11 research outputs found
Exact parent Hamiltonians of bosonic and fermionic Moore-Read states on lattices and local models
We introduce a family of strongly-correlated spin wave functions on arbitrary
spin-1/2 and spin-1 lattices in one and two dimensions. These states are
lattice analogues of Moore-Read states of particles at filling fraction 1/q,
which are non-Abelian Fractional Quantum Hall states in 2D. One parameter
enables us to perform an interpolation between the continuum limit, where the
states become continuum Moore-Read states of bosons (odd q) and fermions (even
q), and the lattice limit. We show numerical evidence that the topological
entanglement entropy stays the same along the interpolation for some of the
states we introduce in 2D, which suggests that the topological properties of
the lattice states are the same as in the continuum, while the 1D states are
critical states. We then derive exact parent Hamiltonians for these states on
lattices of arbitrary size. By deforming these parent Hamiltonians, we
construct local Hamiltonians that stabilize some of the states we introduce in
1D and in 2D.Comment: 15 pages, 7 figure
Quantum spin Hamiltonians for the SU(2)_k WZW model
We propose to use null vectors in conformal field theories to derive model
Hamiltonians of quantum spin chains and corresponding ground state wave
function(s). The approach is quite general, and we illustrate it by
constructing a family of Hamiltonians whose ground states are the chiral
correlators of the SU(2)_k WZW model for integer values of the level k. The
simplest example corresponds to k=1 and is essentially a nonuniform
generalization of the Haldane-Shastry model with long-range exchange couplings.
At level k=2, we analyze the model for N spin 1 fields. We find that the Renyi
entropy and the two-point spin correlator show, respectively, logarithmic
growth and algebraic decay. Furthermore, we use the null vectors to derive a
set of algebraic, linear equations relating spin correlators within each model.
At level k=1, these equations allow us to compute the two-point spin
correlators analytically for the finite chain uniform Haldane-Shastry model and
to obtain numerical results for the nonuniform case and for higher-point spin
correlators in a very simple way and without resorting to Monte Carlo
techniques.Comment: 38 pages, 6 figure
Entanglement of excited states in critical spin chians
Renyi and von Neumann entropies quantifying the amount of entanglement in
ground states of critical spin chains are known to satisfy a universal law
which is given by the Conformal Field Theory (CFT) describing their scaling
regime. This law can be generalized to excitations described by primary fields
in CFT, as was done in reference (Alcaraz et. al., Phys. Rev. Lett. 106, 201601
(2011)), of which this work is a completion. An alternative derivation is
presented, together with numerical verifications of our results in different
models belonging to the c=1,1/2 universality classes. Oscillations of the Renyi
entropy in excited states and descendant fields are also discussed.Comment: 23 pages, 13 figure
Simulation of gauge transformations on systems of ultracold atoms
We show that gauge transformations can be simulated on systems of ultracold
atoms. We discuss observables that are invariant under these gauge
transformations and compute them using a tensor network ansatz that escapes the
phase problem. We determine that the Mott-insulator-to-superfluid critical
point is monotonically shifted as the induced magnetic flux increases. This
result is stable against the inclusion of a small amount of entanglement in the
variational ansatz.Comment: 14 pages, 6 figure
Complete-Graph Tensor Network States: A New Fermionic Wave Function Ansatz for Molecules
We present a new class of tensor network states that are specifically
designed to capture the electron correlation of a molecule of arbitrary
structure. In this ansatz, the electronic wave function is represented by a
Complete-Graph Tensor Network (CGTN) ansatz which implements an efficient
reduction of the number of variational parameters by breaking down the
complexity of the high-dimensional coefficient tensor of a
full-configuration-interaction (FCI) wave function. We demonstrate that CGTN
states approximate ground states of molecules accurately by comparison of the
CGTN and FCI expansion coefficients. The CGTN parametrization is not biased
towards any reference configuration in contrast to many standard quantum
chemical methods. This feature allows one to obtain accurate relative energies
between CGTN states which is central to molecular physics and chemistry. We
discuss the implications for quantum chemistry and focus on the spin-state
problem. Our CGTN approach is applied to the energy splitting of states of
different spin for methylene and the strongly correlated ozone molecule at a
transition state structure. The parameters of the tensor network ansatz are
variationally optimized by means of a parallel-tempering Monte Carlo algorithm
Entanglement entropy of two disjoint blocks in XY chains
We study the Renyi entanglement entropies of two disjoint intervals in XY
chains. We exploit the exact solution of the model in terms of free Majorana
fermions and we show how to construct the reduced density matrix in the spin
variables by taking properly into account the Jordan-Wigner string between the
two blocks. From this we can evaluate any Renyi entropy of finite integer
order. We study in details critical XX and Ising chains and we show that the
asymptotic results for large blocks agree with recent conformal field theory
predictions if corrections to the scaling are included in the analysis
correctly. We also report results in the gapped phase and after a quantum
quench.Comment: 34 pages, 11 figure
Entanglement entropy of excited states
We study the entanglement entropy of a block of contiguous spins in excited states of spin chains. We consider the XY model in a transverse field and the XXZ Heisenberg spin chain. For the latter, we developed a numerical application of the algebraic Bethe ansatz. We find two main classes of states with logarithmic and extensive behavior in the dimension of the block, characterized by the properties of excitations of the state. This behavior can be related to the locality properties of the Hamiltonian having a given state as the ground state. We also provide several details of the finite size scaling