相关论文: Reflection Positivity for Majoranas

An expression for the lattice effective action induced by chiral fermions in any even dimensions in terms of an overlap of two states is shown to have promising properties in two and four dimensions: The correct abelian anomaly is…

We propose an optical lattice setup to investigate spin chains and ladders. Electric and magnetic fields allow us to vary at will the coupling constants, producing a variety of quantum phases including the Haldane phase, critical phases,…

Quantum many-body systems exhibit an extremely diverse range of phases and physical phenomena. Here, we prove that the entire physics of any other quantum many-body system is replicated in certain simple, "universal" spin-lattice models. We…

Let $(M,g)$ be a compact connected spin manifold of dimension $n\geq 3$ whose Yamabe invariant is positive. We assume that $(M,g)$ is locally conformally flat or that $n \in \{3,4,5\}$. According to a positive mass theorem of Witten, the…

We consider two interacting quantum dots coupled by standard superconductors. We derive an effective Hamiltonian, and show that over a wide parameter range a degenerate ground state can be obtained. An exotique form of Majorana bound states…

We show that reflection symmetry has a strong influence on quantum transport properties. Using a random S-matrix theory approach, we derive the weak-localization correction, the magnitude of the conductance fluctuations, and the…

For linear bose field theories, I show that if a classical Hamiltonian function is strictly positive, then there is a canonical transformation making the evolution orthogonal. This structure theorem is used to analyze the corresponding…

In contrast to elementary Majorana particles, emergent Majorana fermions (MFs) in condensed-matter systems may have electromagnetic multipoles. We developed a general theory of magnetic multipoles for surface helical MFs on…

We prove (by a case-by-case analysis) a conjecture of Bernstein/Schwarzman to the effect that quotients of abelian varieties by suitable actions of (complex) reflection groups are weighted projective spaces, and show that this remains true…

We deal with the fragment of modal logic consisting of implications of formulas built up from the variables and the constant `true' by conjunction and diamonds only. The weaker language allows one to interpret the diamonds as the uniform…

Conformal field theory has turned out to be a powerful tool to derive interesting lattice models with analytical ground states. Here, we investigate a class of critical, one-dimensional lattice models of fermions and hardcore bosons related…

We consider Majorana lattices with two-site interactions consisting of a general function of the fermion bilinear. The models are exactly solvable in the limit of a large number of on-site fermions. The four-site chain exhibits a quantum…

We present a simplification of Lieb's proof of the flux phase conjecture for interacting fermion systems -- such as the Hubbard model --, at half filling on a general class of graphs. The main ingredient is a procedure which transforms a…

An interacting lattice model describing the subspace spanned by a set of strongly-correlated bands is rigorously coupled to density functional theory to enable ab initio calculations of geometric and topological material properties. The…

Majorana fermions are the real (in a mathematical sense) counterparts of complex fermions like ordinary electrons. The promise of topological quantum computing has lead to substantial experimental progress in realizing these particles in…

We show that Calogero-Sutherland models for interacting particles have a natural supersymmetric extension. For the construction, we use Jacobians which appear in certain superspaces. Some of the resulting Hamiltonians have a direct physics…

We show that, under certain combinations of the parameters governing the interaction of a harmonically trapped ion with a laser beam, it is possible to find one or more exact eigenstates of the Hamiltonian, with no approximations except the…

Lieb-Robinson-type bounds are reported for a large class of classical Hamiltonian lattice models. By a suitable rescaling of energy or time, such bounds can be constructed for interactions of arbitrarily long range. The bound quantifies the…

Based on the symmetry properties of graphene lattice, we derive the effective Hamiltonian of graphene under spatially non-uniform acoustic and optical strains. We show that with the proper selection of the parameters, the obtained…

We present a simple criterion for solvability of lattice spin systems on the basis of the graph theory and the simplicial homology. The lattice systems satisfy algebras with graphical representations. It is shown that the null spaces of…