Competing orders in a magnetic field:  Spin and charge order in the cuprate superconductors

Abstract

We describe two-dimensional quantum spin fluctuations in a superconducting Abrikosov flux lattice induced by a magnetic field applied to a doped Mott insulator. Complete numerical solutions of a self-consistent large-N theory provide detailed information on the phase diagram and on the spatial structure of the dynamic spin spectrum. Our results apply to phases with and without long-range spin-density-wave order, and to the magnetic quantum critical point separating these phases. We discuss the relationship of our results to a number of recent neutron-scattering measurements on the cuprate superconductors in the presence of an applied field. We compute the pinning of static charge order by the vortex cores in the ''spin-gap'' phase where the spin order remains dynamically fluctuating, and argue that these results apply to recent scanning-tunneling-microscopy ͑STM͒ measurements. We show that, with a single typical set of values for the coupling constants, our model describes the field dependence of the elastic-neutron-scattering intensities, the absence of satellite Bragg peaks associated with the vortex lattice in existing neutron-scattering observations, and the spatial extent of charge order in STM observations. We mention implications of our theory for NMR experiments. We also present a theoretical discussion of more exotic states that can be built out of the spin-and charge-order parameters, including spin nematics and phases with ''exciton fractionalization.''

Understanding correlated electron systems by a classification of Mott insulators

“…We will find that the paramagnetic states with fluctuating collinear spin order are entirely different from those present for non-collinear spins in Section 2.2. The order parameter manifold, from (7) is now (S 2 × S 1 )/Z 2 , and the appearance of a Z 2 quotient means that the physics can again be described in a generalized phase diagram of a Z 2 gauge theory [36]. However, the Z 2 flux now identifies a new type of defect which we will discuss in Section 3.2.…”

Stripe fractionalization: the quantum spin nematic and the Abrikosov lattice

“…(1.12) in Ref. [4]) with the consequence that charge order directly accumulates in the vicinity of the vortex cores at any value of the external field. Zhang et al present some numerical results on the behavior of the charge order in the magnetic field (Figs.…”

“…15, 16 in Ref. [4]). A caveat is that these are calculated in the presence of a low lying magnetic exciton and it is not immediately clear if these results are directly applicable to the spin nematic case.…”

“…However, there is yet another state possible [3][4][5]. As long as the stripe dislocations do not proliferate, the spin system is not frustrated in essential ways; it can be argued that the domain wall-ness of the static stripes has everything to do with organizing the motions of the holes in such a way that the frustrating effect of the isolated hole motions are avoided.…”

“…Zhang, Demler and Sachdev [4] have developed a general phenomenological theory, dealing with the case that the antiferromagnetic order is created by the field, arriving at a number of strong predictions. Their starting point is a soft-spin, Ginzburg-Landau-Wilson description of the antiferromagnetic order parameter field f and the superconducting field Y.…”