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An external magnetic field is needed to drive a nanowire in proximity to an s-wave superconductor into a topological regime which supports Majorana end states. However, a magnetic field generally suppresses the proximity superconducting gap induced on the nanowire. In recent experiments using InSb nanowires coupled to Al, the induced proximity gap vanishes at magnetic fields B~1T. This results in a small superconducting gap on the wire and a narrow topological regime which is proportional to the strength of the magnetic field. In this work, we show that by placing nanowires in proximity to recently discovered Ising superconductors such as the atomically thin transition-metal dichalcogenide(TMD) NbSe2, the topological superconducting gap on the wire can maintain at a large magnetic field as strong as B~10T. This robust topological superconducting gap is induced by the unique equal-spin triplet Cooper pairs of the parent Ising superconductor. The strong magnetic field allows a topological regime ten times larger than those in InSb wires coupled to Al. Our work establishes a realistic platform for building robust Majorana-based qubits., 6 pages, 4 figures. Comments are welcome

In this paper, we study doped HgTe/CdTe quantum well with Hubbard-type interaction under perpendicular magnetic field using a lattice Bernevig-Hughes-Zhang (BHZ) model with a bulk inversion asymmetry (BIA) term. We show that the BIA term is strongly enhanced by interaction around the region when the band inversion of the topological insulator is destroyed by a magnetic field. The enhanced BIA term creates edge-like electronic states which can explain the experimentally discovered edge conductance in doped HgTe/CdTe quantum well at similar magnetic field regime., 8 pages and 7 figures

In this paper we extend the Falicov-Kimball model (FKM) to the case where the "quasi-particles" entering the FKM are not "ordinary" fermions. As an example we first discuss how the FKM can be generalized to the case with spin-dependent hopping. Afterwards we discuss several cases where the "quasi-particles" entering the FKM are Majorana fermions (extended Majorana-Falicov-Kimball Model (MFKM). Two examples of extended MFKM are discussed in detail: (i) a $p$-wave BCS superconductor on a bipartite lattice and (ii) a BCS-Anderson model. We also discuss the most general forms of extended MFKM, including a brief discussion on the case where the Majorana fermions represent spins, but not real fermion particles., 9 pages, 6 figures

We study $S=1$ spin liquid states on the kagome lattice constructed by Gutzwiller-projected ${p}_{x}+i{p}_{y}$ superconductors. We show that the obtained spin liquids are either non-Abelian or Abelian topological phases, depending on the topology of the fermionic mean-field state. By calculating the modular matrices $S$ and $T$, we confirm that projected topological superconductors are non-Abelian chiral spin liquid (NACSL). The chiral central charge and the spin Hall conductance we obtained agree very well with the $SO{(3)}_{1}$ (or, equivalently, $SU{(2)}_{2}$) field-theory predictions. We propose a local Hamiltonian which may stabilize the NACSL. From a variational study, we observe a topological phase transition from the NACSL to the ${Z}_{2}$ Abelian spin liquid.

We provide an overview of some modern developments in the theory of phases and phase transitions in classical and quantum systems. We show the link between non-ergodicity and fidelity in quantum systems and discuss topological phase transitions. We show that the quantum phase transitions are associated with qualitative changes in some properties of the quantum wavefunctions across the phase transition. We discuss the topological phase transition associated with p-wave superconductor since it is a topic of wide interest because of the possible observation of Majorana fermions.

We introduce in this paper an exact solvable BCS-Hubbard model in arbitrary dimensions. The model describes a p-wave BCS superconductor with equal spin pairing moving on a bipartite (cubic, square etc.) lattice with on site Hubbard interaction $U$. We show that the model becomes exactly solvable for arbitrary $U$ when the BCS pairing amplitude $\Delta$ equals the hopping amplitude $t$. The nature of the solution is described in detail in this paper. The construction of the exact solution is parallel to the exactly solvable Kitaev honeycomb model for $S=1/2$ quantum spins and can be viewed as a generalization of Kitaev's construction to $S=1/2$ interacting lattice fermions. The BCS-Hubbard model discussed in this paper is just an example of a large class of exactly solvable lattice fermion models that can be constructed similarly., Comment: 5 pages, 3 figures

