Studies of bosons and fermions in lower dimensional systems

Jian-Hao Zhang, Qing-Rui Wang, Shuo Yang +2 more

The construction and classification of symmetry-protected topological (SPT) phases in interacting bosonic and fermionic systems have been intensively studied in the past few years. Very recently, a complete classification and construction of space-group SPT phases were also proposed for interacting bosonic systems. In this Rapid Communication, we attempt to generalize this classification and construction scheme systematically into interacting fermion systems. In particular, we construct and classify point-group SPT phases for two-dimensional (2D) interacting fermion systems via lower-dimensional block-state decorations. We discover several intriguing fermionic SPT states that can only be realized in interacting fermion systems (i.e., not in free-fermion or bosonic SPT systems). Moreover, we also verify the recently conjectured crystalline equivalence principle for 2D interacting fermion systems. Finally, the potential experimental realization of these different classes of point-group SPT phases in 2D correlated superconductors is addressed.

Yoshio Kuramoto

Filippo Bovo

In this work we examine the dynamics of one-dimensional systems. We present a continuum approach to the construction of the non-equilibrium Keldysh functional integral and derive a relation between the classical and quantum fields of the Keldysh formalism and the occupation of a state. Using the Keldysh formalism, we give a self-contained presentation of bosonization and refermionisation of fermionic and bosonic interacting particles. We derive the first two non-linear corrections to linear bosonization due to the fermionic spectrum curvature using the functional integral formalism. Using the previous results, we study the thermal dynamics of one-dimensional systems. We consider both the phonons, coming from bosonization, and fermionic quasiparticles, coming from refermionisation, in a single theory. Having them in a single theory is justified by a scale separation between them. Studying the dynamical structure factor we find three regimes. From higher to lower energies we have a ballistic and a collisional regimes of fermionic quasiparticles and a hydrodynamical regime of non-linear phonons. The phase field of the non-linear bosons satisfies the Kardar-Parisi-Zhang equation, thereby linking the dynamics of one-dimensional quantum systems to the universality class of surface growth. The time-scale separating the phononic and fermionic quasiparticle regimes is very long for up-to-date experiments, meaning that the ballistic regime of fermionic quasiparticles is the only one likely to be observed. Since this approach has a limited range of validity for weakly interacting bosons, we derive their dynamical structure factor using a semiclassical approach.

Leon N. Cooper

L. B. Ioffe, David Lidsky, B. L. Altshuler

We study a system of fermions interacting with a gauge field which can be used to describe either a spin liquid or the \ensuremath{\nu}=1/2 quantum Hall state. We propose a generalized model with a dimensionless parameter N. We evaluate the properties of the model in both limits N\ensuremath{\gg}1 and N\ensuremath{\ll}1 and deduce the properties of the model in the most physically interesting case of N=1,2. At N\ensuremath{\ll}1 the motion of the fermions becomes one dimensional. By applying the bosonization method in this limit, we obtain the fermion Green function and response functions.