Recently, it was pointed out that quantum orders and the associated projective symmetry groups can produce and protect massless gauge bosons and massless fermions in local bosonic models. In this paper, we demonstrate that a state with such kinds of quantum order can be viewed as a condensed state of nets of strings. The emergent gauge bosons and fermions in local bosonic models can be regarded as a direct consequence of string-net condensation. The gauge bosons are fluctuations of large closed string nets. The ends of open strings are the charged particles of the corresponding gauge field. For certain types of strings, the ends of open strings can even be fermions. According to the string-net picture, fermions always carry gauge charges. This suggests the existence of a new discrete gauge field that couples to neutrinos and neutrons. We also discuss how chiral symmetry that protects massless Dirac fermions can emerge from the projective symmetry of quantum order.
Recently, it was pointed out that quantum orders and the associated projective symmetry groups can produce and protect massless gauge bosons and massless fermions in local bosonic models. In this paper, we demonstrate that a state with such kinds of quantum order can be viewed as a condensed state of nets of strings. The emergent gauge bosons and fermions in local bosonic models can be regarded as a direct consequence of string-net condensation. The gauge bosons are fluctuations of large closed string nets. The ends of open strings are the charged particles of the corresponding gauge field. For certain types of strings, the ends of open strings can even be fermions. According to the string-net picture, fermions always carry gauge charges. This suggests the existence of a new discrete gauge field that couples to neutrinos and neutrons. We also discuss how chiral symmetry that protects massless Dirac fermions can emerge from the projective symmetry of quantum order.
This book has three types of theories: boson, fermion, and gauge theories. It asks which theories describe the elementary particles in our universe. Surprisingly, elementary particles are described by the two more complicated and non-local theories: fermion theory and gauge theory. In the last chapter and in this chapter it is demonstrated that fermion and gauge theory are not really needed. Boson theory may be able to explain everything, since both fermion theory and gauge theory can emerge from local bosonic models (or qbit models), if bosons (qbits) are organized to have a string-net condensed order. This chapter studies soluble quantum spin models to explain string-net condensation. It finds that gauge bosons are simply collective excitations associated with string density wave (with the electric field corresponding to the string density). The fermons can appear as the ends of open strings. Thus the string-net order explains the emergence of gauge bosons and fermions. It unifies gauge interaction and Fermi statistics. The chapter shows that non-orientable strings give rise to Z_2 gauge theory while the orientable string give rise to U(1) gauge theory.
Recent advances in condensed-matter theory have revealed that new and exotic phases of matter can exist in spin models (or more precisely, local bosonic models) via a simple physical mechanism, known as ``string-net condensation.'' These new phases of matter have the unusual property that their collective excitations are gauge bosons and fermions. In some cases, the collective excitations can behave just like the photons, electrons, gluons, and quarks in our vacuum. This suggests that photons, electrons, and other elementary particles may have a unified origin---string-net condensation in our vacuum. In addition, the string-net picture indicates how to make artificial photons, artificial electrons, and artificial quarks and gluons in condensed-matter systems.
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.
For a long time, people believe that all possible states of matter are described by Landau symmetry-breaking theory. Recently we found that string-net condensation provide a mechanism to produce states of matter beyond the symmetry-breaking description. The collective excitations of the string-net condensed states turn out to be our old friends, photons and electrons (and other gauge bosons and fermions). This suggests that our vacuum is a string-net condensed state. Light and electrons in our vacuum have a unified origin — string-net condensation.
For a long time, people believe that all possible states of matter are described by Landau symmetry-breaking theory. Recently we find that string-net condensation provide a mechanism to produce states of matter beyond the symmetry-breaking description. The collective excitations of the string-net condensed states turn out to be our old friends, photons and electrons (and other gauge bosons and fermions). This suggests that our vacuum is a string-net condensed state. Light and electrons in our vacuum have a unified origin – string-net condensation. 1
For most of the last century, condensed matter physics has been dominated by band theory and Landau's symmetry breaking theory. In the last twenty years, however, there has been an emergence of a new paradigm associated with fractionalization, emergent gauge bosons and fermions, topological order, string-net condensation, and long range entanglements. These new physical concepts are so fundamental that they may even influence our understanding of the origin of light and electrons in the universe. This book is a pedagogical and systematic introduction to the new concepts and quantum field theoretical methods in condensed matter physics. It discusses many basic notions in theoretical physics which underlie physical phenomena in nature, including a notion that unifies light and electrons. Topics covered include dissipative quantum systems, boson condensation, symmetry breaking and gapless excitations, phase transitions, Fermi liquids, spin density wave states, Fermi and fractional statistics, quantum Hall effects, topological/quantum order, and spin liquid and string-net condensation. Methods discussed include the path integral, Green's functions, mean-field theory, effective theory, renormalization group, bosonization in one- and higher dimensions, non-linear sigma-model, quantum gauge theory, dualities, projective construction, and exactly soluble models beyond one-dimension.