This article is an introductory review of the physics of quantum spin liquid (QSL) states. Quantum magnetism is a rapidly evolving field, and recent developments reveal that the ground states and low-energy physics of frustrated spin systems may develop many exotic behaviors once we leave the regime of semi-classical approaches. The purpose of this article is to introduce these developments. The article begins by explaining how semi-classical approaches fail once quantum mechanics become important and then describes the alternative approaches for addressing the problem. We discuss mainly spin $1/2$ systems, and we spend most of our time in this article on one particular set of plausible spin liquid states in which spins are represented by fermions. These states are spin-singlet states and may be viewed as an extension of Fermi liquid states to Mott insulators, and they are usually classified in the category of so-called $SU(2)$, $U(1)$ or $Z_2$ spin liquid states. We review the basic theory regarding these states and the extensions of these states to include the effect of spin-orbit coupling and to higher spin ($S>1/2$) systems. Two other important approaches with strong influences on the understanding of spin liquid states are also introduced: (i) matrix product states and projected entangled pair states and (ii) the Kitaev honeycomb model. Experimental progress concerning spin liquid states in realistic materials, including anisotropic triangular lattice systems ($\kappa$-(ET)$_{2}$Cu$_{2}$(CN)$_{3}$ and EtMe$_{3}$Sb[(Pd(dmit)$_{2}$]$_{2}$), kagome lattice systems (ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$) and hyperkagome lattice systems (Na$_{4}$Ir$_{3}$O$_{8}$), is reviewed and compared against the corresponding theories., Comment: Invited by RMP

In this paper we study the properties of cold bosons in two-dimensional optical lattices where Bose condensation occurs at a momentum point $\mathbf{k}$ with nonzero $k$-space Berry curvature. By combining results from both analytic and numerical approaches, the bulk and edge excitation spectra of the system are derived. We show that the boson system carries nonuniversal, nontopological temperature-dependent equilibrium angular momentum and edge current at low temperatures. The differences between boson systems with real- and $k$-space Berry curvature are pointed out. In particular, using a simple variational wave-function approach, we show that for bosons in a harmonic trap, the stability of the Bose-condensed state towards vortex formation is rather different in the two cases because of the different angular momentum scalings in the ground states.

In this paper we study the nonlinear current response of $U(1)$ spin liquids with large spinon Fermi surfaces under the perturbation of a time-dependent ac electric field $\mathbf{E}(t)$ within the framework of an effective $U(1)$ gauge theory. In particular, the third-order nonlinear current response to ac electric fields is derived. We show that as in the case of linear current response, an in-gap power-law ($\sim\omega^{\eta}$) response is found for the nonlinear current at low frequency. The nonlinear susceptibility may also induce through process of third harmonic generation propagating EM wave with frequency $3\omega$ inside the spin liquids., Comment: 5 pages, 2 figures

We discuss the superfluid properties of a Bose-Einstein condensed gas with spin-orbit coupling, recently realized in experiments. We find a finite normal fluid density $\rho_n$ at zero temperature which turns out to be a function of the Raman coupling. In particular, the entire fluid becomes normal at the transition point from the zero momentum to the plane wave phase, even though the condensate fraction remains finite. We emphasize the crucial role played by the gapped branch of the elementary excitations and discuss its contributions to various sum rules. Finally, we prove that an independent definition of superfluid density $\rho_s$, using the phase twist method, satisfies the equality $\rho_n+\rho_s=\rho$, the total density, despite the breaking of Galilean invariance.

We study theoretically two Kitaev chains placed in parallel, i.e., Kitaev ladder, connected through Josephson coupling. The π-junction between the Majorana bound states at the ends of the chains co...

In this paper we study the optical properties of $U(1)$ spin liquids with large spinon Fermi surfaces based on a simple formula for the bulk optical conductivity obtained through the Ioffe-Larkin composition rule. We show that the optical conductivity of $U(1)$ spin liquids at energies above the charge gap has a unique feature that distinguishes them from ordinary insulators. In particular we show the existence of a long-life surface plasmon mode propagating along the interface between a linear medium and the spin liquid at frequencies above the charge gap, which can be detected by the widely used Kretschmann-Raether three-layer configuration.

