Density Wave States of Non-Zero Angular Momentum

We study the properties of states in which particle-hole pairs of non-zero angular momentum condense. These states generalize charge- and spin-density-wave states, in which s-wave particle-hole pairs condense. We show that the p-wave spin-singlet state of this type has Peierls ordering, while the d-wave spin-singlet state is the staggered flux state. We discuss model Hamiltonians which favor p-wave and d-wave density wave order. There are analogous orderings for pure spin models, which generalize spin-Peierls order. The spin-triplet density wave states are accompanied by spin-1 Goldstone bosons, but these excitations do not contribute to the spin-spin correlation function. Hence, they must be detected with NQR or Raman scattering experiments. Depending on the geometry and topology of the Fermi surface, these states may admit gapless fermionic excitations. As the Fermi surface geometry is changed, these excitations disappear at a transition which is third-order in mean-field theory. The singlet d-wave and triplet p-wave density wave states are separated from the corresponding superconducting states by zero-temperature O(4)-symmetric critical point

Possible Electronic Structure of Domain Walls in Mott Insulators

We discuss the quantum numbers of domain walls of minimal length induced by doping Mott insulators, carefully distinguishing between holon and hole walls. We define a minimal wall hypothesis that uniquely correlates the observed spatial structure with the doping level for the low-temperature commensurate insulating state of La$_{2-x}$Ba$_x$CuO$_4$ and related materials at $x={1\over 8}$. We remark that interesting walls can be supported not only by conventional antiferromagnetic but also by orbital antiferromagnetic (staggered flux phase, $d$-density) bulk order. We speculate on the validity of the minimal wall hypothesis more generally, and argue that it plausibly explains several of the most striking anomalous features of the cuprate high-temperature superconductors.Comment: Small Additional Comments and References Added, 19 pages, 3 figure

Non-Abelian Anyon Superconductivity

Non-Abelian Anyons exist in certain spin models and may exist in Quantuam Hall systems at certain filling fractions. In this work we studied the ground state of dynamical SU(2) level-$\kappa$ Chern Simons non-Abelian anyons at finite density and no external magnetic field. We find that in the large-$\kappa$ limit the topological interaction induces a pairing instability and the ground state is a superconductor with $\it{d+id}$ gap symmetry. We also develop a picture of pairing for the special value $\kappa=2$ and argue that the ground state is a superfluid of pairs for all values of $\kappa$.Comment: 5 pages, no figure

Time crystals in periodically driven systems

When the discrete time-translation symmetry of isolated, periodically driven systems is spontaneously broken, a new phase of matter can emerge. We review some recent developments on both the theoretical underpinnings and experimental realizations of time crystalline order. Particular attention is placed on delineating the key features of time crystals, which distinguish them from other oscillatory non-equilibrium phenomena.Comment: 7 pages, 5 figures, 1 tabl

Odd-Frequency Density Waves: Non-Fermi-Liquid Metals with an Order Parameter

We consider states with a charge- or spin-density wave order parameter which is odd in frequency, so that the order parameter vanishes at zero frequency and there is a conventional Fermi surface. Such states break translational symmetry and, therefore, are not conventional Fermi liquids. In the odd-frequency spin-density wave case, there are Goldstone bosons and the low-energy spectrum is manifestly different from that of a Fermi liquid. We discuss a simple model which gives rise to such ordered states. The frequency-dependence of the gap leads to an unusual temperature dependence for various thermodynamic and transport properties, notably the resistivity.Comment: References added, one footnote moved into the tex

Perfect Metal Phases of One-Dimensional and Anisotropic Higher-Dimensional Systems

We show that a 1D quantum wire with $23$ channels of interacting fermions has a perfect metal phase in which all weak perturbations that could destabilize this phase are irrelevant. Consequently, weak disorder does not localize it, a weak periodic potential does not open a gap, and contact with a superconductor also fails to open a gap. Similar phases occur for $N \geq 24$ channels of fermions, except for $N=25$, and for $8k$ channels of interacting bosons, with $k\geq 3$. Arrays of perfect metallic wires form higher-dimensional fermionic or bosonic perfect metals, albeit highly-anisotropic ones.Comment: 6 pages. Supplementary information: large matrices in a Mathematica notebook and in 12 text file