Majorana Spin Liquids on a two-leg ladder

We realize a gapless Majorana Orbital Liquid (MOL) using orbital degrees of freedom and also an SU(2)-invariant Majorana Spin Liquid (MSL) using both spin and orbital degrees of freedom in Kitaev-type models on a 2-leg ladder. The models are exactly solvable by Kitaev's parton approach, and we obtain long-wavelength descriptions for both Majorana liquids. The MOL has one gapless mode and power law correlations in energy at incommensuare wavevectors, while the SU(2) MSL has three gapless modes and power law correlations in spin, spin-nematic, and local energy observables. We study the stability of such states to perturbations away from the exactly solvable points. We find that both MOL and MSL can be stable against allowed short-range parton interactions. We also argue that both states persist upon allowing $Z_2$ gauge field fluctuations, in that the number of gapless modes is retained, although with an expanded set of contributions to observables compared to the free parton mean field.Comment: 15 pages, 6 figures. Revised versio

Spin Bose-Metal phase in a spin-1/2 model with ring exchange on a two-leg triangular strip

Recent experiments on triangular lattice organic Mott insulators have found evidence for a 2D spin liquid in proximity to the metal-insulator transition. A Gutzwiller wavefunction study of the triangular lattice Heisenberg model with appropriate four-spin ring exchanges has found that the projected spinon Fermi sea state has a low variational energy. This wavefunction, together with a slave particle gauge theory, suggests that such spin liquid possesses spin correlations that are singular along surfaces in momentum space ("Bose surfaces"). Signatures of this state, which we refer to as a "Spin Bose-Metal" (SBM), are expected to be manifest in quasi-1D ladder systems: The discrete transverse momenta cut through the 2D Bose surface leading to a distinct pattern of 1D gapless modes. Here we search for a quasi-1D descendant of the triangular lattice SBM state by exploring the Heisenberg plus ring model on a two-leg strip (zigzag chain). Using DMRG, variational wavefunctions, and a Bosonization analysis, we map out the full phase diagram. Without ring exchange the model is equivalent to the J_1 - J_2 Heisenberg chain, and we find the expected Bethe-chain and dimerized phases. Remarkably, moderate ring exchange reveals a new gapless phase over a large swath of the phase diagram. Spin and dimer correlations possess particular singular wavevectors and allow us to identify this phase as the hoped for quasi-1D descendant SBM state. We derive a low energy theory and find three gapless modes and one Luttinger parameter controlling all power laws. Potential instabilities out of the zigzag SBM give rise to other interesting phases such as a period-3 VBS or a period-4 Chirality order, which we discover in the DMRG; we also find an interesting SBM state with partial ferromagnetism.Comment: 30 pages, 23 figure

RVB gauge theory and the Topological degeneracy in the Honeycomb Kitaev model

We relate the Z$_2$ gauge theory formalism of the Kitaev model to the SU(2) gauge theory of the resonating valence bond (RVB) physics. Further, we reformulate a known Jordan-Wigner transformation of Kitaev model on a torus in a general way that shows that it can be thought of as a Z$_2$ gauge fixing procedure. The conserved quantities simplify in terms of the gauge invariant Jordan-Wigner fermions, enabling us to construct exact eigen states and calculate physical quantities. We calculate the fermionic spectrum for flux free sector for different gauge field configurations and show that the ground state is four-fold degenerate on a torus in thermodynamic limit. Further on a torus we construct four mutually anti-commuting operators which enable us to prove that all eigenstates of this model are four fold degenerate in thermodynamic limit.Comment: 12 pages, 3 figures. Added affiliation and a new section, 'Acknowledgements'.Typos correcte

A Quantum Theory of Cold Bosonic Atoms in Optical Lattices

Ultracold atoms in optical lattices undergo a quantum phase transition from a superfluid to a Mott insulator as the lattice potential depth is increased. We describe an approximate theory of interacting bosons in optical lattices which provides a qualitative description of both superfluid and insulator states. The theory is based on a change of variables in which the boson coherent state amplitude is replaced by an effective potential which promotes phase coherence between different number states on each lattice site. It is illustrated here by applying it to uniform and fully frustrated lattice cases, but is simple enough that it can easily be applied to spatially inhomogeneous lattice systems

The reconfigurable Josephson circulator/directional amplifier

Circulators and directional amplifiers are crucial non-reciprocal signal routing and processing components involved in microwave readout chains for a variety of applications. They are particularly important in the field of superconducting quantum information, where the devices also need to have minimal photon losses to preserve the quantum coherence of signals. Conventional commercial implementations of each device suffer from losses and are built from very different physical principles, which has led to separate strategies for the construction of their quantum-limited versions. However, as recently proposed theoretically, by establishing simultaneous pairwise conversion and/or gain processes between three modes of a Josephson-junction based superconducting microwave circuit, it is possible to endow the circuit with the functions of either a phase-preserving directional amplifier or a circulator. Here, we experimentally demonstrate these two modes of operation of the same circuit. Furthermore, in the directional amplifier mode, we show that the noise performance is comparable to standard non-directional superconducting amplifiers, while in the circulator mode, we show that the sense of circulation is fully reversible. Our device is far simpler in both modes of operation than previous proposals and implementations, requiring only three microwave pumps. It offers the advantage of flexibility, as it can dynamically switch between modes of operation as its pump conditions are changed. Moreover, by demonstrating that a single three-wave process yields non-reciprocal devices with reconfigurable functions, our work breaks the ground for the development of future, more-complex directional circuits, and has excellent prospects for on-chip integration

Superconductivity in zigzag CuO chains

Superconductivity has recently been discovered in Pr$_{2}$Ba$_{4}$Cu$_{7}$O$_{15-\delta}$ with a maximum $T_c$ of about 15K. Since the CuO planes in this material are believed to be insulating, it has been proposed that the superconductivity occurs in the double (or zigzag) CuO chain layer. On phenomenological grounds, we propose a theoretical interpretation of the experimental results in terms of a new phase for the zigzag chain, labelled by C$_1$S$_{3/2}$. This phase has a gap for some of the relative spin and charge modes but no total spin gap, and can have a divergent superconducting susceptibility for repulsive interactions. A microscopic model for the zigzag CuO chain is proposed, and on the basis of density matrix renormalization group (DMRG) and bosonization studies of this model, we adduce evidence that supports our proposal.Comment: 10 pages, 5 figures; Journal-ref. adde