Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userPhase diagram for hard-core $mathbb{Z}_3$ anyons on the ladder
126
0
0.0
(
0
)
Authors
Robert N. C. Pfeifer
Ask ChatGPT about the research
No Arabic abstract
Studies of free particles in low-dimensional quantum systems such as two-leg ladders provide insight into the influence of statistics on collective behaviour. The behaviours of bosons and fermions are well understood, but two-dimensional systems also admit excitations with alternative statistics known as anyons. Numerical analysis of hard-core $mathbb{Z}_3$ anyons on the ladder reveals qualitatively distinct behaviour, including a novel phase transition associated with crystallisation of hole degrees of freedom into a periodic foam. Qualitative predictions are extrapolated for all Abelian $mathbb{Z}_q$ anyon models.
rate research
Read More
We show that a $mathbb{Z}_3$ quantum double can be realized in an array of superconducting wires coupled via Josephson junctions. With a suitably chosen magnetic flux threading the system, the inter-wire Josephson couplings take the form of a complex Hadamard matrix, which possesses combinatorial gauge symmetry -- a local $mathbb{Z}_3$ symmetry involving permutations and shifts by $pm 2pi/3$ of the superconducting phases. The sign of the star potential resulting from the Josephson energy is inverted in this physical realization, leading to a massive degeneracy in the non-zero flux sectors. A dimerization pattern encoded in the capacitances of the array lifts up these degeneracies, resulting in a $mathbb{Z}_3$ topologically ordered state. Moreover, this dimerization pattern leads to a larger effective vison gap as compared to the canonical case with the usual (uninverted) star term. We further show that our model maps to a quantum three-state Potts model under a duality transformation. We argue, using a combination of bosonization and mean field theory, that altering the dimerization pattern of the capacitances leads to a transition from the $mathbb{Z}_3$ topological phase into a quantum XY-ordered phase. Our work highlights that combinatorial gauge symmetry can serve as a design principle to build quantum double models using systems with realistic interactions.
We continue recent efforts to discover examples of deconfined quantum criticality in one-dimensional models. In this work we investigate the transition between a $mathbb{Z}_3$ ferromagnet and a phase with valence bond solid (VBS) order in a spin chain with $mathbb{Z}_3timesmathbb{Z}_3$ global symmetry. We study a model with alternating projective representations on the sites of the two sublattices, allowing the Hamiltonian to connect to an exactly solvable point having VBS order with the character of SU(3)-invariant singlets. Such a model does not admit a Lieb-Schultz-Mattis theorem typical of systems realizing deconfined critical points. Nevertheless, we find evidence for a direct transition from the VBS phase to a $mathbb{Z}_3$ ferromagnet. Finite-entanglement scaling data are consistent with a second-order or weakly first-order transition. We find in our parameter space an integrable lattice model apparently describing the phase transition, with a very long, finite, correlation length of 190878 lattice spacings. Based on exact results for this model, we propose that the transition is extremely weakly first order, and is part of a family of DQCP described by walking of renormalization group flows.
The effect of next-nearest-neighbor hopping $t_{2}$ on the ground-state phase diagram of the one-dimensional Kondo lattice is studied with density-matrix renormalization-group techniques and by comparing with the phase diagram of the classical-spin variant of the same model. For a finite $t_{2}$, i.e., for a zigzag-ladder geometry, indirect antiferromagnetic interactions between the localized spins are geometrically frustrated. We demonstrate that $t_{2}$ at the same time triggers several magnetic phases which are absent in the model with nearest-neighbor hopping only. For strong $J$, we find a transition from antiferromagnetic to incommensurate magnetic short-range order, which can be understood entirely in the classical-spin picture. For weaker $J$, a spin-dimerized phase emerges, which spontaneously breaks the discrete translation symmetry. The phase is not accessible to perturbative means but is explained, on a qualitative level, by the classical-spin model as well. Spin dimerization alleviates magnetic frustration and is interpreted as a key to understand the emergence of quasi-long-range spiral magnetic order which is found at weaker couplings. The phase diagram at weak $J$, with gapless quasi-long-range order on top of the two-fold degenerate spin-dimerized ground state, competing with a nondegenerate phase with gapped spin (and charge) excitations, is unconventional and eludes an effective low-energy spin-only theory.
We consider the braid group representation which describes the non-abelian braiding statistics of the spin 1/2 particle world lines of an SU(2)$_4$ Chern-Simons theory. Up to an abelian phase, this is the same as the non-Abelian statistics of the elementary quasiparticles of the $k=4$ Read-Rezayi quantum Hall state. We show that these braiding statistics are identical to those of Z$_3$ Parafermions.
Recent experiments on a one-dimensional chain of trapped alkali atoms [arXiv:1707.04344] have observed a quantum transition associated with the onset of period-3 ordering of pumped Rydberg states. This spontaneous $mathbb{Z}_3$ symmetry breaking is described by a constrained model of hard-core bosons proposed by Fendley $et, ,al.$ [arXiv:cond-mat/0309438]. By symmetry arguments, the transition is expected to be in the universality class of the $mathbb{Z}_3$ chiral clock model with parameters preserving both time-reversal and spatial-inversion symmetries. We study the nature of the order-disorder transition in these models, and numerically calculate its critical exponents with exact diagonalization and density-matrix renormalization group techniques. We use finite-size scaling to determine the dynamical critical exponent $z$ and the correlation length exponent $ u$. Our analysis presents the only known instance of a strongly-coupled transition between gapped states with $z e 1$, implying an underlying nonconformal critical field theory.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
