156 research outputs found
Hardcore dimer aspects of the SU(2) Singlet wavefunction
We demonstrate that any SU(2) singlet wavefunction can be characterized by a
set of Valence Bond occupation numbers, testing dimer presence/vacancy on pairs
of sites. This genuine quantum property of singlet states (i) shows that SU(2)
singlets share some of the intuitive features of hardcore quantum dimers, (ii)
gives rigorous basis for interesting albeit apparently ill-defined quantities
introduced recently in the context of Quantum Magnetism or Quantum Information
to measure respectively spin correlations and bipartite entanglement and, (iii)
suggests a scheme to define consistently a wide family of quantities analogous
to high order spin correlation. This result is demonstrated in the framework of
a general functional mapping between the Hilbert space generated by an
arbitrary number of spins and a set of algebraic functions found to be an
efficient analytical tool for the description of quantum spins or qubits
systems.Comment: 5 pages, 2 figure
The structure of spinful quantum Hall states: a squeezing perspective
We provide a set of rules to define several spinful quantum Hall model
states. The method extends the one known for spin polarized states. It is
achieved by specifying an undressed root partition, a squeezing procedure and
rules to dress the configurations with spin. It applies to both the
excitation-less state and the quasihole states. In particular, we show that the
naive generalization where one preserves the spin information during the
squeezing sequence, may fail. We give numerous examples such as the Halperin
states, the non-abelian spin-singlet states or the spin-charge separated
states. The squeezing procedure for the series (k=2,r) of spinless quantum Hall
states, which vanish as r powers when k+1 particles coincide, is generalized to
the spinful case. As an application of our method, we show that the counting
observed in the particle entanglement spectrum of several spinful states
matches the one obtained through the root partitions and our rules. This
counting also matches the counting of quasihole states of the corresponding
model Hamiltonians, when the latter is available.Comment: 19 pages, 7 figures; v2: minor changes, and added references.
Mathematica packages are available for downloa
Master equation approach to computing RVB bond amplitudes
We describe a "master equation" analysis for the bond amplitudes h(r) of an
RVB wavefunction. Starting from any initial guess, h(r) evolves (in a manner
dictated by the spin hamiltonian under consideration) toward a steady-state
distribution representing an approximation to the true ground state. Unknown
transition coefficients in the master equation are treated as variational
parameters. We illustrate the method by applying it to the J1-J2
antiferromagnetic Heisenberg model. Without frustration (J2=0), the amplitudes
are radially symmetric and fall off as 1/r^3 in the bond length. As the
frustration increases, there are precursor signs of columnar or plaquette VBS
order: the bonds preferentially align along the axes of the square lattice and
weight accrues in the nearest-neighbour bond amplitudes. The Marshall sign rule
holds over a large range of couplings, J2/J1 < 0.418. It fails when the r=(2,1)
bond amplitude first goes negative, a point also marked by a cusp in the ground
state energy. A nonrigourous extrapolation of the staggered magnetic moment
(through this point of nonanalyticity) shows it vanishing continuously at a
critical value J2/J1 = 0.447. This may be preempted by a first-order transition
to a state of broken translational symmetry.Comment: 8 pages, 7 figure
Dynamical Structure Factor of the J1 12J2 Heisenberg Model on the Triangular Lattice: Magnons, Spinons, and Gauge Fields
Understanding the nature of the excitation spectrum in quantum spin liquids is of fundamental importance, in particular for the experimental detection of candidate materials. However, current theoretical and numerical techniques have limited capabilities, especially in obtaining the dynamical structure factor, which gives a crucial characterization of the ultimate nature of the quantum state and may be directly assessed by inelastic neutron scattering. In this work, we investigate the low-energy properties of the S = 1/2 Heisenberg model on the triangular lattice, including both nearest-neighbor J1 and next-nearestneighbor J2 superexchanges, by a dynamical variational Monte Carlo approach that allows accurate results on spin models. For J2 0 0, our calculations are compatible with the existence of a well-defined magnon in the whole Brillouin zone, with gapless excitations at K points (i.e., at the corners of the Brillouin zone). The strong renormalization of the magnon branch (also including rotonlike minima around the M points, i.e., midpoints of the border zone) is described by our Gutzwiller-projected state, where Abrikosov fermions are subject to a nontrivial magnetic \u3c0 flux threading half of the triangular plaquettes. When increasing the frustrating ratio J2/J1, we detect a progressive softening of the magnon branch at M, which eventually becomes gapless within the spin-liquid phase. This feature is captured by the band structure of the unprojected wave function (with two Dirac points for each spin component). In addition, we observe an intense signal at low energies around the K points, which cannot be understood within the unprojected picture and emerges only when the Gutzwiller projection is considered, suggesting the relevance of gauge fields for the low-energy physics of spin liquids
Valence Bond Entanglement and Fluctuations in Random Singlet Phases
The ground state of the uniform antiferromagnetic spin-1/2 Heisenberg chain
can be viewed as a strongly fluctuating liquid of valence bonds, while in
disordered chains these bonds lock into random singlet states on long length
scales. We show that this phenomenon can be studied numerically, even in the
case of weak disorder, by calculating the mean value of the number of valence
bonds leaving a block of contiguous spins (the valence-bond entanglement
entropy) as well as the fluctuations in this number. These fluctuations show a
clear crossover from a small regime, in which they behave similar to those
of the uniform model, to a large regime in which they saturate in a way
consistent with the formation of a random singlet state on long length scales.
