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The discovery of relativistic spin-1/2 fermions such as Dirac and Weyl fermions in condensed-matter or artificial systems opens a new era in modern physics. An interesting but rarely explored question is whether other relativistic spinal…

Non-Abelian toplogical superconductors are characterized by the existence of {zero-energy} Majorana fermions bound in the quantized vortices. This is a consequence of the nontrivial bulk topology characterized by an {\em odd} Chern number.…

We present rigorous results for several variants of the Hubbard model in the strong-coupling regime. We establish a mathematically controlled perturbation expansion which shows how previously proposed effective interactions are, in fact,…

This is a colloquium-style introduction to the midgap excitations in superconductors known as Majorana fermions. These elusive particles, equal to their own antiparticle, may or may not exist in Nature as elementary building blocks, but in…

We show that topological phases with fractional excitations can occur in two-dimensional ultracold dipolar gases on a particular class of optical lattices. Due to the dipolar interaction and lattice confinement, a quantum dimer model…

We examine recent claims that nonperturbative effects can prevent the decoupling of a heavy fermion whose mass arises from a Yukawa coupling to a scalar field. We show that in weakly coupled, four dimensional models such as the standard…

A two-dimensional field theory of a fermion chirally coupled to Toda field plus a scalar self-coupling potential is considered. Using techniques of integrable systems we obtain analytical zero modes, in-gap states and bound states in the…

Quantum ladder models, consisting of coupled chains, form intriguing systems bridging one and two dimensions and have been well studied in the context of quantum magnets and fermionic systems. Here we consider ladder systems made of more…

We show that a one dimensional ultra-cold Fermi gas with Rashba-like spin orbit coupling, a Zeeman field and intrinsic attractive interactions exhibits a novel topological superfluid state, which forms in spite of total number conservation…

We present a microscopic model of interacting fermions where the ground state degeneracy is topologically protected. The model is based on a double-wire setup with local interactions in a particle number conserving setting. A compelling…

Among the broad spectrum of systems predicted to exhibit topological superconductivity and Majorana fermions, one-dimensional wires with strong spin-orbit coupling provide one of the most promising experimental candidates. Here we…

In optical lattices attractive ultracold fermions with three hyperfine-spin components (colors) can form three fermionic configurations depending on interactions: unbound fermion, on-site trion and off-site trion, leading to the coexistence…

We study the ground-state entanglement Hamiltonian of free nonrelativistic fermions for semi-infinite domains in one dimension. This is encoded in the two-point correlations projected onto the subsystem, an operator that commutes with the…

In this article we provide a general mechanism for generating interaction-enabled fermionic topological phases. We illustrate the mechanism with crystalline symmetry-protected topological phases in 1D and 2D. These non-trivial phases…

A 2+1 dimensional fermion field theory is proposed as a model for the low-energy electronic excitations in monolayer graphene. The model consists of N=2 four-component Dirac fermions moving in the plane and interacting via a contact…

In the present paper, we study a system of doped antiferromagnet in three dimensions at finite temperatures by using the t-J model, a canonical model of strongly-correlated electrons. We employ the slave-fermion representation of electrons…

We introduce a model of interacting Majorana fermions that describes a superconducting phase with a topological order characterized by the Fibonacci topological field theory. Our theory, which is based on a $SO(7)_1/(G_2)_1$ coset…

The search for Majorana excitations has seen tremendous efforts in recent years, ultimately aiming for their individual controllability in future topological quantum computers. A promising framework to realize such exotic Majorana fermions…

We consider a setup consisting of two coupled sheets of bilayer graphene in the regime of strong spin-orbit interaction, where electrostatic confinement is used to create an array of effective quantum wires. We show that for suitable…

Topological one-dimensional superconductors can sustain in their extremities zero energy modes that are protected by different kinds of symmetries. The observation of these excitations in the form of Majorana fermions is one of the most…