A total of 1,068 asymptomatic close contacts of patients with severe acute respiratory (SARS) from the 2003 epidemic in Hong Kong were serologically tested, and 2 (0.19%) were positive for SARS coronavirus immunoglobulin G antibody. SARS rarely manifests as a subclinical infection, and at present, wild animal species are the only important natural reservoirs of the virus.

When an Anderson impurity is immersed in the bulk of a topological insulator that has an ``inverted-Mexican-hat'' band dispersion, a Kondo resonant peak appears simultaneously with an in-gap bound state. The latter generates another spin state thereby screening the Kondo effect. Using a weak-coupling RG scheme, it is shown that the system exhibits complex crossover behavior between different symmetry configurations and may evolve into a self-screened Kondo or an $\mathrm{SO}(n)\phantom{\rule{0.28em}{0ex}}(n=3,4)$ low-energy fixed point. Experimental consequences of these scenarios are pointed out.

We discuss in this paper the low energy properties of a liquid of fermions coupling to a U(1) gauge field at wavevectors q F at dimensions larger than one, where Λ≪k F is a high momentum cutoff and k F is the Fermi wave vector. In particular, we shall consider the e2→∞ limit where charge and current fluctuations at wave vectors q

We study the current noise spectra of a tunnel junction of a metal with strong pairing phase fluctuation and a superconductor. It is shown that there is a characteristic peak in the noise spectrum at the intrinsic Josephson frequency $\omega_J=2eV$ when $\omega_J$ is smaller than the pairing gap but larger than the pairing scattering rate. In the presence of an AC voltage, the tunnelling current noise shows a series of characteristic peaks with increasing DC voltage. Experimental observation of these peaks will give direct evidence of the pair fluctuation in the normal state of high-$T_c$ superconductors and from the half width of the peaks the pair decay rate can be estimated., Comment: 4 pages, 3 figures

We study in this paper the properties of a gas of fermions interacting via a scalar potential $v(q)=4\ensuremath{\pi}{e}^{2}{/q}^{2}$ for $ql\ensuremath{\Lambda}\ensuremath{\ll}{k}_{F}$ at dimensions larger than 1, where $\ensuremath{\Lambda}\ensuremath{\ll}{k}_{F}$ is a high-momentum cutoff and ${k}_{F}$ is the Fermi wave vector. In particular, we shall consider the ${e}^{2}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, where charge fluctuations at wave vectors $ql\ensuremath{\Lambda}$ are forbidden. Within a bosonization approximation, effective actions describing the low-energy physics of the system are constructed, where we show that the system can be described as a Fermi liquid formed by chargeless quasiparticles, which has vanishing wave function overlap with the bare fermions in the system.

In this paper we study the effect of substituting R (rare-earth ion) by non-magnetic ions in the spin-1 chain material $R_2BaNiO_5$. Using a strong-coupling expansion and numerical density matrix renormalization group calculations, we show that spin-wave bound states are formed at the impurity site. Experimental consequences of the bound states are pointed out.

Force−distance curves were obtained using a home-built atomic force microscope (AFM) at different temperatures (T = 30−65 °C) and probe rates (f = 31.25−50 000 Hz) on a 150 nm thick film of a model sample, poly(tert-butyl acrylate) (Mw = 148K Da, Mw/Mn = 17, and Tgbulk = 50 °C according to DSC). The pull-off force, Fad, at which detachment between the AFM tip and the sample occurred was measured as adhesion. By limiting the loading force, F, to ∼2.5 nN, the tip penetrated by no more than 2 nm into the sample in the glassy state. Therefore, evolution of the rheological properties of the polymer at the free surface with increasing T could be studied. In the vicinity of Tgbulk, Fad was seen to increase rapidly with increasing T or decreasing f. Equivalence between T and f was found using time−temperature superposition in which, upon rescale of f by a temperature-dependent shift factor aTAFM(T), a master curve Fad(aTAFM(T) f) resulted. We showed that Fad(aTAFM(T)f) could be fully accounted for by using an app...

