Condensation of charged bosons hybridised with fermions

Xiao-Gang Wen

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.

Adriano N. De Souza, Victo S. Filho

Aseem Talukdar

Jincheng Zhang

The concept of electric charge is traditionally associated with elementary fermionic particles such as electrons. In contrast, bosonic quasiparticles like photons, magnons, and phonons are usually regarded as electrically neutral. Here we propose that a macroscopic occupation of a bosonic mode can give rise to an emergent collective charge, denoted as Qm_collective. We formulate a theoretical framework based on the many-body wavefunction of a Bose–Einstein condensate and show that the collective charge can be expressed as the expectation value of the total charge operator over the condensate state. When the number of bosons in the condensate becomes large, the collective charge tends to a finite value even though each individual boson remains neutral. We discuss possible experimental platforms for observing this effect, including photon condensation in microcavities, polariton condensates in semiconductor microstructures, and acoustic phonon condensates in nanomechanical systems. The emergence of a collective charge in bosonic systems opens a new avenue for investigating quasiparticle interactions, non-linear optical phenomena, and the design of novel quantum devices with controllable charge properties.

Peng Ye, Xiao-Gang Wen

Recently, there is a considerable study on gapped symmetric phases of bosons that do not break any symmetry. Even without symmetry breaking, the bosons can still be in many exotic new states of matter, such as symmetry-protected topological (SPT) phases, which are short-range entangled and symmetry-enriched topological (SET) phases, which are long-range entangled. It is well known that noninteracting fermionic topological insulators are SPT states protected by time-reversal symmetry and U(1) fermion number conservation symmetry. In this paper, we construct three-dimensional exotic phases of bosons with time-reversal symmetry and boson number conservation U(1) symmetry by means of fermionic projective construction. We first construct an algebraic bosonic insulator, which is a symmetric bosonic state with an emergent U(1) gapless gauge field. We then obtain many gapped bosonic states that do not break the time-reversal symmetry and boson number conservation via proper dyon condensations. We identify the constructed states by calculating the allowed electric and magnetic charges of their excitations, as well as the statistics and the symmetric transformation properties of those excitations. This allows us to show that our constructed states can be trivial SPT states (i.e., trivial Mott insulators of bosons with symmetry), nontrivial SPT states (i.e., bosonic topological insulators), and SET states (i.e., fractional bosonic topological insulators). In nontrivial SPT states, the elementary monopole (carrying zero electric charge but unit magnetic charge) and elementary dyon (carrying both unit electric charge and unit magnetic charge) are fermionic and bosonic, respectively. In SET states, intrinsic excitations may carry fractional charge.

Oleg Tchernyshyov, J.-B. Fouet, Frédéric Mila +1 more