278 research outputs found
The Flux-Phase of the Half-Filled Band
The conjecture is verified that the optimum, energy minimizing magnetic flux
for a half-filled band of electrons hopping on a planar, bipartite graph is
per square plaquette. We require {\it only} that the graph has
periodicity in one direction and the result includes the hexagonal lattice
(with flux 0 per hexagon) as a special case. The theorem goes beyond previous
conjectures in several ways: (1) It does not assume, a-priori, that all
plaquettes have the same flux (as in Hofstadter's model); (2) A Hubbard type
on-site interaction of any sign, as well as certain longer range interactions,
can be included; (3) The conclusion holds for positive temperature as well as
the ground state; (4) The results hold in dimensions if there is
periodicity in directions (e.g., the cubic lattice has the lowest energy
if there is flux in each square face).Comment: 9 pages, EHL14/Aug/9
Ordering of Energy Levels in Heisenberg Models and Applications
In a recent paper we conjectured that for ferromagnetic Heisenberg models the
smallest eigenvalues in the invariant subspaces of fixed total spin are
monotone decreasing as a function of the total spin and called this property
ferromagnetic ordering of energy levels (FOEL). We have proved this conjecture
for the Heisenberg model with arbitrary spins and coupling constants on a
chain. In this paper we give a pedagogical introduction to this result and also
discuss some extensions and implications. The latter include the property that
the relaxation time of symmetric simple exclusion processes on a graph for
which FOEL can be proved, equals the relaxation time of a random walk on the
same graph. This equality of relaxation times is known as Aldous' Conjecture.Comment: 20 pages, contribution for the proceedings of QMATH9, Giens,
September 200
Effective lattice actions for correlated electrons
We present an exact, unconstrained representation of the electron operators
in terms of operators of opposite statistics. We propose a path--integral
representation for the - model and introduce a parameter controlling the
semiclassical behaviour. We extend the functional approach to the Hubbard model
and show that the mean--field theory is equivalent to considering, at
Hamiltonian level, the Falikov--Kimball model. Connections with a bond-charge
model are also discussed.Comment: 12 pages, REVTeX 3.0, no figure
Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems
Gapped ground states of quantum spin systems have been referred to in the
physics literature as being `in the same phase' if there exists a family of
Hamiltonians H(s), with finite range interactions depending continuously on , such that for each , H(s) has a non-vanishing gap above its
ground state and with the two initial states being the ground states of H(0)
and H(1), respectively. In this work, we give precise conditions under which
any two gapped ground states of a given quantum spin system that 'belong to the
same phase' are automorphically equivalent and show that this equivalence can
be implemented as a flow generated by an -dependent interaction which decays
faster than any power law (in fact, almost exponentially). The flow is
constructed using Hastings' 'quasi-adiabatic evolution' technique, of which we
give a proof extended to infinite-dimensional Hilbert spaces. In addition, we
derive a general result about the locality properties of the effect of
perturbations of the dynamics for quantum systems with a quasi-local structure
and prove that the flow, which we call the {\em spectral flow}, connecting the
gapped ground states in the same phase, satisfies a Lieb-Robinson bound. As a
result, we obtain that, in the thermodynamic limit, the spectral flow converges
to a co-cycle of automorphisms of the algebra of quasi-local observables of the
infinite spin system. This proves that the ground state phase structure is
preserved along the curve of models .Comment: Updated acknowledgments and new email address of S
A Multi-Dimensional Lieb-Schultz-Mattis Theorem
For a large class of finite-range quantum spin models with half-integer
spins, we prove that uniqueness of the ground state implies the existence of a
low-lying excited state. For systems of linear size L, of arbitrary finite
dimension, we obtain an upper bound on the excitation energy (i.e., the gap
above the ground state) of the form (C\log L)/L. This result can be regarded as
a multi-dimensional Lieb-Schultz-Mattis theorem and provides a rigorous proof
of a recent result by Hastings.Comment: final versio
A short proof of stability of topological order under local perturbations
Recently, the stability of certain topological phases of matter under weak
perturbations was proven. Here, we present a short, alternate proof of the same
result. We consider models of topological quantum order for which the
unperturbed Hamiltonian can be written as a sum of local pairwise
commuting projectors on a -dimensional lattice. We consider a perturbed
Hamiltonian involving a generic perturbation that can be written
as a sum of short-range bounded-norm interactions. We prove that if the
strength of is below a constant threshold value then has well-defined
spectral bands originating from the low-lying eigenvalues of . These bands
are separated from the rest of the spectrum and from each other by a constant
gap. The width of the band originating from the smallest eigenvalue of
decays faster than any power of the lattice size.Comment: 15 page
Universality class of S=1/2 quantum spin ladder system with the four spin exchange
We study s=1/2 Heisenberg spin ladder with the four spin exchange. Combining
numerical results with the conformal field theory(CFT), we find a phase
transition with central charge c=3/2. Since this system has an SU(2) symmetry,
we can conclude that this critical theory is described by k=2 SU(2)
Wess-Zumino-Witten model with Z symmetry breaking
Loop Distribution and Fusion with Timing and Code Size Optimization for Embedded DSPs
International Conference on Embedded and Ubiquitous Computing (EUC 2005), Nagasaki, Japan,6-9 Dec 2005Loop distribution and loop fusion are two e.ective loop transformation techniques to optimize the execution of the programs in DSP applications. In this paper, we propose a new technique combining loop distribution with direct loop fusion, which will improve the timing performance without jeopardizing the code size. We .rst develop the loop distribution theorems that state the legality conditions of loop distribution for multi-level nested loops. We show that if the summation of the edge weights of the dependence cycle satis.es a certain condition, then the statements involved in the dependence cycle can be distributed; otherwise, they should be put in the same loop after loop distribution. Then, we propose the technique of maximum loop distribution with direct loop fusion. The experimental results show that the execution time of the transformed loops by our technique is reduced 21.0compared to the original loops and the code size of the transformed loops is reduced 7.0% on average compared to the original loops.Department of Computin
Influence of Hybridization on the Properties of the Spinless Falicov-Kimball Model
Without a hybridization between the localized f- and the conduction (c-)
electron states the spinless Falicov-Kimball model (FKM) is exactly solvable in
the limit of high spatial dimension, as first shown by Brandt and Mielsch. Here
I show that at least for sufficiently small c-f-interaction this exact
inhomogeneous ground state is also obtained in Hartree-Fock approximation. With
hybridization the model is no longer exactly solvable, but the approximation
yields that the inhomogeneous charge-density wave (CDW) ground state remains
stable also for finite hybridization V smaller than a critical hybridization
V_c, above which no inhomogeneous CDW solution but only a homogeneous solution
is obtained. The spinless FKM does not allow for a ''ferroelectric'' ground
state with a spontaneous polarization, i.e. there is no nonvanishing
-expectation value in the limit of vanishing hybridization.Comment: 7 pages, 6 figure
Phase transitions in the spinless Falicov-Kimball model with correlated hopping
The canonical Monte-Carlo is used to study the phase transitions from the
low-temperature ordered phase to the high-temperature disordered phase in the
two-dimensional Falicov-Kimball model with correlated hopping. As the
low-temperature ordered phase we consider the chessboard phase, the axial
striped phase and the segregated phase. It is shown that all three phases
persist also at finite temperatures (up to the critical temperature )
and that the phase transition at the critical point is of the first order for
the chessboard and axial striped phase and of the second order for the
segregated phase. In addition, it is found that the critical temperature is
reduced with the increasing amplitude of correlated hopping in the
chessboard phase and it is strongly enhanced by in the axial striped and
segregated phase.Comment: 17 pages, 6 figure
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