Trade, Capital Redistribution and Firm Structure

A model of heterogeneous firms with multiple products and two production factors (labor and capital) is used to study how trade liberalization affects firms’choices through both product and factor markets. Trade liberalization is shown to always redistribute capital toward more efficient firms and always to improve an industry’s total factor productivity. However, it may reduce capital prices and cause labor productivity to drop. Low efficiency firms are affected mainly by changes in the factor market, while high efficiency firms are affected mainly by changes in the product market. In response to trade liberalization, low efficiency firms always reduce their product scope, but high efficiency firms may expand their scope. The model demonstrates the importance of the interplay between product and factor markets.firm heterogeneity, trade liberalization, multiproduct, multifactor, firm structure, scale, scope, mergers and acquisitions

Quantum ether: photons and electrons from a rotor model

We give an example of a purely bosonic model -- a rotor model on the 3D cubic lattice -- whose low energy excitations behave like massless U(1) gauge bosons and massless Dirac fermions. This model can be viewed as a ``quantum ether'': a medium that gives rise to both photons and electrons. It illustrates a general mechanism for the emergence of gauge bosons and fermions known as ``string-net condensation.'' Other, more complex, string-net condensed models can have excitations that behave like gluons, quarks and other particles in the standard model. This suggests that photons, electrons and other elementary particles may have a unified origin: string-net condensation in our vacuum.Comment: 10 pages, 6 figures, RevTeX4. Home page http://dao.mit.edu/~we

Translation-symmetry protected topological orders on lattice

In this paper we systematically study a simple class of translation-symmetry protected topological orders in quantum spin systems using slave-particle approach. The spin systems on square lattice are translation invariant, but may break any other symmetries. We consider topologically ordered ground states that do not spontaneously break any symmetry. Those states can be described by Z2A or Z2B projective symmetry group. We find that the Z2A translation symmetric topological orders can still be divided into 16 sub-classes corresponding to 16 new translation-symmetry protected topological orders. We introduced four $Z_2$ topological indices $\zeta_{\v{k}}=0,1$ at $\v {k}=(0,0)$, $(0,\pi)$, $(\pi, 0)$, $(\pi ,\pi)$ to characterize those 16 new topological orders. We calculated the topological degeneracies and crystal momenta for those 16 topological phases on even-by-even, even-by-odd, odd-by-even, and odd-by-odd lattices, which allows us to physically measure such topological orders. We predict the appearance of gapless fermionic excitations at the quantum phase transitions between those symmetry protected topological orders. Our result can be generalized to any dimensions. We find 256 translation-symmetry protected Z2A topological orders for a system on 3D lattice

Fractional topological superconductors with fractionalized Majorana fermions

In this paper, we introduce a two-dimensional fractional topological superconductor (FTSC) as a strongly correlated topological state which can be achieved by inducing superconductivity into an Abelian fractional quantum Hall state, through the proximity effect. When the proximity coupling is weak, the FTSC has the same topological order as its parent state and is thus Abelian. However, upon increasing the proximity coupling, the bulk gap of such an Abelian FTSC closes and reopens resulting in a new topological order: a non-Abelian FTSC. Using several arguments we will conjecture that the conformal field theory (CFT) that describes the edge state of the non-Abelian FTSC is $U(1)/Z_2$ orbifold theory and use this to write down the ground-state wave function. Further, we predict FTSC based on the Laughlin state at $\nu=1/m$ filling to host fractionalized Majorana zero modes bound to superconducting vortices. These zero modes are non-Abelian quasiparticles which is evident in their quantum dimension of $d_m=\sqrt{2m}$. Using the multi-quasi-particle wave function based on the edge CFT, we derive the projective braid matrix for the zero modes. Finally, the connection between the non-Abelian FTSCs and the $Z_{2m}$ rotor model with a similar topological order is illustrated.Comment: 15 pages, 2 figure

Quantum orders in an exact soluble model

We find all the exact eigenstates and eigenvalues of a spin-1/2 model on square lattice: $H=16g \sum_i S^y_i S^x_{i+x} S^y_{i+x+y} S^x_{i+y}$. We show that the ground states for $g0$ have different quantum orders described by Z2A and Z2B projective symmetry groups. The phase transition at $g=0$ represents a new kind of phase transitions that changes quantum orders but not symmetry. Both the Z2A and Z2B states are described by $Z_2$ lattice gauge theories at low energies. They have robust topologically degenerate ground states and gapless edge excitations.Comment: 4 pages, RevTeX4, More materials on topological/quantum orders and quantum computing can be found in http://dao.mit.edu/~we

Trade, Capital Redistribution and Firm Structure

A model of heterogeneous firms with multiple products and two production factors (labor and capital) is used to study how trade liberalization affects firms' choices through both product and factor markets. Trade liberalization is shown to always redistribute capital toward more efficient firms and always to improve an industry's total factor productivity. However, it may reduce capital prices and cause labor productivity to drop. Low efficiency firms are affected mainly by changes in the factor market, while high efficiency firms are affected mainly by changes in the product market. In response to trade liberalization, low efficiency firms always reduce their product scope, but high efficiency firms may expand their scope. The model demonstrates the importance of the interplay between product and factor markets.firm heterogeneity, trade liberalization, multiproduct, multifactor, firm structure, scale, scope, mergers and acquisitions

Continuous topological phase transitions between clean quantum Hall states

Continuous transitions between states with the {\em same} symmetry but different topological orders are studied. Clean quantum Hall (QH) liquids with neutral quasiparticles are shown to have such transitions. For clean bilayer (nnm) states, a continous transition to other QH states (including non-Abelian states) can be driven by increasing interlayer repulsion/tunneling. The effective theories describing the critical points at some transitions are derived.Comment: 4 pages, RevTeX, 2 eps figure