In this paper we re-examine the problem of electronic transports through a system consisting of a quantum dot which has well-defined discrete energy levels connected to an infinite quantum wire, using the bosonization method and phase-shift representation. We show that all previously known results can be obtained through our method in a very simple way. Furthermore, the evolution of the system from ultraviolet to infrared critical fixed points appears naturally in our method.

In this paper we study a model of an s-wave marginal Fermi liquid superconductor in two dimensions. Besides the usual Bardeen-Cooper-Schrieffer (BCS) point attractive interaction, the fermions in our system also interact via a long-range repulsive interaction y q gD q2. We find that although superconductivity is not destroyed by the long-ranged repulsive interaction (demonstrated by the response to electromagnetic magnetic fields), the BCS pairing function DBCS is strongly suppressed, resulting in a power-law correlation DBCS x DBCS 0 j xj22g . This observation is explained within a general picture of the marginal Fermi liquid.

In this paper we discuss the construction and the dynamics of vortex-like topological spin excitations in the Schwinger-boson description of Heisenberg antiferromagnets in two dimensions. The topological spin excitations are Dirac fermions (with gap) when spin value $S$ is a half-integer. Experimental and theoretical implications of these excitations are being investigated., Comment: Latex file, no figure

A supersymmetric way of imposing the constraint of no double occupancy in models with strong on-site Coulomb repulsion is presented in this paper. In this formulation the physical operators in the constrainted Hilbert space are invariant under local unitary transformations mixing boson and fermion representations. As an illustration the formulation is applied to the $t-J$ model. The model is studied in the mean-field level in the J=0 limit where we show how both the slave-boson and slave-fermion formulations are included naturally in the present approach and how further results beyond both approaches are obtained.

The noise characteristics of a single Anderson impurity coupled to two leads at different chemical potential is studied using the equation of motion method. We find that the current noise spectral density has an upturn as the frequency matches the chemical potential difference at low temperature. The low-frequency noise shows resonant behavior at equilibrium at low temperature because of the Kondo effect, and is suppressed significantly due to the Coulomb blockade effect on the impurity site when $\ensuremath{\Delta}\ensuremath{\mu}\ensuremath{\gg}T\ensuremath{\sim}{T}_{K}.$

The flux-line lattice in the compound $ErNi_2B_2C$, which has a tendency to ferromagnetic order in the a-b plane is studied with external magnetic field direction close to the c-axis. We show the existence of an instability where the direction of flux-lines spontaneously tilts away from that of the applied field near the onset of ferromagnetic order. The enhanced fluctuations in the flux lattice and the square flux lattice recently observed are explained and further experiments suggested., 12 pages, Latex file, no figure

We study in this paper quantum spin liquid states (QSLs) at the vicinity of metal-insulator transition. Assuming that the low energy excitations in the QSLs are labeled by "spinon" occupation numbers with the same Fermi surface structure as in the corresponding metal (Fermi-liquid) side, we propose a phenomenological Landau-like low energy theory for the QSLs and show that the usual U(1) QSLs is a representative member of this class of spin liquids. Based on our effective low energy theory, an alternative picture to the Brinkman-Rice picture of Mott metal-insulator transition is proposed. The charge, spin and thermal responses of QSLs are discussed under such a phenomenology., Comment: 8 pages, extended version to appear in PRB

Chern insulators are band insulators which exhibit a gap in the bulk and gapless excitations in the edge. Detection of Chern insulators is a serious challenge in cold atoms since the Hall transport measurements are technically unrealistic for neutral atoms. By establishing a natural correspondence between the time-reversal invariant topological insulator and quantum anomalous Hall system, we show for a class of Chern insulators that the topology can be determined by only measuring Bloch eigenstates at highly symmetric points of the Brillouin zone (BZ). Furthermore, we introduce two experimental schemes including the spin-resolved Bloch oscillation to carry out the measurement. These schemes are highly feasible under realistic experimental conditions. Our results may provide a powerful tool to detect topological phases in cold atoms., 4+pages and 4 figures; Supplementary Material is added, with new results obtained in the honeycomb lattice system

