperature remains an open question despite decades of theoretical work. In particular, it is not fully understood how long wavelength excitations contribute to significant broadening of the experimentally observable spectrum. Motivated by this problem, we consider the XYXYXY model of easy-plane antiferromagnets, and compute the dynamic structure factor by direct summation of diagrams. In doing so, we find that noninteracting quasiparticles with infinite lifetimes can still lead to a broad response. This forms the basis for a new paradigm describing the interaction of experimental probes with a physical system, where broadening is due neither to the lifetime, nor to the emergence of fractional quasiparticles. Instead, strong fluctuations drive the probe to absorb and radiate an infinite number of arbitrarily low energy quasiparticles, leading us to draw parallels with the infrared catastrophe in quantum electrodynamics.
Strong quantum fluctuations in magnetic systems can create disordered quantum spin liquid phases of matter which are not predicted by classical physics. The complexity of the exotic phenomena on display in spin liquids has led to a great deal of theoretical and experimental interest. However, understanding the fundamental nature of the excitations in these systems remains challenging. In this work, we consider the Lifshitz quantum critical point in a two-dimensional frustrated XYXYXY antiferromagnet. At this point, quantum fluctuations destroy long-range order, leading to the formation of an algebraic Lifshitz spin liquid. We demonstrate that the bosonic magnon excitations are long-lived and well-defined in the Lifshitz spin liquid phase, though paradoxically, the dynamic structure factor has a broad non-Lorentzian frequency distribution with no single-particle weight. We resolve this apparent contradiction by showing that the Lifshitz spin liquid suffers from an infrared catastrophe: An external physical probe always excites an infinite number of arbitrarily low-energy quasiparticles, which leads to significant radiative broadening of the spectrum.
We study the behavior of linear and nonlinear spectroscopic quantities in two-dimensional topologically ordered systems, which host anyonic excitations exhibiting fractional statistics. We highlight the role that braiding phases between anyons have on the dynamics of such quasiparticles, which as we show dictates the behavior of both linear response coefficients at finite temperatures, as well as nonlinear pump-probe response coefficients. These quantities, which act as probes of temporal correlations in the system, are shown to obey distinctive universal forms at sufficiently long timescales. As well as providing an experimentally measurable fingerprint of anyonic statistics, the universal behavior that we find also demonstrates anomalously fast thermal relaxation: correlation functions decay as a “squished exponential” C ( t ) ∼ exp ( − [ t / τ ] 3 / 2 ) at long times. We attribute this unusual asymptotic form to the nonlocal nature of interactions between anyons, which allows relaxation to occur much faster than in systems with quasiparticles interacting via local, nonstatistical interactions. While our results apply to any Abelian or non-Abelian topological phase in two-dimensions, we discuss in particular the implications for candidate quantum spin liquid materials, wherein the relevant quantities can be measured using pre-existing time-resolved terahertz-domain spectroscopic techniques. Published by the American Physical Society 2024
It is widely believed that magnetic excitations become increasingly incoherent as the temperature is raised due to random collisions which limit their lifetime. This picture is based on spin-wave calculations for gapless magnets in 2 and 3 dimensions and is observed experimentally as a symmetric Lorentzian broadening in energy. Here, we investigate a three-dimensional dimer antiferromagnet and find unexpectedly that the broadening is asymmetric-indicating that far from thermal decoherence, the excitations behave collectively like a strongly correlated gas. This result suggests that a temperature activated coherent state of quasiparticles is not confined to special cases like the highly dimerized spin-1/2 chain but is found generally in dimerized antiferromagnets of all dimensionalities and perhaps gapped magnets in general.
Theory of quantum electrodynamics in three spatial-time dimensions is applied to the two-dimensional S=1∕2S=1∕2S=1∕2 quantum Heisenberg antiferromagnet in order to investigate a doped hole in high-temperature superconductors. Strong coupling analysis of the U(1) gauge field interaction is carried out to describe spectral broadening observed in the undoped compounds. It is found that the fermionic quasiparticle spectrum is of Gaussian form with the width about 3J3J3J, with JJJ being the superexchange interaction energy. The energy shift of the spectrum is on the order of the quasiparticle bandwidth, which suggests that the system is in the strong coupling regime with respect to the gauge field interaction describing the phase fluctuations about the $\ensuremath{\pi}$-flux state.
Two-dimensional quantum gases provide a distinctive setting in which enhanced thermal fluctuations, finite-size effects, and two-body bound-state formation are intrinsically intertwined. In this work, we study a single attractive impurity immersed in a finite, weakly interacting two-dimensional Bose gas, where finite size stabilizes a nonzero condensate fraction by introducing an infrared momentum scale, thereby enabling a Bogoliubov description of the bath. Using a hybrid approach that combines finite-temperature many-body scattering theory with input from path-integral Monte Carlo, we analyze the impurity quasiparticle energy across the condensate and normal regimes. The infrared scale generates a phonon-activation temperature below which the impurity energy remains nearly temperature independent. Once the resolved phonon modes become thermally populated, their contribution competes with condensate depletion, producing a nonmonotonic temperature dependence of the polaron energy. These results suggest that attractive Bose polarons may serve as sensitive probes of finite-size thermal fluctuations, phonon dressing, and bound-state physics in low-dimensional Bose gases.