42 research outputs found
Quantum critical phase with infinite projected entangled paired states
A classification of SU(2)-invariant Projected Entangled Paired States (PEPS)
on the square lattice, based on a unique site tensor, has been recently
introduced by Mambrini et al.~\cite{Mambrini2016}. It is not clear whether such
SU(2)-invariant PEPS can either i) exhibit long-range magnetic order (like in
the N\'eel phase) or ii) describe a genuine quantum critical point (QCP) or
quantum critical phase (QCPh) separating two ordered phases. Here, we identify
a specific family of SU(2)-invariant PEPS of the classification which provides
excellent variational energies for the frustrated Heisenberg model,
especially at , corresponding to the approximate location of the QCP
or QCPh separating the N\'eel phase from a dimerized phase. The PEPS are build
from virtual states belonging to the
SU(2)-representation, i.e. with "colors" of virtual
\hbox{spin-}. Using a full update infinite-PEPS approach directly
in the thermodynamic limit, based on the Corner Transfer Matrix renormalization
algorithm supplemented by a Conjugate Gradient optimization scheme, we provide
evidence of i) the absence of magnetic order and of ii) diverging correlation
lengths (i.e. showing no sign of saturation with increasing environment
dimension) in both the singlet and triplet channels, when the number of colors
. We argue that such a PEPS gives a qualitative description of the QCP
or QCPh of the model.Comment: 11 pages, 13 figures, supplementary material as a zip file in source
package, v4: minor adds to text + Table I and Appendix D (with 1 figure)
adde
Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry
We elaborate a simple classification scheme of all rank-5 SU(2)-spin
rotational symmetric tensors according to i) the on-site physical spin-,
(ii) the local Hilbert space of the four virtual (composite)
spins attached to each site and (iii) the irreducible representations of the
point group of the square lattice. We apply our scheme to draw a
complete list of all SU(2)-symmetric translationally and rotationally-invariant
Projected Entangled Pair States (PEPS) with bond dimension . All
known SU(2)-symmetric PEPS on the square lattice are recovered and simple
generalizations are provided in some cases. More generally, to each of our
symmetry class can be associated a -dimensional manifold of spin
liquids (potentially) preserving lattice symmetries and defined in terms of
independent tensors of a given bond dimension . In addition,
generic (low-dimensional) families of PEPS explicitly breaking either (i)
particular point-group lattice symmetries (lattice nematics) or (ii) time
reversal symmetry (chiral spin liquids) or (iii) SU(2)-spin rotation symmetry
down to (spin nematics or N\'eel antiferromagnets) can also be
constructed. We apply this framework to search for new topological chiral spin
liquids characterized by well-defined chiral edge modes, as revealed by their
entanglement spectrum. In particular, we show how the symmetrization of a
double-layer PEPS leads to a chiral topological state with a gapless edge
described by a SU(2) Wess-Zumino-Witten model.Comment: 29 pages, 9 figures, 3 Appendices, revised version. Supplementary
material with classification up to D=6 in the source file, and exact tensor
expressions available as a Supplementary Material in the PRB published
articl
Effective Quantum Dimer Model for the Kagome Heisenberg Antiferromagnet: Nearby Quantum Critical Point and Hidden Degeneracy
The low-energy singlet dynamics of the Quantum Heisenberg Antiferromagnet on
the Kagome lattice is described by a quantitative Quantum Dimer Model. Using
advanced numerical tools, the latter is shown to exhibit Valence Bond Crystal
order with a large 36-site unit cell and hidden degeneracy between even and odd
parities. Evidences are given that this groundstate lies in the vicinity of a
dimer liquid region separated by a Quantum Critical Point.
Implications regarding numerical analysis and experiments are discussed.Comment: 4 pages, 4 figures, deep revision of manuscript including new data,
revised figures, new Fig. 2(c) and new reference
Generalized Hardcore Dimer Models approach to low-energy Heisenberg frustrated antiferromagnets: general properties and application to the kagome antiferromagnet
We propose a general non-perturbative scheme that quantitatively maps the
low-energy sector of spin-1/2 frustrated Heisenberg antiferromagnets to
effective Generalized Quantum Dimer Models. We develop the formal lattice
independent frame and establish some important results on (i) the locality of
the generated Hamiltonians (ii) how full resummations can be performed in this
renormalization scheme. The method is then applied to the much debated kagome
antiferromagnet for which a fully resummed effective Hamiltonian - shown to
capture the essential properties and provide deep insights on the microscopic
model [D. Poilblanc, M. Mambrini and D. Schwandt, arXiv:0912.0724] - is
derived.Comment: 26 pages, 4 figures, EPAPS inlined, manuscript revised, corrected
minor typos (notably figure 2)
Engineering SU(2) invariant spin models to mimic quantum dimer physics on the square lattice
We consider the spin-1/2 hamiltonians proposed by Cano and Fendley [J. Cano
and P. Fendley, Phys. Rev. Lett. 105, 067205 (2010)] which were built to
promote the well-known Rokshar-Kivelson (RK) point of quantum dimer models to
spin-1/2 wavefunctions. We first show that these models, besides the exact
degeneracy of RK point, support gapless spinless excitations as well as a spin
gap in the thermodynamic limit, signatures of an unusual spin liquid. We then
extend the original construction to create a continuous family of SU(2)
invariant spin models that reproduces the phase diagram of the quantum dimer
model, and in particular show explicit evidences for existence of columnar and
staggered phases. The original models thus appear as multicritical points in an
extended phase diagram. Our results are based on the use of a combination of
numerical exact simulations and analytical mapping to effective generalized
quantum dimer models.Comment: 12 pages, 8 figure
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
Entanglement of quantum spin systems: a valence-bond approach
In order to quantify entanglement between two parts of a quantum system, one
of the most used estimator is the Von Neumann entropy. Unfortunately, computing
this quantity for large interacting quantum spin systems remains an open issue.
