Imaging Bond Order near Nonmagnetic Impurities in Square-Lattice Antiferromagnets

Abstract

We study the textures of generalized "charge densities" (scalar objects invariant under time reversal), in the vicinity of non-magnetic impurities in square-lattice quantum anti-ferromagnets, by order parameter field theories. Our central finding is the structure of the "vortex" in the generalized density wave order parameter centered at the non-magnetic impurity. Using exact numerical data from quantum Monte Carlo simulations on an antiferromagnetic spin model, we are able to verify the results of our field theoretic study. We extend our phenomenological approach to the period-4 bond-centered density wave found in the underdoped cuprates Introduction: The response of quantum many-body systems to impurities is a rich subject with important experimental consequences. At vanishingly small concentrations, the impurities behave independently and hence experimental measurements directly probe the physics of a single isolated impurity. The response of an otherwise translationally invariant quantum system to the introduction of a single quantum impurity can teach us fundamentally new things about many-body quantum physics; perhaps the most famous example is the introduction of magnetic impurities in non-magnetic metals, the so-called Kondo problem [1]. Although the role of single non-magnetic impurities is innocuous in conventional metals, it has been recognized that they can have profound consequences on strongly correlated quantum magnets, because the removal of a moment from the lattice results in an uncompensated Berry phase Even small amounts of frustration are known to lead to enhanced fluctuations of competing order parameters in quantum magnets. One of the most important class of such competing orders are generalized "charge density" waves [5]. We use the phrase " charge density" in a very general sense, to imply any order parameter that is scalar under spin rotation and even under time reversal, and hence includes, e.g., stripes [6,7,8,9,10] and valence bond solids [11,12,13,14]. Non-magnetic impurities couple efficiently to these fluctuation since they break translational symmetry and like the "charge density" waves do not carry any spin. Hence the response of a magnet to non-magnetic impurities contains important information about competing orders and their quantum fluctuations.In this paper we address the pattern of "charge density" modulations in real space around a non-magnetic impurity in square lattice anti-ferromagnets through order parameter field theories as well as exact quantum Monte Carlo (QMC) simulations. One of our central results, that we verify explicitly by QMC, is the de-

Edge and impurity response in two-dimensional quantum antiferromagnets

“…V, we briefly discussed some related issues on the problem of a single nonmagnetic impurity, complementary to the more detailed discussion of this case in Ref. 9.…”

“…9, this perturbation induces "vortices" in the VBS order around the impurity. We now discuss the origins of the term S imp,V in the critical theory of the Néel-VBS transition in the insulator.…”

Lattice symmetry breaking in cuprate superconductors: stripes, nematics, and superconductivity

“…21 A detailed analysis of the impurity-induced patterns in a magnet with a tendency towards valence-bond order is in Ref. (67).…”

Many-body calculation of the spatial extent of the wave function of a nonmagnetic impurity in ad-wave high-temperature superconductor using thet−Jmodel

“…͑5͒ in Ref. 21. However, despite many similarities ͑e.g., crystallization of dimer bonds in the vicinity of the impurity͒, the vortex structure is not recognizable in our simulation.…”

“…When the system is close to a quantum transition from a magnetically ordered Néel state to a spin-gap state with long-range VBS order, a missing spin gives rise to a VBS pinwheel ͑or "vortex"͒ around the impurity. 21 To compare with these predictions we have computed the VBS order parameter of Eq. ͑5͒ in Ref.…”