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

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

Broadband lightcurve characteristics of GRBs 980425 and 060218 and comparison with long-lag, wide-pulse GRBs

It has been recently argued that low-luminosity gamma-ray bursts (LL-GRBs) are likely a unique GRB population. Here, we present systematic analysis of the lightcurve characteristics from X-ray to gamma-ray energy bands for the two prototypical LL-GRBs 980425 and 060218. It is found that both the pulse width ($w$) and the ratio of the rising width to the decaying width ($r/d$) of theses two bursts are energy-dependent over a broad energy band. There exists a significant trend that the pulses tend to be narrower and more symmetry with respect to the higher energy bands for the two events. Both the X-rays and the gamma-rays follow the same $w - E$ and $r/d - E$ relations. These facts may indicate that the X-ray emission tracks the gamma-ray emission and both are likely to be originated from the same physical mechanism. Their light curves show significant spectral lags. We calculate the three types of lags with the pulse peaking time ($t_{peak}$), the pulse centroid time ($t_{cen}$), and the cross-correlation function (CCF). The derived $t_{peak}$ and $t_{cen}$ are a power-law function of energy. The lag calculated by CCF is strongly correlated with that derived from $t_{peak}$. But the lag derived from $t_{cen}$ is less correlated with that derived from $t_{peak}$ and CCF. The energy dependence of the lags is shallower at higher energy bands. These characteristics are well consistent with that observed in typical long-lag, wide-pulse GRBs, suggesting that GRBs 980425 and 060218 may share the similar radiation physics with them.Comment: 26 pages, 10 figures, 3 tables, accepted for publication in Ap

String and Membrane condensation on 3D lattices

In this paper, we investigate the general properties of lattice spin models that have string and/or membrane condensed ground states. We discuss the properties needed to define a string or membrane operator. We study three 3D spin models which lead to Z_2 gauge theory at low energies. All the three models are exactly soluble and produce topologically ordered ground states. The first model contains both closed-string and closed-membrane condensations. The second model contains closed-string condensation only. The ends of open-strings behave like fermionic particles. The third model also has condensations of closed membranes and closed strings. The ends of open strings are bosonic while the edges of open membranes are fermionic. The third model contains a new type of topological order.Comment: 10 pages, RevTeX

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

A geometric proof of the equality between entanglement and edge spectra

The bulk-edge correspondence for topological quantum liquids states that the spectrum of the reduced density matrix of a large subregion reproduces the thermal spectrum of a physical edge. This correspondence suggests an intricate connection between ground state entanglement and physical edge dynamics. We give a simple geometric proof of the bulk-edge correspondence for a wide variety of physical systems. Our unified proof relies on geometric techniques available in Lorentz invariant and conformally invariant quantum field theories. These methods were originally developed in part to understand the physics of black holes, and we now apply them to determine the local structure of entanglement in quantum many-body systems.Comment: 7 pages, 3 figure

A scheme for demonstration of fractional statistics of anyons in an exactly solvable model

We propose a scheme to demonstrate fractional statistics of anyons in an exactly solvable lattice model proposed by Kitaev that involves four-body interactions. The required many-body ground state, as well as the anyon excitations and their braiding operations, can be conveniently realized through \textit{dynamic}laser manipulation of cold atoms in an optical lattice. Due to the perfect localization of anyons in this model, we show that a quantum circuit with only six qubits is enough for demonstration of the basic braiding statistics of anyons. This opens up the immediate possibility of proof-of-principle experiments with trapped ions, photons, or nuclear magnetic resonance systems.Comment: 4 pages, 3 figure

Irrational charge from topological order

Topological or deconfined phases of matter exhibit emergent gauge fields and quasiparticles that carry a corresponding gauge charge. In systems with an intrinsic conserved U(1) charge, such as all electronic systems where the Coulombic charge plays this role, these quasiparticles are also characterized by their intrinsic charge. We show that one can take advantage of the topological order fairly generally to produce periodic Hamiltonians which endow the quasiparticles with continuously variable, generically irrational, intrinsic charges. Examples include various topologically ordered lattice models, the three dimensional RVB liquid on bipartite lattices as well as water and spin ice. By contrast, the gauge charges of the quasiparticles retain their quantized values.Comment: 4 pages, 1 figure with two panel