A scaling analysis of these fluctuations is used to study the dependence on
disorder strength of the length scale characterizing the crossover between
these two regimes. Results are obtained for a class of models which include, in
addition to the spin-1/2 Heisenberg chain, the uniform and disordered critical
1D transverse-field Ising model and chains of interacting non-Abelian anyons.Comment: 8 pages, 6 figure
Infinite-Randomness Fixed Points for Chains of Non-Abelian Quasiparticles
One-dimensional chains of non-Abelian quasiparticles described by
Chern-Simons-Witten theory can enter random singlet phases analogous to that of
a random chain of ordinary spin-1/2 particles (corresponding to ). For this phase provides a random singlet description of the
infinite randomness fixed point of the critical transverse field Ising model.
The entanglement entropy of a region of size in these phases scales as for large , where is the quantum
dimension of the particles.Comment: 4 pages, 4 figure
Linear independence of nearest neighbor valence bond states on the kagome lattice and construction of SU(2)-invariant spin-1/2-Hamiltonian with a Sutherland-Rokhsar-Kivelson quantum liquid ground state
A class of local SU(2)-invariant spin-1/2 Hamiltonians is studied that has
ground states within the space of nearest neighbor valence bond states on the
kagome lattice. Cases include "generalized Klein'' models without obvious
non-valence bond ground states, as well as a "resonating-valence-bond"
Hamiltonian whose unique ground states within the nearest neighbor valence bond
space are four topologically degenerate "Sutherland-Rokhsar-Kivelson'' (SRK)
type wavefunctions, which are expected to describe a gapped spin
liquid. The proof of this uniqueness is intimately related to the linear
independence of the nearest neighbor valence bond states on quite general and
arbitrarily large kagome lattices, which is also established in this work. It
is argued that the SRK ground states are also unique within the entire Hilbert
space, depending on properties of the generalized Klein models. Applications of
the strategies developed in this work to other lattice types are also
discussed.Comment: published version, many references added, some typos correcte
Variational ground states of 2D antiferromagnets in the valence bond basis
We study a variational wave function for the ground state of the
two-dimensional S=1/2 Heisenberg antiferromagnet in the valence bond basis. The
expansion coefficients are products of amplitudes h(x,y) for valence bonds
connecting spins separated by (x,y) lattice spacings. In contrast to previous
studies, in which a functional form for h(x,y) was assumed, we here optimize
all the amplitudes for lattices with up to 32*32 spins. We use two different
schemes for optimizing the amplitudes; a Newton/conjugate-gradient method and a
stochastic method which requires only the signs of the first derivatives of the
energy. The latter method performs significantly better. The energy for large
systems deviates by only approx. 0.06% from its exact value (calculated using
unbiased quantum Monte Carlo simulations). The spin correlations are also well
reproduced, falling approx. 2% below the exact ones at long distances. The
amplitudes h(r) for valence bonds of long length r decay as 1/r^3. We also
discuss some results for small frustrated lattices.Comment: v2: 8 pages, 5 figures, significantly expanded, new optimization
method, improved result
Microscopic Model for High-spin vs. Low-spin ground state in () magnetic clusters
Conventional superexchange rules predict ferromagnetic exchange interaction
between Ni(II) and M (M=Mo(V), W(V), Nb(IV)). Recent experiments show that in
some systems this superexchange is antiferromagnetic. To understand this
feature, in this paper we develop a microscopic model for Ni(II)-M systems and
solve it exactly using a valence bond approach. We identify the direct exchange
coupling, the splitting of the magnetic orbitals and the inter-orbital electron
repulsions, on the M site as the parameters which control the ground state spin
of various clusters of the Ni(II)-M system. We present quantum phase diagrams
which delineate the high-spin and low-spin ground states in the parameter
space. We fit the spin gap to a spin Hamiltonian and extract the effective
exchange constant within the experimentally observed range, for reasonable
parameter values. We also find a region in the parameter space where an
intermediate spin state is the ground state. These results indicate that the
spin spectrum of the microscopic model cannot be reproduced by a simple
Heisenberg exchange Hamiltonian.Comment: 8 pages including 7 figure
Properties of the strongly paired fermionic condensates
We study a gas of fermions undergoing a wide resonance s-wave BCS-BEC
crossover, in the BEC regime at zero temperature. We calculate the chemical
potential and the speed of sound of this Bose-condensed gas, as well as the
condensate depletion, in the low density approximation. We discuss how higher
order terms in the low density expansion can be constructed. We demonstrate
that the standard BCS-BEC gap equation is invalid in the BEC regime and is
inconsistent with the results obtained here. We indicate how our theory can in
principle be extended to nonzero temperature. The low density approximation we
employ breaks down in the intermediate BCS-BEC crossover region. Hence our
theory is unable to predict how the chemical potential and the speed of sound
evolve once the interactions are tuned towards the BCS regime. As a part of our
theory, we derive the well known result for the bosonic scattering length
diagrammatically and check that there are no bound states of two bosons.Comment: 16 pages, 15 figures. References added and typos correcte
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