In this work, we find that Majorana fermions induce selective equal spin Andreev reflections (SESARs), in which incoming electrons with certain spin polarization in the lead are reflected as counter propagating holes with the same spin. The spin polarization direction of the electrons of this Andreev reflected channel is selected by the Majorana fermions. Moreover, electrons with opposite spin polarization are always reflected as electrons with unchanged spin. As a result, the charge current in the lead is spin-polarized. Therefore, a topological superconductor which supports Majorana fermions can be used as a novel device to create fully spin-polarized currents in paramagnetic leads. We point out that SESARs can also be used to detect Majorana fermions in topological superconductors., Comment: 5 pages, 3 figures. Comments are welcome. Title changed to match published version

Majorana zero bound mode exists in the vortex core of a chiral $p+ip$ superconductor or superfluid, which can be driven from an s-wave pairing state by two-dimensional (2D) spin-orbit (SO) coupling. We propose here a novel scheme based on realistic cold atom platforms to generate 2D SO interactions in a blue-detuned square optical lattice, and predict both the quantum anomalous Hall effect and chiral topological superfluid phase in the experimentally accessible parameter regimes. This work opens a new direction with experimental feasibility to observe non-Abelian topological orders in cold atom systems., Comment: 4+pages, 3 figures; supplementary material is added to provide all details of the model realization based on experimental data of realistic cold atoms

In this paper we study in a large-S expansion effects of substituting spins by non-magnetic impurities in two- and three- dimensional Heisenberg antiferromagnets in a weak magnetic field. In particular, we demonstrate a novel mechanism where magnetic moments are induced around non-magnetic impurities when magnetic field is present. As a result, Curie-type behaviour in magnetic susceptibility can be observed well below the Neel temperature, in agreement with what is being observed in $La_2Cu_{1-x}Zn_{x}O_4$ and $Sr(Cu_{1-x}Zn_x)_2O_3$ compounds., Latex file

We report a density-matrix renormalization-group ~DMRG! study of S51/2 antiferromagnetic Heisenberg spin chains. We show the Friedel oscillations in open spin chains within bosonization theory. The bosonization predictions are in excellent agreement with the DMRG calculation. The chain length dependence of the ground state and several low-energy excited state energies are compared with conformal field theory results. Based upon the DMRG calculations for various quantities, the interplay between the system size and the number of optimal states kept in the DMRG is carefully discussed. @S0163-1829~96!05337-4#

In this letter we report our results in investigating edge effects of open antiferromagnetic Heisenberg spin chains with spin magnitudes $S=1/2, 1,3/2,2$ using the density-matrix renormalization group (DMRG) method initiated by White. For integer spin chains, we find that edge states with spin magnitude $S_{edge}=S/2$ exist, in agreement with Valence-Bond-Solid model picture. For half-integer spin chains, we find that no edge states exist for $S=1/2$ spin chain, but edge state exists in $S=3/2$ spin chain with $S_{edge}=1/2$, in agreement with previous conjecture by Ng. Strong finite size effects associated with spin dimmerization in half-integer spin chains will also be discussed., 4 pages, RevTeX 3.0, 5 figures in a separate uuencoded postscript file. Replaced once to enlarge the acknowlegement.

We find an optical Raman lattice without spin-orbit coupling showing chiral topological orders for cold atoms. Two incident plane-wave lasers are applied to generate simultaneously a double-well square lattice and periodic Raman couplings, the latter of which drive the nearest-neighbor hopping and create a staggered flux pattern across the lattice. Such a minimal setup is can yield the quantum anomalous Hall effect in the single particle regime, while in the interacting regime it achieves the $J_1$-$J_2$-$K$ model with all parameters controllable, which supports a chiral spin liquid phase. We further show that heating in the present optical Raman lattice is reduced by more than one order of magnitude compared with the conventional laser-assisted tunneling schemes. This suggests that the predicted topological states be well reachable with the current experimental capability., 5 pages, 3 figures, plus supplementary material. The model realization is updated

We investigate physical properties of an Anderson impurity embedded in the bulk of a topological insulator. The slave-boson mean-field approximation is used to account for the strong electron correlation at the impurity. Different from the results of a quantum impurity on the surface of a topological insulator, we find for the band-inverted case, a Kondo resonant peak and in-gap bound states can be produced simultaneously. However, only one type of them appears for the normal case. It is shown that the mixed-valence regime is much broader in the band-inverted case, while it shrinks to a very narrow regime in the normal case. Furthermore, a self-screening of the Kondo effect may appear when the interaction between the bound-state spin and impurity spin is taken into account., 11 pages, 8 figures

