11,296 research outputs found
Combinatorial point for higher spin loop models
Integrable loop models associated with higher representations (spin k/2) of
U_q(sl(2)) are investigated at the point q=-e^{i\pi/(k+2)}. The ground state
eigenvalue and eigenvectors are described. Introducing inhomogeneities into the
models allows to derive a sum rule for the ground state entries.Comment: latest version adds some reference
Characterizing topological order by studying the ground states of an infinite cylinder
Given a microscopic lattice Hamiltonian for a topologically ordered phase, we
describe a tensor network approach to characterize its emergent anyon model
and, in a chiral phase, also its gapless edge theory. First, a tensor network
representation of a complete, orthonormal set of ground states on a cylinder of
infinite length and finite width is obtained through numerical optimization.
Each of these ground states is argued to have a different anyonic flux
threading through the cylinder. In a chiral phase, the entanglement spectrum of
each ground state is seen to reveal a different sector of the corresponding
gapless edge theory. A quasi-orthogonal basis on the torus is then produced by
chopping off and reconnecting the tensor network representation on the
cylinder. Elaborating on the recent proposal of [Y. Zhang et al. Phys. Rev. B
85, 235151 (2012)], a rotation on the torus yields an alternative basis of
ground states and, through the computation of overlaps between bases, the
modular matrices S and U (containing the mutual and self statistics of the
different anyon species) are extracted. As an application, we study the
hard-core boson Haldane model by using the two-dimensional density matrix
renormalization group. A thorough characterization of the universal properties
of this lattice model, both in the bulk and at the edge, unambiguously shows
that its ground space realizes the \nu=1/2 bosonic Laughlin state.Comment: 10 pages, 11 figure
The solution of the quantum T-system for arbitrary boundary
We solve the quantum version of the -system by use of quantum
networks. The system is interpreted as a particular set of mutations of a
suitable (infinite-rank) quantum cluster algebra, and Laurent positivity
follows from our solution. As an application we re-derive the corresponding
quantum network solution to the quantum -system and generalize it to
the fully non-commutative case. We give the relation between the quantum
-system and the quantum lattice Liouville equation, which is the quantized
-system.Comment: 24 pages, 18 figure
The Razumov-Stroganov conjecture: Stochastic processes, loops and combinatorics
A fascinating conjectural connection between statistical mechanics and
combinatorics has in the past five years led to the publication of a number of
papers in various areas, including stochastic processes, solvable lattice
models and supersymmetry. This connection, known as the Razumov-Stroganov
conjecture, expresses eigenstates of physical systems in terms of objects known
from combinatorics, which is the mathematical theory of counting. This note
intends to explain this connection in light of the recent papers by Zinn-Justin
and Di Francesco.Comment: 6 pages, 4 figures, JSTAT News & Perspective
Non-local scaling operators with entanglement renormalization
The multi-scale entanglement renormalization ansatz (MERA) can be used, in
its scale invariant version, to describe the ground state of a lattice system
at a quantum critical point. From the scale invariant MERA one can determine
the local scaling operators of the model. Here we show that, in the presence of
a global symmetry , it is also possible to determine a class of
non-local scaling operators. Each operator consist, for a given group element
, of a semi-infinite string \tGamma_g with a local operator
attached to its open end. In the case of the quantum Ising model,
, they correspond to the disorder operator ,
the fermionic operators and , and all their descendants.
Together with the local scaling operators identity , spin
and energy , the fermionic and disorder scaling operators ,
and are the complete list of primary fields of the Ising
CFT. Thefore the scale invariant MERA allows us to characterize all the
conformal towers of this CFT.Comment: 4 pages, 4 figures. Revised versio
Integrability of graph combinatorics via random walks and heaps of dimers
We investigate the integrability of the discrete non-linear equation
governing the dependence on geodesic distance of planar graphs with inner
vertices of even valences. This equation follows from a bijection between
graphs and blossom trees and is expressed in terms of generating functions for
random walks. We construct explicitly an infinite set of conserved quantities
for this equation, also involving suitable combinations of random walk
generating functions. The proof of their conservation, i.e. their eventual
independence on the geodesic distance, relies on the connection between random
walks and heaps of dimers. The values of the conserved quantities are
identified with generating functions for graphs with fixed numbers of external
legs. Alternative equivalent choices for the set of conserved quantities are
also discussed and some applications are presented.Comment: 38 pages, 15 figures, uses epsf, lanlmac and hyperbasic
Chern-Simons matrix models and Stieltjes-Wigert polynomials
Employing the random matrix formulation of Chern-Simons theory on Seifert
manifolds, we show how the Stieltjes-Wigert orthogonal polynomials are useful
in exact computations in Chern-Simons matrix models. We construct a
biorthogonal extension of the Stieltjes-Wigert polynomials, not available in
the literature, necessary to study Chern-Simons matrix models when the geometry
is a lens space. We also discuss several other results based on the properties
of the polynomials: the equivalence between the Stieltjes-Wigert matrix model
and the discrete model that appears in q-2D Yang-Mills and the relationship
with Rogers-Szego polynomials and the corresponding equivalence with an unitary
matrix model. Finally, we also give a detailed proof of a result that relates
quantum dimensions with averages of Schur polynomials in the Stieltjes-Wigert
ensemble.Comment: 25 pages, AMS-LaTe
Algorithms for entanglement renormalization
We describe an iterative method to optimize the multi-scale entanglement
renormalization ansatz (MERA) for the low-energy subspace of local Hamiltonians
on a D-dimensional lattice. For translation invariant systems the cost of this
optimization is logarithmic in the linear system size. Specialized algorithms
for the treatment of infinite systems are also described. Benchmark simulation
results are presented for a variety of 1D systems, namely Ising, Potts, XX and
Heisenberg models. The potential to compute expected values of local
observables, energy gaps and correlators is investigated.Comment: 23 pages, 28 figure
Thermopower in the Coulomb blockade regime for Laughlin quantum dots
Using the conformal field theory partition function of a Coulomb-blockaded
quantum dot, constructed by two quantum point contacts in a Laughlin quantum
Hall bar, we derive the finite-temperature thermodynamic expression for the
thermopower in the linear-response regime. The low-temperature results for the
thermopower are compared to those for the conductance and their capability to
reveal the structure of the single-electron spectrum in the quantum dot is
analyzed.Comment: 11 pages, 3 figures, Proceedings of the 10-th International Workshop
"Lie Theory and Its Applications in Physics", 17-23 June 2013, Varna,
Bulgari
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