Related papers: Dual algebraic structures for the two-level pairin…
We show how classical and quantum dualities, as well as duality relations that appear only in a sector of certain theories ("emergent dualities"), can be unveiled, and systematically established. Our method relies on the use of morphisms of…
We argue that fermion-boson mapping techniques represent a natural tool for studying many-body supersymmetry in fermionic systems with pairing. In particular, using the generalized Dyson mapping of a many-level fermion superalgebra with the…
The ground state of the toric code, that of the two-dimensional class D superconductor, and the partition sum of the two-dimensional Ising model are dual to each other. This duality is remarkable inasmuch as it connects systems commonly…
Gaussian unitary transformations are generated by quadratic Hamiltonians, i.e., Hamiltonians containing quadratic terms in creations and annihilation operators, and are heavily used in many areas of quantum physics, ranging from quantum…
We use the Kantor-Susskind\cite{kantsuss} model of fermions as "dumbbells" connecting points on a cubic lattice to points on its dual, to define a duality between local fermionic models invariant under a $Z_2$ gauge symmetry and models of…
Using certain pairings of couples, we obtain a large class of two-sided non-degenerated graded Hopf pairings for quantum symmetric algebras.
Weak-strong coupling duality relations are shown to be present in the quantum-mechanical many-body system with the interacting potential proportional to the pair-wise inverse-squared distance in addition to the harmonic potential. Using…
We explore an exact duality in $(2+1)$d between the fermionization of a bosonic theory with a $\mathbb{Z}_2$ subsystem symmetry and a fermionic theory with a $\mathbb{Z}_2$ subsystem fermion parity symmetry. A typical example is the duality…
We present an algebraic method to derive the structure at the basis of the mapping of bosonic algebras of creation and annihilation operators into fermionic algebras, and vice versa, introducing a suitable identification between bosonic and…
One-dimensional quantum systems admit duality relations that put hard core spinless bosons and fermions in one-to-one correspondence via Girardeau's mapping theorem. The simplest models of soft bosons interacting via zero-range potentials…
In nuclei with valence nucleons are say identical nucleons and say these nucleons occupy several-$j$ orbits, then it is possible to consider pair creation operator $S_+$ to be a sum of the single-$j$ shell pair creation operators $S_+(j)$…
An algebraic theory of dualities is developed based on the notion of bond algebras. It deals with classical and quantum dualities in a unified fashion explaining the precise connection between quantum dualities and the low temperature…
We study the interplay of duality and stacking of bosonic and fermionic symmetry-protected topological phases in one spatial dimension. In general the classifications of bosonic and fermionic phases have different group structures under the…
In a recent work, Murmann {\it et. al.} [Phys. Rev. Lett. {\bf114}, 080402 (2015)] have experimentally prepared and manipulated a double-well optical potential containing a pair of Fermi atoms as a possible building block of Hubbard model.…
We analyze the possible types of ordering in a boson--fermion model. The Hamiltonian is inherently related to the Bose--Hubbard model for vector two-species bosons in optical lattices. We show that such model can be reduced to the…
We propose novel infrared dualities connecting 2+1 dimensional non-Abelian gauge theories (with unitary or special unitary gauge groups) to Abelian gauge theories. The dual Abelian theories are characterized by a planar quiver structure,…
The first two Hamiltonian structures and the recursion operator connecting all evolution systems and Hamiltonian structures of the N=2 supersymmetric (n,m)-GNLS hierarchy are constructed in terms of N=2 superfields in two different…
As generalizations of the fermion seniority model, four multi-mode Hamiltonians are considered to investigate some of the consequences of the pairing of parafermions of order two. 2-particle and 4-particle states are explicitly constructed…
Given a two-dimensional bosonic theory with a non-anomalous $\mathbb{Z}_2$ symmetry, the orbifolding and fermionization can be understood holographically using three-dimensional BF theory with level $2$. From a Hamiltonian perspective, the…
Number-non-conserving terms in quadratic bosonic Hamiltonians can induce unwanted dynamical instabilities. By exploiting the pseudo-Hermitian structure built in to these Hamiltonians, we show that as long as dynamical stability holds, one…