We study in this paper a series of Gutzwiller Projected wavefunctions for S=1 spin chains obtained from a fermionic mean-field theory for general S>1/2 spin systems [Phys. Rev. B 81, 224417] applied to the bilinear-biquadratic (J-K) model. The free-fermion mean field states before the projection are 1D paring states. By comparing the energies and correlation functions of the projected pairing states with those obtained from known results, we show that the optimized Gutzwiller projected wavefunctions are very good trial ground state wavefunctions for the antiferromagnetic bilinear-biquadratic model in the regime K0). We find that different topological phases of the free-fermion paring states correspond to different spin phases: the weak pairing (topologically non-trivial) state gives rise to the Haldane phase, whereas the strong pairing (topologically trivial) state gives rise to the dimer phase. In particular the mapping between the Haldane phase and Gutwziller wavefunction is exact at the AKLT point K=1/3. The transition point between the two phases determined by the optimized Gutzwiller Projected wavefunction is in good agreement with the known result. The effect of Z2 gauge fluctuations above the mean field theory is analyzed., Comment: 10 pages,7 figures

Using elastic and inelastic neutron scattering techniques with and without application of an external magnetic field $H$, the magnetic ground states of Zn${}_{x}$Co${}_{4\ensuremath{-}x}$(OD)${}_{6}$Cl${}_{2}$ ($x=0,1$) were studied. Our results show that for $x=0$, the ground state is a magnetic long-range ordered (LRO) state where each tetrahedron forms an ``umbrella''-type structure. On the other hand, for $x=1$, no static ordering was observed down to 1.5 K, which resembles the behavior found in the isostructural quantum system Zn${}_{x}$Cu${}_{4\ensuremath{-}x}$(OD)${}_{6}$Cl${}_{2}$. When $H$ field is applied, however, the $x=1$ system develops the same LRO state as $x=0$. This indicates that the $x=1$ disordered state is in the vicinity of the $x=0$ ordered state.

The electronic contribution to thermal conductivity is studied in models of underdoped cuprates where the normal state has a pocketed Fermi surface with circumference ∼x (hole concentration) and the superconducting state is formed by opening a gap in the Fermi pocket. The physical consequences of the Fermi pocket are studied by comparing the thermal conductivity computed in four different models: (1) an ordinary d-wave superconductor with four Dirac Fermi points; (2) a normal metal with a pocketed Fermi surface; (3) a superconductor formed by spinon-holon binding in the t-J model; (4) a phenomenological d-wave Bardeen-Cooper-Schrieffer (BCS) superconductor with superconductivity formed by opening a gap on the pocketed Fermi surface. Our results suggest that thermal conductivity provides useful information to distinguish between different scenarios of the normal-to-superconducting transition in underdoped cuprates.

We study in this paper time-reversal $\delta$-impurity scattering effects in the bulk of topological insulators (TI) in two and three dimensions. Specifically we consider how impurity scattering strength is affected by the bulk band structure of topological insulators. An interesting band inversion effect associated with the change of the system from ordinary to topological insulator is pointed out. Experimental consequences of our findings are discussed., Comment: 5 pages, comments are welcome

The problem of nonlinear resonant tunneling through an Anderson impurity is investigated in this letter using a combined -approach of Keldysh formalism and 1/N expansion at zero temperature. We find that to order 1/N, the Kondo resonance is not destroyed by any finite potential difference between external probes. The resulting one-electron Green's functions and differential conductance are presented. The effect of finite temperature is discussed

