665 research outputs found
Parafermionic phases with symmetry-breaking and topological order
Parafermions are the simplest generalizations of Majorana fermions that
realize topological order. We propose a less restrictive notion of topological
order in 1D open chains, which generalizes the seminal work by Fendley [J.
Stat. Mech., P11020 (2012)]. The first essential property is that the
groundstates are mutually indistinguishable by local, symmetric probes, and the
second is a generalized notion of zero edge modes which cyclically permute the
groundstates. These two properties are shown to be topologically robust, and
applicable to a wider family of topologically-ordered Hamiltonians than has
been previously considered. An an application of these edge modes, we formulate
a new notion of twisted boundary conditions on a closed chain, which guarantees
that the closed-chain groundstate is topological, i.e., it originates from the
topological manifold of degenerate states on the open chain. Finally, we
generalize these ideas to describe symmetry-breaking phases with a
parafermionic order parameter. These exotic phases are condensates of
parafermion multiplets, which generalizes Cooper pairing in superconductors.
The stability of these condensates are investigated on both open and closed
chains.Comment: 27 pages, 9 figure
Quantum frustration in organic Mott insulators: from spin liquids to unconventional superconductors
We review the interplay of frustration and strong electronic correlations in
quasi-two-dimensional organic charge transfer salts, such as k-(BEDT-TTF)_2X
and Et_nMe_{4-n}Pn[Pd(dmit)2]2. These two forces drive a range of exotic phases
including spin liquids, valence bond crystals, pseudogapped metals, and
unconventional superconductivity. Of particular interest is that in several
materials there is a direct transition as a function of pressure from a spin
liquid Mott insulating state to a superconducting state. Experiments on these
materials raise a number of profound questions about the quantum behaviour of
frustrated systems, particularly the intimate connection between spin liquids
and superconductivity. Insights into these questions have come from a wide
range of theoretical techniques including first principles electronic
structure, quantum many-body theory and quantum field theory. In this review we
introduce the basic ideas of the field by discussing a simple frustrated
Heisenberg model with four spins. We then describe the key experimental
results, emphasizing that for two materials, k-(BEDT-TTF)_2Cu_2(CN)_3 and
EtMe_3Sb[Pd(dmit)_2]_2, there is strong evidence for a spin liquid ground
state, and for EtMe_3P[Pd(dmit)_2]_2, a valence bond solid ground state. We
review theoretical attempts to explain these phenomena, arguing that this can
be captured by a Hubbard model on the anisotropic triangular lattice at half
filling, and that resonating valence bond wavefunctions can capture most of the
essential physics. We review evidence that this model can have a spin liquid
ground state for a range of parameters that are realistic for the relevant
materials. We conclude by summarising the progress made thus far and
identifying some of the key questions still to be answered.Comment: Major rewrite. New material added and many typos corrected. 67 pages,
41 figures. Thanks to those who commented on the previous versio
Order and Disorder in AKLT Antiferromagnets in Three Dimensions
The models constructed by Affleck, Kennedy, Lieb, and Tasaki describe a
family of quantum antiferromagnets on arbitrary lattices, where the local spin
S is an integer multiple M of half the lattice coordination number. The equal
time quantum correlations in their ground states may be computed as finite
temperature correlations of a classical O(3) model on the same lattice, where
the temperature is given by T=1/M. In dimensions d=1 and d=2 this mapping
implies that all AKLT states are quantum disordered. We consider AKLT states in
d=3 where the nature of the AKLT states is now a question of detail depending
upon the choice of lattice and spin; for sufficiently large S some form of Neel
order is almost inevitable. On the unfrustrated cubic lattice, we find that all
AKLT states are ordered while for the unfrustrated diamond lattice the minimal
S=2 state is disordered while all other states are ordered. On the frustrated
pyrochlore lattice, we find (conservatively) that several states starting with
the minimal S=3 state are disordered. The disordered AKLT models we report here
are a significant addition to the catalog of magnetic Hamiltonians in d=3 with
ground states known to lack order on account of strong quantum fluctuations.Comment: 7 pages, 2 figure
Magnetic responses of randomly depleted spin ladders
The magnetic responses of a spin-1/2 ladder doped with non-magnetic
impurities are studied using various methods and including the regime where
frustration induces incommensurability. Several improvements are made on the
results of the seminal work of Sigrist and Furusaki [J. Phys. Soc. Jpn. 65,
2385 (1996)]. Deviations from the Brillouin magnetic curve due to interactions
are also analyzed. First, the magnetic profile around a single impurity and
effective interactions between impurities are analyzed within the bond-operator
mean-field theory and compared to density-matrix renormalization group
calculations. Then, the temperature behavior of the Curie constant is studied
in details. At zero-temperature, we give doping-dependent corrections to the
results of Sigrist and Furusaki on general bipartite lattice and compute
exactly the distribution of ladder cluster due to chain breaking effects. Using
exact diagonalization and quantum Monte-Carlo methods on the effective model,
the temperature dependence of the Curie constant is compared to a random dimer
model and a real-space renormalization group scenario. Next, the low-part of
the magnetic curve corresponding to the contribution of impurities is computed
using exact diagonalization. The random dimer model is shown to capture the
bulk of the curve, accounting for the deviation from the Brillouin response. At
zero-temperature, the effective model prediction agrees relatively well with
density-matrix renormalization group calculations. Finite-temperature effects
are displayed within the effective model and for large depleted ladder models
using quantum Monte-Carlo simulations. In all, the effect of incommensurability
does not display a strong qualitative effect on both the magnetic
susceptibility and the magnetic curve. Consequences for experiments on the
BiCu2PO6 compound and other spin-gapped materials are briefly discussed.Comment: 24 pages, 20 figure
Correlated electron states and transport in triangular arrays
We study correlated electron states in frustrated geometry of a triangular
lattice. The interplay of long range interactions and finite residual entropy
of a classical system gives rise to unusual effects in equilibrium ordering as
well as in transport. A novel correlated fluid phase is identified in a wide
range of densities and temperatures above freezing into commensurate solid
phases. The charge dynamics in the correlated phase is described in terms of a
height field, its fluctuations, and topological defects. We demonstrate that
the height field fluctuations give rise to a ``free'' charge flow and finite dc
conductivity. We show that freezing into the solid phase, controlled by the
long range interactions, manifests itself in singularities of transport
properties.Comment: 19 pages, 10 figure
Dynamical mean-field theories of correlation and disorder
We provide a review of recently-develop dynamical mean-field theory (DMFT)
approaches to the general problem of strongly correlated electronic systems
with disorder. We first describe the standard DMFT approach, which is exact in
the limit of large coordination, and explain why in its simplest form it cannot
capture either Anderson localization or the glassy behavior of electrons.
Various extensions of DMFT are then described, including statistical DMFT,
typical medium theory, and extended DMFT, methods specifically designed to
overcome the limitations of the original formulation. We provide an overview of
the results obtained using these approaches, including the formation of
electronic Griffiths phases, the self-organized criticality of the Coulomb
glass, and the two-fluid behavior near Mott-Anderson transitions. Finally, we
outline research directions that may provide a route to bridge the gap between
the DMFT-based theories and the complementary diffusion-mode approaches to the
metal-insulator transition.Comment: 78 pages, 19 figures; To be published in "Conductor Insulator Quantum
Phase Transitions", edited by V. Dobrosavljevic, N. Trivedi, and J.M. Valles
Jr., Oxford University Press, 2013, ISBN 978019959259
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