100 research outputs found
Fibonacci (p, r)-cubes which are median graphs
AbstractThe Fibonacci (p, r)-cube is an interconnection topology, which unifies a wide range of connection topologies, such as hypercube, Fibonacci cube, postal network, etc. It is known that the Fibonacci cubes are median graphs [S. Klavžar, On median nature and enumerative properties of Fibonacci-like cubes, Discrete Math. 299 (2005) 145–153]. The question for determining which Fibonacci (p, r)-cubes are median graphs is solved completely in this paper. We show that Fibonacci (p, r)-cubes are median graphs if and only if either r≤p and r≤2, or p=1 and r=n
Fractonic order and emergent fermionic gauge theory
We consider fermionic systems in which fermion parity is conserved within rigid subsystems, and describe an explicit procedure for gauging such subsystem fermion parity symmetries to obtain bosonic spin Hamiltonians. We show that gauging planar or fractal subsystem fermion parity symmetry in three spatial dimensions gives rise to a plethora of exactly solvable spin models exhibiting novel gapped fractonic orders characterized by emergent fermionic gauge theory. The low energy excitations of these models include fractional quasiparticles with constrained mobility and emergent fermionic statistics. We illustrate this phenomenon through a series of examples including fermionic analogs of both foliated fracton phases and fractal spin liquids. We find that the foliated analogs actually exhibit the same fractonic order as their bosonic counterparts, while this is not generally the case for fermionic fractal spin liquids
General phase spaces: from discrete variables to rotor and continuum limits
We provide a basic introduction to discrete-variable, rotor, and
continuous-variable quantum phase spaces, explaining how the latter two can be
understood as limiting cases of the first. We extend the limit-taking
procedures used to travel between phase spaces to a general class of
Hamiltonians (including many local stabilizer codes) and provide six examples:
the Harper equation, the Baxter parafermionic spin chain, the Rabi model, the
Kitaev toric code, the Haah cubic code (which we generalize to qudits), and the
Kitaev honeycomb model. We obtain continuous-variable generalizations of all
models, some of which are novel. The Baxter model is mapped to a chain of
coupled oscillators and the Rabi model to the optomechanical radiation pressure
Hamiltonian. The procedures also yield rotor versions of all models, five of
which are novel many-body extensions of the almost Mathieu equation. The toric
and cubic codes are mapped to lattice models of rotors, with the toric code
case related to U(1) lattice gauge theory.Comment: 22 pages, 3 figures; part of special issue on Rabi model; v2 minor
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