The fermion representation for $S=\frac{1}{2}$ spins is generalized to spins with arbitrary magnitudes. The symmetry properties of the representation is analyzed where we find that the particle-hole symmetry in the spinon Hilbert space of $S=\frac{1}{2}$ fermion representation is absent for $Sg\frac{1}{2}$. As a result, different path-integral representations and mean-field theories can be formulated for spin models. In particular, we construct a Lagrangian with restored particle-hole symmetry, and apply the corresponding mean-field theory to one-dimensional (1D) $S=1$ and $S=3/2$ antiferromagnetic (AFM) Heisenberg models, with results that agree with Haldane's conjecture. For a $S=1$ open chain, we show that Majorana fermion edge states exist in our mean-field theory. The generalization to spins with arbitrary magnitude $S$ is discussed. Our approach can be applied to higher dimensional spin systems. As an example, we study the geometrically frustrated $S=1$ AFM on triangular lattice. Two spin liquids with different pairing symmetries are discussed: the gapped ${p}_{x}+i{p}_{y}$-wave spin liquid and the gapless $f$-wave spin liquid. We compare our mean-field result with the experiment on ${\text{NiGa}}_{2}{\text{S}}_{4}$, which remains disordered at low temperature and was proposed to be in a spin-liquid state. Our fermionic mean-field theory provide a framework to study $Sg\frac{1}{2}$ spin liquids with fermionic spinon excitations.

In this paper we generalize the fermionic representation for $S=1/2$ spins to arbitrary spins. Within a mean field theory we obtain several spin liquid states for spin $S=1$ antiferromagnets on triangular lattices, including gapless f-wave spin liquid and topologically nontrivial $p_x+ip_y$ spin liquid. After considering different competing orders, we construct a phase diagram for the $J_1$-$J_3$-$K$ model. The application to recently discovered material $\mathrm{NiGa_2S_4}$ is discussed., 5 pages, 3 figures

A Josephson junction consisting of an Anderson impurity weakly coupled with two-band and single-band superconductors exposes a time reversal breaking ground state when the coupling between the two bands exceeds a certain threshold. The critical regime occurs around local moment formation. This indicates a fundamental and distinct role of strong correlations: Driving a system into a time reversal breaking ground state. One of the observable consequences is that the impurity magnetization in this phase is reduced.

We followed the Shastry--Shraiman formulation of Raman scattering in Hubbard systems and considered the Raman intensity profile in the spin-1/2 "perfect" kagome lattice herbertsmithite ZnCu_3(OH)_6Cl_2, assuming the ground state is well-described by the U(1) Dirac spin-liquid state. In the derivation of the Raman T-matrix, we found that the spin chirality term appears in the A_{2g} channel in the kagome lattice at the t^4/(\omega_i-U)^3 order, but (contrary to the claims by Shastry and Shraiman) vanishes in the square lattice to that order. In the ensuing calculations on the spin-1/2 kagome lattice, we found that the Raman intensity profile in the E_g channel is invariant under an arbitrary rotation in the kagome plane, and that in all (A_{1g}, E_g, and A_{2g}) symmetry channels the Raman intensity profile contains broad continua that display power-law behaviors at low energy, with exponent approximately equal to 1 in the A_{2g} channel and exponent approximately equal to 3 in the E_g and the A_{1g} channels. For the A_{2g} channel, the Raman profile also contains a characteristic 1/\omega singularity, which arose in our model from an excitation of the emergent U(1) gauge field.

A quantum dot coupled to two helical edge states of a two-dimensional topological insulator through electron tunnelings is studied. We show that if the electron interactions on the edge states are repulsive, with Luttinger liquid parameter $Kl1$, the system reaches a stable two-channel Kondo fixed point at low temperatures. This is in contrast to the Luttinger liquid leads case in which $Kl1/2$ is needed. This two-channel fixed point is described by a boundary sine-Gordon Hamiltonian with a $K$ dependent boundary term. The impurity entropy, the impurity specific heat and the conductance are calculated.

In this paper we study a non-equilibrium resonant tunnelling problem where a non-interacting quantum dot is connected to two leads, one being the edge of an interacting 2-D topological insulator (Luttinger liquid) and the other being a usual Fermi liquid. We show that the current passing through the system can be expressed in terms of a non-equilibrium local single-particle Green's function of the Luttinger liquid lead which can be analysed using standard bosonization- Renormalization Group (RG) technique. In particular, some exact results can be extracted in the small bias limit with repulsive electron-electron interaction. A simple formula which captures the qualitative feature of the I-V relation over whole temperature and voltage bias range is being proposed and studied., Comment: 10 pages, 3 figures