Faced with this difficulty, other estimators have been proposed to measure
entanglement efficiently, mostly by using simulations in the valence-bond
basis. We review the different proposals and try to clarify the connections
between their geometric definitions and proper observables. We illustrate this
analysis with new results of entanglement properties of spin 1 chains.Comment: Proceedings of StatPhys 24 satellite conference in Hanoi; submitted
for a special issue of Modern Physics Letters
Valence bond entanglement entropy of frustrated spin chains
We extend the definition of the recently introduced valence bond entanglement
entropy to arbitrary SU(2) wave functions of S=1/2 spin systems. Thanks to a
reformulation of this entanglement measure in terms of a projection, we are
able to compute it with various numerical techniques for frustrated spin
models. We provide extensive numerical data for the one-dimensional J1-J2 spin
chain where we are able to locate the quantum phase transition by using the
scaling of this entropy with the block size. We also systematically compare
with the scaling of the von Neumann entanglement entropy. We finally underline
that the valence-bond entropy definition does depend on the choice of
bipartition so that, for frustrated models, a "good" bipartition should be
chosen, for instance according to the Marshall sign.Comment: 10 pages, 6 figures; v2: published versio
Numerical Contractor Renormalization Method for Quantum Spin Models
We demonstrate the utility of the numerical Contractor Renormalization (CORE)
method for quantum spin systems by studying one and two dimensional model
cases. Our approach consists of two steps: (i) building an effective
Hamiltonian with longer ranged interactions using the CORE algorithm and (ii)
solving this new model numerically on finite clusters by exact diagonalization.
This approach, giving complementary information to analytical treatments of the
CORE Hamiltonian, can be used as a semi-quantitative numerical method. For
ladder type geometries, we explicitely check the accuracy of the effective
models by increasing the range of the effective interactions. In two dimensions
we consider the plaquette lattice and the kagome lattice as non-trivial test
cases for the numerical CORE method. On the plaquette lattice we have an
excellent description of the system in both the disordered and the ordered
phases, thereby showing that the CORE method is able to resolve quantum phase
transitions. On the kagome lattice we find that the previously proposed twofold
degenerate S=1/2 basis can account for a large number of phenomena of the spin
1/2 kagome system. For spin 3/2 however this basis does not seem to be
sufficient anymore. In general we are able to simulate system sizes which
correspond to an 8x8 lattice for the plaquette lattice or a 48-site kagome
lattice, which are beyond the possibilities of a standard exact diagonalization
approach.Comment: 15 page
Finite-temperature symmetric tensor network for spin-1/2 Heisenberg antiferromagnets on the square lattice
Within the tensor network framework, the (positive) thermal density operator
can be approximated by a double layer of infinite Projected Entangled Pair
Operator (iPEPO) coupled via ancilla degrees of freedom. To investigate the
thermal properties of the spin-1/2 Heisenberg model on the square lattice, we
introduce a family of fully spin- and lattice- symmetric on-site
tensors (of bond dimensions or ) and a plaquette-based
Trotter-Suzuki decomposition of the imaginary-time evolution operator. A
variational optimization is performed on the plaquettes, using a full (for
) or simple (for ) environment obtained from the single-site Corner
Transfer Matrix Renormalization Group fixed point. The method is benchmarked by
a comparison to quantum Monte Carlo in the thermodynamic limit. Although the
iPEPO spin correlation length starts to deviate from the exact exponential
growth for inverse-temperature , the behavior of various
observables turns out to be quite accurate once plotted w.r.t the inverse
correlation length. We also find that a direct variational energy
optimization provides results in full agreement with the
limit of finite-temperature data, hence validating the
imaginary-time evolution procedure. Extension of the method to frustrated
models is described and preliminary results are shown.Comment: 20 pages, 9 figure