Person:

Sachdev, Subir

We calculate the Fermi surface of electrons in hole-doped, extended t-J models on a square lattice in a regime where no long-range antiferromagnetic order is present, and no symmetries are broken. Using the “spinon-dopon” formalism of Ribeiro and Wen, we show that short-range antiferromagnetic correlations lead to a reconstruction of the Fermi surface into hole pockets which are not necessarily centered at the antiferromagnetic Brillouin zone boundary. The Brillouin zone area enclosed by the Fermi surface is proportional to the density of dopants away from half-filling, in contrast to the conventional Luttinger theorem, which counts the total electron density. This state realizes a “fractionalized Fermi liquid” (FL*), which has been proposed as a possible ground state of the underdoped cuprates; we note connections to recent experiments. We also discuss the quantum phase transition from the FL* state to the Fermi liquid state with long-range antiferromagnetic order.

The critical theory of the onset of antiferromagnetism in metals, with concomitant Fermi surface reconstruction, has recently been shown to be strongly coupled in two spatial dimensions. The onset of unconventional superconductivity near this critical point is reviewed: it involves a subtle interplay between the breakdown of fermionic quasiparticle excitations on the Fermi surface and the strong pairing glue provided by the antiferromagnetic fluctuations. The net result is a logarithm-squared enhancement of the pairing vertex for generic Fermi surfaces, with a universal dimensionless coefficient independent of the strength of interactions, which is expected to lead to superconductivity at the scale of the Fermi energy. We also discuss the possibility that the antiferromagnetic critical point can be replaced by an intermediate 'fractionalized Fermi liquid' phase, in which there is Fermi surface reconstruction but no long-range antiferromagnetic order. We discuss the relevance of this phase to the underdoped cuprates and the heavy fermion materials.

We present a projective symmetry group (PSG) analysis of the spinless excitations of (Z_2) spin liquids on the kagome lattice. In the simplest case, vortices carrying (Z_2) magnetic flux (“visons”) are shown to transform under the 48 element group (GL(2,Z_3)). Alternative exchange couplings can also lead to a second case with visons transforming under 288-element group (GL(2,Z_3)×D_3). We study the quantum phase transition in which visons condense into confining states with valence bond solid order. The critical field theories and confining states are classified using the vison PSGs.

Recent neutron scattering experiments on the spin-1/2 kagome lattice antiferromagnet ZnCu(_3)(OH)(6)C({12}) (Herbertsmithite) provide the first evidence of fractionalized excitations in a quantum spin liquid state in two spatial dimensions. In contrast to existing theoretical models of spin liquids, the measured dynamic structure factor reveals an excitation continuum which is remarkably at as a function of frequency and has almost no momentum dependence along several high-symmetry directions. Here we show that many experimentally observed features can be explained by the presence of topological vison excitations in a Z(_2) spin liquid. These visons form at bands on the kagome lattice, and thus act as a momentum sink for spin-carrying excitations which are probed by neutron scattering. We compute the dynamic structure factor for two di fferent Z(_2) spin liquids and find that one of them describes Herbertsmithite well above a very low energy cutoff.

We consider Z2 spin liquids on the kagome lattice on the verge of a valence bond solid (VBS) transition, where vortex excitations carrying Z2 magnetic flux—so-called visons—condense. We show that these vison excitations can couple directly to the external electromagnetic field, even though they carry neither spin nor charge. This is possible via a magnetoelastic coupling mechanism recently identified. [Potter, Senthil, and Lee, arXiv:1301.3495; Hao, Phys. Rev. B 85, 174432 (2012)] For the case of transitions to a 36-site unit cell VBS state, the corresponding finite ac conductivity has a specific power-law frequency dependence, which is related to the crossover exponent of the quantum critical point. The visons’ contribution to the optical conductivity at transitions to VBS states with a 12-site unit cell vanishes, however.

We consider bosonic atoms in an optical lattice at integer filling, tuned to the superfluid-Mott insulator critical point, and coupled to a single, mobile impurity atom of a di↵erent species. This setup is inspired by current experiments with quantum gas microscopes, which enable tracking of the impurity motion. We describe the evolution of the impurity motion from quantum wave packet spread at short times, to Brownian diffusion at long times. This dynamics is controlled by the interplay between dangerously irrelevant perturbations at the strongly-interacting field theory describing the superfluid-insulator transition in two spatial dimensions.

Many correlated materials display a quantum-critical point between a paramagnetic and a spin-density wave (SDW) state. The SDW wave vector connects points, so-called hot spots, on opposite sides of the Fermi surface. The Fermi velocities at these pairs of points are in general not parallel. Here, we consider the case where pairs of hot spots coalesce, and the wave vector (π,π) of the SDW connects hot spots with parallel Fermi velocities. Using the specific example of electron-doped cuprates, we first show that Kanamori screening and generic features of the Lindhard function make this case experimentally relevant. The temperature dependence of the correlation length, the spin susceptibility, and the self-energy at the hot spots are found using the two-particle self-consistent theory and specific numerical examples worked out for band and interaction parameters characteristic of the electron-doped cuprates. While the curvature of the Fermi surface at the hot spots leads to deviations from perfect nesting, the pseudonesting conditions lead to drastic modifications of the temperature dependence of these physical observables: Neglecting logarithmic corrections, the correlation length ξ scales like 1/T, namely, z=1 instead of the naive z=2, the (π,π) static spin susceptibility χ like 1/(\sqrt{T}), and the imaginary part of the self-energy at the hot spots like T(^{3/2}). The correction T(_1)(^{−1})∼T(^{3/2}) to the Korringa NMR relaxation rate is subdominant. We also consider this problem at zero temperature, or for frequencies larger than temperature, using a field-theoretical model of gapless collective bosonic modes (SDW fluctuations) interacting with fermions. The imaginary part of the retarded fermionic self-energy close to the hot spots scales as −ω(^{3/2})lnω. This is less singular than earlier predictions of the form −ωlnω. The difference arises from the effects of umklapp terms that were not included in previous studies.

We propose a quantum dimer model for the metallic state of the hole-doped cuprates at low hole density, p. The Hilbert space is spanned by spinless, neutral, bosonic dimers and spin S=1/2S=1/2, charge +e+e fermionic dimers. The model realizes a “fractionalized Fermi liquid” with no symmetry breaking and small hole pocket Fermi surfaces enclosing a total area determined by p. Exact diagonalization, on lattices of sizes up to 8×88×8, shows anisotropic quasiparticle residue around the pocket Fermi surfaces. We discuss the relationship to experiments.

We consider two-dimensional metals near a Pomeranchuk instability which breaks 90∘ lattice rotation symmetry. Such metals realize strongly coupled non-Fermi liquids with critical fluctuations of an Ising-nematic order. At low temperatures, impurity scattering provides the dominant source of momentum relaxation and, hence, a nonzero electrical resistivity. We use the memory matrix method to compute the resistivity of this non-Fermi liquid to second order in the impurity potential, without assuming the existence of quasiparticles. Impurity scattering in the d-wave channel acts as a random “field” on the Ising-nematic order. We find contributions to the resistivity with a nearly linear temperature dependence, along with more singular terms; the most singular is the random-field contribution which diverges in the limit of zero temperature.