相关论文: Boundary States for Chiral Symmetries in Two Dimen…

In the 1+1D ultra-local lattice Hamiltonian for staggered fermions with a finite-dimensional Hilbert space, there are two conserved, integer-valued charges that flow in the continuum limit to the vector and axial charges of a massless Dirac…

Random Dirac fermions in a two-dimensional space are studied numerically. We realize them on a square lattice using the $\pi$-flux model with random hopping. The system preserves two symmetries, the time-reversal symmetry and the symmetry…

It is a well known feature of odd space-time dimensions $d$ that there exist two inequivalent fundamental representations $A$ and $B$ of the Dirac gamma matrices. Moreover, the parity transformation swaps the fermion fields living in $A$…

We propose a simple theoretical construction of certain short-range entangled phases of interacting fermions, by putting the bound states of three fermions (which we refer to as clustons) into topological bands. We give examples in two and…

We investigate the implications of the quantized vectorial and axial charges in the lattice Hamiltonian of multi-flavor staggered fermions in $(1+1)$ dimensions. These lattice charges coincide with those of the $U(1)_V$ and $U(1)_A$ global…

We analyze the dynamics of an $SU_L(2)\otimes U_R(1)$ chiral theory on the lattice with a strong multifermion coupling. It is shown that no spontaneous symmetry breaking occurs; the ``spectator'' fermion $\psi_R$ is a free mode; doublers…

In the presence of boundaries, the quantum anomalies acquire additional boundary terms. In odd dimensions the integrated conformal anomaly, for which the bulk contribution is known to be absent, is non-trivial due to the boundary terms.…

We introduce a novel class of low-dimensional topological tight-binding models that allow for bound states that are fractionally charged fermions and exhibit non-Abelian braiding statistics. The proposed model consists of a double (single)…

We investigate a 6d Dirac fermion on a rectangle. It is found that the 4d spectrum is governed by $N=2$ supersymmetric quantum mechanics. Then we demonstrate that the supersymmetry is very useful for classifying all the allowed boundary…

In a Hamiltonian formalism we study chiral symmetry for lattice Fermions formulated in terms of Shockley surface states bound to a wall in an extra spatial dimension. For hadronic physics this provides a natural scheme for taking quark…

We present a Fermionic Cellular Automaton model which describes massless Dirac fermion in 1+1 dimension coupled with local, number preserving interaction. The diagonalization of the two particle sector shows that specific values of the…

We demonstrate that Dirac fermions in 2+1 dimensions, coupled to Abelian gauge fields in multiply-connected regions, exhibit a parity anomaly that directly manifests as Aharonov-Bohm (AB) type topological phases. Using the Fujikawa method,…

We construct the complete set of boundary states of two-dimensional fermionic CFTs using that of the bosonic counterpart. We see that there are two groups of boundary conditions, which contributes to the open-string partition function by…

The fermionic minimal models are a recently-introduced family of two-dimensional spin conformal field theories. We determine all of their conformal boundary states and potentially anomalous $\mathbb{Z}_2$ global symmetries. The latter task…

The quantum-mechanical problem of constructing a self-adjoint Hamiltonian for the Dirac equation in an Aharonov--Bohm field in 2+1 dimensions is solved with taking into account the fermion spin. The one-parameter family of self-adjoint…

The Dirac-like equation governing dynamics of free anomalous fermions is derived. The basis bispinors controlling the obtained solutions of this equation turn out to be normalized by the area confining a region in the bispinor Clifford…

We study the dynamics and phase structure of Abelian gauge theories in $d=1+1$ dimensions. These include $U(1)$ gauge theory coupled to a scalar and a fermion, as well as the two-flavour Schwinger model with different charges. Both theories…

Fractional statistics give rise to quantum behaviors that differ fundamentally from those of bosons and fermions. While two-dimensional anyons play a major role in strongly correlated systems and topological quantum computing, the nature of…

It has recently been demonstrated that protected supersymmetry emerges on the boundaries of one-dimensional intrinsically fermionic symmetry protected trivial (SPT) phases. Here we investigate the boundary supersymmetry of one-dimensional…

I demonstrate how chiral fermions with an exact gauge symmetry can appear on the d-dimensional boundary of a finite volume (d+1)-dimensional manifold, without any light mirror partners. The condition for the d-dimensional boundary theory to…