Distinct Spin Liquids and their Transitions in Spin-1/2 XXZ Kagome Antiferromagnets

By using the density matrix renormalization group, we study the spin-liquid phases of spin-$1/2$ XXZ kagome antiferromagnets. We find that the emergence of spin liquid phase does not depend on the anisotropy of the XXZ interaction. In particular, the two extreme limits---Ising (strong $S^z$ interaction) and XY (zero $S^z$ interaction)---host the same spin-liquid phases as the isotropic Heisenberg model. Both the time-reversal-invariant spin liquid and the chiral spin liquid with spontaneous time-reversal symmetry breaking are obtained. We show they evolve continuously into each other by tuning the second- and third-neighbor interactions. At last, we discuss the possible implication of our results on the nature of spin liquid in nearest neighbor XXZ kagome antiferromagnets, including the most studied nearest neighbor spin-$1/2$ kagome anti-ferromagnetic Heisenberg model

Measuring Majorana fermions qubit state and non-Abelian braiding statistics in quenched inhomogeneous spin ladders

We study the Majorana fermions (MFs) in a spin ladder model. We propose and numerically show that the MFs qubit state can be read out by measuring the fusion excitation in the quenched inhomogeneous spin ladders. Moreover, we construct an exactly solvable T-junction spin ladder model, which can be used to implement braiding operations of MFs. With the braiding processes simulated numerically as non-equilibrium quench processes, we verify that the MFs in our spin ladder model obey the non-Abelian braiding statistics. Our scheme not only provides a promising platform to study the exotic properties of MFs, but also has broad range of applications in topological quantum computation.Comment: 5+3 pages, 6 figure

Externalities, income taxes and indeterminacy in OLG models

Using an aggregate two-periods overlapping generations model with endogenous labor, consumption in both periods of life, homothetic preferences and productive external effects [Lloyd-Braga et al., 2007. Indeterminacy in dynamic models: When Diamond meets Ramsey. Journal of Economic Theory 134, 513-536], we examine the effects of alternative government financing methods on the range of values of increasing returns leading to indeterminacy. We show that under a large enough share of first period consumption over the wage income, local indeterminacy can easily occur for mild externalities if constant government expenditure is financed through either labor or capital income taxes. More precisely, we show that, with labor income taxes and mild externalities, small government expenditures are helpful to local indeterminacy, while large government expenditures are useful to stabilize the economy. With capital income taxes and mild externalities, local indeterminacy always exists. Moreover, we explore how our previous results are changed once government expenditure is endogenously determined for fixed rates on labor and capital income under the balanced-budget rule.Indeterminacy; Endogenous income tax rates; Externalities.

Are Progressive Income Taxes Stabilizing? : A Reply

Dromel and Pintus [Are Progressive Income Taxes Stabilizing?, Journal of Public Economic Theory 10, (2008) 329-349] have shown that labor-income tax progressivity reduces the likelihood of local indeterminacy, sunspots and cycles in a one sector monetary economy with constant returns to scale. In this note, we extend Dromel and Pintus (2008) into a two sector monetary economy with constant returns to scale studied by Bosi et al. (2007) and reassess the stabilizing effect of progressive income taxes. We show that the result in Dromel and Pintus (2008) is robust to this extension, which means that changes of the production structure won't affect the stabilizing effect of progressive income taxes, i.e., tax progressivity (regressivity) reduces (increases) the likelihood of local indeterminacy, sunspots and cycles.Tax Progressivity, local indeterminacy

Endogenous income taxes in OLG economies: A clarification

This paper introduces endogenous capital income tax rates as in Schmitt-Grohe and Uribe (1997), into the overlapping generations model with endogenous labor and consumption in both periods of life (e.g., Cazzavillan and Pintus, 2004). In contrast with the previous result that the existence of endogenous labor income taxes raises the possibility of local indeterminacy (Chen and Zhang 2009), it shows that increasing the size of capital income taxes can make shrink the range of values of the consumption--to--wage ratio associated with local indeterminacy, because of two conflicting effects on savings that operate through wage and interest rate.Indeterminacy; Endogenous capital income tax rate.

Endogenous income taxes and indeterminacy in dynamic models: When Diamond meets Ramsey again.

This paper introduces fiscal increasing returns, through endogenous labor income tax rates as in Schmitt-Grohe and Uribe (1997), into the overlapping generations model with endogenous labor, consumption in both periods of life and homothetic preferences (e.g., Lloyd-Braga, Nourry and Venditti, 2007). We show that under numerical calibrations of the parameters, local indeterminacy can occur for distortionary tax rates that are empirically plausible for the U.S. economy, provided that the elasticity of capital-labor substitution and the wage elasticity of the labor supply are large enough, and the elasticity of intertemporal substitution in consumption is slightly greater than unity. These indeterminacy conditions are similar to those obtained within infinite horizon models and from this point of view, Diamond meets Ramsey again.Indeterminacy; Endogenous labor income tax rate.

Tariff and Equilibrium Indeterminacy--A Note

We explore the equivalence between the factor income taxes (in Schmitt-Grohe and Uribe 1997) in the closed economy and the tariff in the open economy, in the sense that they share similar propagation mechanism of sunspot and fundamental shocks under a balanced-budget rule.Sunspots; Endogenous Tariff Rate; Comovement

Dynamic effects of government expenditure in a finance constrained economy: A Note

Gokan [Dynamic effects of government expenditure in a finance constrained economy, J. Econ. Theory 127 (2006) 323-333] introduces constant government expenditure (financed by labor income taxes) in Woodford's model with capital-labor substitution and investigates how local dynamics near two steady states depend upon the elasticity of substitution between capital and labor. In this paper, we show that the local dynamics will change dramatically if the government transfers its revenue to the households (workers) in a lump sum way. In particular, we question the result that the rate of money growth has no impact on the model dynamics. In a numerical example, we illustrate that the result previously obtained is not robust to the alternative assumption.a lump sum transfer; indeterminacy.