Effects of Zeeman field on a Spin Bose-Metal phase

We consider Zeeman field effects on a Spin Bose-Metal (SBM) phase on a two-leg triangular ladder. This phase was found in a spin-1/2 model with ring exchanges [D. N. Sheng et. al., Phys. Rev. B {\bf 79}, 205112 (2009)], and was also proposed to appear in an interacting electronic model with longer-ranged repulsion [Lai et. al., Phys. Rev. B {\bf 81}, 045105 (2010)]. Using bosonization of a spinon-gauge theory, we study the stability of the SBM phase and its properties under the field. We also explore phases arising from potential instabilities of the SBM; in all cases, we find a gap to spin-1 excitations while spin-nematic correlations are power law. We discuss two-dimensional analogues of these phases where spinons can pair with their own species.Comment: 10 pages, 6 figure

Effects of impurities in Spin Bose-Metal phase on a two-leg triangular strip

We study effects of nonmagnetic impurities in a Spin Bose-Metal (SBM) phase discovered in a two-leg triangular strip spin-1/2 model with ring exchanges (D. N. Shenget al, arXiv:0902.4210). This phase is a quasi-1D descendant of a 2D spin liquid with spinon Fermi sea, and the present study aims at interpolating between the 1D and 2D cases. Different types of defects can be treated as local energy perturbations, which we find are always relevant. As a result, a nonmagnetic impurity generically cuts the system into two decoupled parts. We calculate bond energy and local spin susceptibility near the defect, both of which can be measured in experiments. The Spin Bose-Metal has dominant correlations at characteristic incommensurate wavevectors that are revealed near the defect. Thus, the bond energy shows a static texture oscillating as a function of distance from the defect and decaying as a slow power law. The local spin susceptibility also oscillates and actually {\it increases} as a function of distance from the defect, similar to the effect found in the 1D chain [S. Eggert and I. Affleck, Phys. Rev. Lett. {\bf 75}, 934 (1995)]. We calculate the corresponding power law exponents for the textures as a function of one Luttinger parameter of the SBM theory.Comment: 6 pages, 1 figur

Two-band electronic metal and neighboring spin liquid (spin Bose-metal) on a zigzag strip with longer-ranged repulsion

We consider an electronic model for realizing the Spin Bose-metal (SBM) phase on a 2-leg triangular strip --a spin liquid phase found by D. N. Sheng et al [Phys. Rev. B {\bf 79}, 205112 (2009)] in a spin-1/2 model with ring exchanges. The SBM can be viewed as a "C1S2" Mott insulator of electrons where the overall charge transporting mode is gapped out. We start from a two-band "C2S2" metal and consider extended repulsion motivated by recent ab initio derivation of electronic model for $\kappa$-ET spin liquid material [K. Nakamura et al, J. Phys. Soc. Jpn. {\bf 78}, 083710(2009)]. Using weak coupling renormalization group analysis, we find that the extended interactions allow much wider C2S2 metallic phase than in the Hubbard model with on-site repulsion only. An eight-fermion Umklapp term plays a crucial role in producing a Mott insulator but can not be treated in weak coupling. We use Bosonization to extend the analysis to intermediate coupling and study phases obtained out of the C2S2 metal upon increasing overall repulsion strength, finding that the SBM phase is a natural outcome for extended interactions.Comment: 12 pages, 9 figure

Insulating phases of electrons on a zigzag strip in the orbital magnetic field

We consider electrons on a two-leg triangular ladder at half-filling and in an orbital magnetic field. In a two-band regime in the absence of the field, the electronic system remains conducting for weak interactions since there is no four-fermion Umklapp term. We find that in the presence of the orbital field there is a four-fermion Umklapp and it is always relevant for repulsive interactions. Thus in this special ladder, the combination of the orbital magnetic field and interactions provides a mechanism to drive metal-insulator transition already at weak coupling. We discuss properties of the possible resulting phases C0S2 and various C0S1 and C0S0.Comment: 7 pages, 4 figures, 2 table

Pollution Taxes and Location Decision under Free Entry Oligopoly

This paper examines the impact of a pollution tax as a pollution control device on the output and location decisions of undifferentiated oligopolistic firms with free entry. It shows that the optimum output and location of an oligopolistic firm is independent of a change in the pollution tax if the demand function is linear. Furthermore, an increase in the pollution tax will increase (decrease) output and move the plant location toward (away from) the CBD if the demand function is concave (convex). It also shows that a higher pollution tax will increase the pollution damage if the demand function is linear and the location effect dominates the demand effect. These results are significantly different from the conventional results based on the monopolistic location model. It indicates that the demand condition plays an important role in the determination of the impact of a pollution tax on the location decision of an oligopolistic firm and the pollution damage to the CBD residents.

Power-Law Behavior of Bond Energy Correlators in a Kitaev-type Model with a Stable Parton Fermi Surface

We study bond energy correlation functions in an exactly solvable quantum spin model of Kitaev type on the kagome lattice with stable Fermi surface of partons proposed recently by Chua et al, Ref.\[arXiv:1010.1035]. Even though any spin correlations are ultra-short ranged, we find that the bond energy correlations have power law behavior with a $1/|{\bm r}|^3$ envelope and oscillations at incommensurate wavevectors. We determine the corresponding singular surfaces in momentum space, which provide a gauge-invariant characterization of this gapless spin liquid.Comment: 6 pages, 5 figure