722 research outputs found
Perfect Sampling with Unitary Tensor Networks
Tensor network states are powerful variational ans\"atze for many-body ground
states of quantum lattice models. The use of Monte Carlo sampling techniques in
tensor network approaches significantly reduces the cost of tensor
contractions, potentially leading to a substantial increase in computational
efficiency. Previous proposals are based on a Markov chain Monte Carlo scheme
generated by locally updating configurations and, as such, must deal with
equilibration and autocorrelation times, which result in a reduction of
efficiency. Here we propose a perfect sampling scheme, with vanishing
equilibration and autocorrelation times, for unitary tensor networks -- namely
tensor networks based on efficiently contractible, unitary quantum circuits,
such as unitary versions of the matrix product state (MPS) and tree tensor
network (TTN), and the multi-scale entanglement renormalization ansatz (MERA).
Configurations are directly sampled according to their probabilities in the
wavefunction, without resorting to a Markov chain process. We also describe a
partial sampling scheme that can result in a dramatic (basis-dependent)
reduction of sampling error.Comment: 11 pages, 9 figures, renamed partial sampling to incomplete sampling
for clarity, extra references, plus a variety of minor change
The Algebraic Bethe Ansatz and Tensor Networks
We describe the Algebraic Bethe Ansatz for the spin-1/2 XXX and XXZ
Heisenberg chains with open and periodic boundary conditions in terms of tensor
networks. These Bethe eigenstates have the structure of Matrix Product States
with a conserved number of down-spins. The tensor network formulation suggestes
possible extensions of the Algebraic Bethe Ansatz to two dimensions
Efficient Tree Tensor Network States (TTNS) for Quantum Chemistry: Generalizations of the Density Matrix Renormalization Group Algorithm
We investigate tree tensor network states for quantum chemistry. Tree tensor
network states represent one of the simplest generalizations of matrix product
states and the density matrix renormalization group. While matrix product
states encode a one-dimensional entanglement structure, tree tensor network
states encode a tree entanglement structure, allowing for a more flexible
description of general molecules. We describe an optimal tree tensor network
state algorithm for quantum chemistry. We introduce the concept of
half-renormalization which greatly improves the efficiency of the calculations.
Using our efficient formulation we demonstrate the strengths and weaknesses of
tree tensor network states versus matrix product states. We carry out benchmark
calculations both on tree systems (hydrogen trees and \pi-conjugated
dendrimers) as well as non-tree molecules (hydrogen chains, nitrogen dimer, and
chromium dimer). In general, tree tensor network states require much fewer
renormalized states to achieve the same accuracy as matrix product states. In
non-tree molecules, whether this translates into a computational savings is
system dependent, due to the higher prefactor and computational scaling
associated with tree algorithms. In tree like molecules, tree network states
are easily superior to matrix product states. As an ilustration, our largest
dendrimer calculation with tree tensor network states correlates 110 electrons
in 110 active orbitals.Comment: 15 pages, 19 figure
Bell correlations at finite temperature
We show that spin systems with infinite-range interactions can violate at
thermal equilibrium a multipartite Bell inequality, up to a finite critical
temperature . Our framework can be applied to a wide class of spin systems
and Bell inequalities, to study whether nonlocality occurs naturally in quantum
many-body systems close to the ground state. Moreover, we also show that the
low-energy spectrum of the Bell operator associated to such systems can be well
approximated by the one of a quantum harmonic oscillator, and that
spin-squeezed states are optimal in displaying Bell correlations for such Bell
inequalities.Comment: 9 pages (7 + Appendix), 2 figures. Version accepted for publication
in Quantu
Block product density matrix embedding theory for strongly correlated spin systems
Density matrix embedding theory (DMET) is a relatively new technique for the
calculation of strongly correlated systems. Recently, block product DMET
(BPDMET) was introduced for the study of spin systems such as the
antiferromagnetic model on the square lattice. In this paper, we
extend the variational Ansatz of BPDMET using spin-state optimization, yielding
improved results. We apply the same techniques to the Kitaev-Heisenberg model
on the honeycomb lattice, comparing the results when using several types of
clusters. Energy profiles and correlation functions are investigated. A
diagonalization in the tangent space of the variational approach yields
information on the excited states and the corresponding spectral functions.Comment: 12 pages, 12 figure
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