Eduardo Gonzalez Lazo, Markus Heyl, Marcello Dalmonte, Adriano Angelone
SciPost Phys. 11, 076 (2021) ·
published 13 October 2021
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We study the phase diagram and critical properties of quantum Ising chains
with long-range ferromagnetic interactions decaying in a power-law fashion with
exponent $\alpha$, in regimes of direct interest for current trapped ion
experiments. Using large-scale path integral Monte Carlo simulations, we
investigate both the ground-state and the nonzero-temperature regimes. We
identify the phase boundary of the ferromagnetic phase and obtain accurate
estimates for the ferromagnetic-paramagnetic transition temperatures. We
further determine the critical exponents of the respective transitions. Our
results are in agreement with existing predictions for interaction exponents
$\alpha > 1$ up to small deviations in some critical exponents. We also address
the elusive regime $\alpha < 1$, where we find that the universality class of
both the ground-state and nonzero-temperature transition is consistent with the
mean-field limit at $\alpha = 0$. Our work not only contributes to the
understanding of the equilibrium properties of long-range interacting quantum
Ising models, but can also be important for addressing fundamental dynamical
aspects, such as issues concerning the open question of thermalization in such
models.
SciPost Phys. 4, 013 (2018) ·
published 28 February 2018
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The efficient representation of quantum many-body states with classical
resources is a key challenge in quantum many-body theory. In this work we
analytically construct classical networks for the description of the quantum
dynamics in transverse-field Ising models that can be solved efficiently using
Monte Carlo techniques. Our perturbative construction encodes time-evolved
quantum states of spin-1/2 systems in a network of classical spins with local
couplings and can be directly generalized to other spin systems and higher
spins. Using this construction we compute the transient dynamics in one, two,
and three dimensions including local observables, entanglement production, and
Loschmidt amplitudes using Monte Carlo algorithms and demonstrate the accuracy
of this approach by comparisons to exact results. We include a mapping to
equivalent artificial neural networks, which were recently introduced to
provide a universal structure for classical network wave functions.
