Condensed Matter Theory

Abstract:

Orthogonal spin ordering is rarely observed in magnetic oxides because nearest-neighbor symmetric Heisenberg superexchange interactions usually dominate. We have discovered that in the quadruple perovskite CaFe3Ti4O12, where only the S=2 Fe2+ ion is magnetic, long-range magnetic order consisting of an unusual arrangement of three interpenetrating orthogonal sublattices is stabilized. Each magnetic sublattice corresponds to a set of FeO4 square planes sharing a common orientation. This multi-k magnetic spin ordering is the result of fourth-neighbor spin couplings with a strong easy-axis anisotropy. In an applied magnetic field, each sublattice tends towards ferromagnetic alignment, but remains polarized by internal magnetic fields generated by the others, thus stabilizing in a noncollinear canted ferromagnetic structure. CaFe3Ti4O12 provides a rare example of how nontrivial long-range spin order can arise when near-neighbor Heisenberg superexchange is quenched.

Abstract:

We introduce a new variational wave function for a quantum Hall bilayer at total filling νT=1, which is based on s-wave BCS pairing between electron composite fermions in one layer and hole composite fermions in the other. In addition, we reexamine a trial wave function based on p-wave BCS pairing between electron composite fermions in both layers. We compute the overlap of the optimized trial functions with the ground state from exact diagonalization calculations of up to 14 electrons in a spherical geometry, and we find excellent agreement over the entire range of values of the ratio between the layer separation and the magnetic length. The s-wave trial wave function naturally allows for charge imbalance between the layers and provides important insights into how the physics at large interlayer separations crosses over to that at small separations in a fashion analogous to the BEC-BCS crossover.

Abstract:

Rydberg chains provide an appealing platform for probing conformal field theories (CFTs) that capture universal behavior in a myriad of physical settings. Focusing on a Rydberg chain at the Ising transition separating charge density wave and disordered phases, we establish a detailed link between microscopics and low-energy physics emerging at criticality. We first construct lattice incarnations of primary fields in the underlying Ising CFT including chiral fermions, a nontrivial task given that the Rydberg chain Hamiltonian does not admit an exact fermionization. With this dictionary in hand, we compute correlations of microscopic Rydberg operators, paying special attention to finite, open chains of immediate experimental relevance. We further develop a method to quantify how second-neighbor Rydberg interactions tune the sign and strength of four-fermion couplings in the Ising CFT. Finally, we determine how the Ising fields evolve when four-fermion couplings drive an instability to Ising tricriticality. Our results pave the way to a thorough experimental characterization of Ising criticality in Rydberg arrays, and can inform the design of novel higher-dimensional phases based on coupled critical chains.