"Spin-phonon interactions on the kagome lattice: Dirac spin liquid versus valence-bond solids"
Francesco Ferrari, Federico Becca, Roser Valenti
Phys. Rev. B 109, 165133 (2024)
We investigate the impact of the spin-phonon coupling on the S=1/2 Heisenberg
model on the kagome lattice. For the pure spin model, there is increasing
evidence that the low-energy properties can be correctly described by a Dirac
spin liquid, in which spinons with a conical dispersion are coupled to emergent
gauge fields. Within this scenario, the ground-state wave function is well
approximated by a Gutzwiller-projected fermionic state [Y. Ran, M. Hermele,
P.A. Lee, and X.-G. Wen, Phys. Rev. Lett. 98, 117205 (2007)]. However, the
existence of U(1) gauge fields may naturally lead to instabilities when small
perturbations are included. Since phonons are ubiquitous in real materials,
they may play a relevant role in the determination of the actual physical
properties of the kagome antiferromagnet. We perform a step forward in this
direction, including phonon degrees of freedom (at the quantum level) and
applying a variational approach based upon Gutzwiller-projected fermionic
Ans\"atze. Our results suggest that the Dirac spin liquid is stable for small
spin-phonon couplings, while valence-bond solids are obtained at large
couplings. Even though different distortions can be induced by the spin-phonon
interaction, the general aspect is that the energy is lowered by maximizing the
density of perfect hexagons in the dimerization pattern.
"A simple linear algebra identity to optimize Large-Scale Neural Network Quantum States"
Riccardo Rende, Luciano Loris Viteritti, Lorenzo Bardone, Federico Becca, Sebastian Goldt
Communications Physics 7, 260 (2024)
Neural-network architectures have been increasingly used to represent quantum
many-body wave functions. These networks require a large number of variational
parameters and are challenging to optimize using traditional methods, as
gradient descent. Stochastic Reconfiguration (SR) has been effective with a
limited number of parameters, but becomes impractical beyond a few thousand
parameters. Here, we leverage a simple linear algebra identity to show that SR
can be employed even in the deep learning scenario. We demonstrate the
effectiveness of our method by optimizing a Deep Transformer architecture with
$3 \times 10^5$ parameters, achieving state-of-the-art ground-state energy in
the $J_1$-$J_2$ Heisenberg model at $J_2/J_1=0.5$ on the $10\times10$ square
lattice, a challenging benchmark in highly-frustrated magnetism. This work
marks a significant step forward in the scalability and efficiency of SR for
Neural-Network Quantum States, making them a promising method to investigate
unknown quantum phases of matter, where other methods struggle.
"Variational Benchmarks for Quantum Many-Body Problems"
Dian Wu, Riccardo Rossi, Filippo Vicentini, Nikita Astrakhantsev, Federico Becca et al.
Science 386, 296-301 (2024)
The continued development of computational approaches to many-body
ground-state problems in physics and chemistry calls for a consistent way to
assess its overall progress. In this work, we introduce a metric of variational
accuracy, the V-score, obtained from the variational energy and its variance.
We provide an extensive curated dataset of variational calculations of
many-body quantum systems, identifying cases where state-of-the-art numerical
approaches show limited accuracy, and future algorithms or computational
platforms, such as quantum computing, could provide improved accuracy. The
V-score can be used as a metric to assess the progress of quantum variational
methods toward a quantum advantage for ground-state problems, especially in
regimes where classical verifiability is impossible.
"Policy-guided Monte Carlo on general state spaces: Application to glass-forming mixtures"
Leonardo Galliano, Riccardo Rende, Daniele Coslovich
J. Chem. Phys. 161, 064503 (2024)
Policy-guided Monte Carlo is an adaptive method to simulate classical
interacting systems. It adjusts the proposal distribution of the
Metropolis-Hastings algorithm to maximize the sampling efficiency, using a
formalism inspired by reinforcement learning. In this work, we first extend the
policy-guided method to deal with a general state space, comprising, for
instance, both discrete and continuous degrees of freedom, and then apply it to
a few paradigmatic models of glass-forming mixtures. We assess the efficiency
of a set of physically inspired moves whose proposal distributions are
optimized through on-policy learning. Compared to conventional Monte Carlo
methods, the optimized proposals are two orders of magnitude faster for an
additive soft sphere mixture but yield a much more limited speed-up for the
well-studied Kob-Andersen model. We discuss the current limitations of the
method and suggest possible ways to improve it.
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We study the quasiparticle properties of a dipolar impurity immersed in a
two-dimensional dipolar bath. We use the ab-initio Diffusion Monte Carlo
technique to determine the polaron energy, effective mass and quasiparticle
residue. We find that both the polaron energy and quasiparticle residue follow
a universal behaviour with respect to the polarization angle when properly
scaled in terms of the scattering length. This trend is maintained over a wide
range of values of the gas parameter, even in the highly correlated regime.
Instead, the effective mass shows growing anisotropy as the tilting angle is
increased, which is induced, mainly, by the anisotropy of the impurity-boson
dipole-dipole interaction. Surprisingly, the effective mass is larger in the
direction of minimum inter-particle repulsion. Finally, we use our Monte Carlo
results to check the accuracy of perturbative approaches and determine their
range of validity in terms of the gas parameter.
"Modified mean field ansatz for charged polarons in a Bose-Einstein condensate"
Ubaldo Cavazos Olivas, Luis A. Peña Ardila, Krzysztof Jachymski
Phys. Rev. A 110, L011301 (2024)
Ionic Bose polarons are quantum entities emerging from the interaction
between an ion and a Bose-Einstein condensate (BEC), featuring long-ranged
interactions that can compete with the gas healing length. This can result in
strong interparticle correlations and enhancement of gas density around the
ion. One possible approach to describe this complex system with high accuracy
relies on numerical treatment such as the quantum Monte Carlo (QMC) techniques.
Nevertheless, it is computationally very expensive and does not easily allow to
study the system dynamics. On the other hand, a mean-field based variational
ansatz in the co-moving frame can capture a sizeable change in the gas density.
We apply it to the case of regularized ion-atom potential and find that it
qualitatively reproduces the full numerical results. In addition, we also study
the system of two pinned ions, focusing on their effective interaction induced
by the bath. This approach seems to be promising for studying transport and
nonequilibrium dynamics of charged (bi)polarons in condensed media.
"Piercing the Dirac spin liquid: From a single monopole to chiral states"
Sasank Budaraju, Yasir Iqbal, Federico Becca, Didier Poilblanc
Phys. Rev. B 108, L201116 (2023)
The parton approach for quantum spin liquids gives a transparent description
of low-energy elementary excitations, e.g., spinons and emergent gauge-field
fluctuations. The latter ones are directly coupled to the hopping/pairing of
spinons. By using the fermionic representation of the $U(1)$ Dirac state on the
kagome lattice and variational Monte Carlo techniques to include the Gutzwiller
projection, we analyse the effect of modifying the gauge fields in the spinon
kinematics. In particular, we construct low-energy monopole excitations, which
are shown to be gapless in the thermodynamic limit. States with a finite number
of monopoles or with a finite density of them are also considered, with
different patterns of the gauge fluxes. We show that these chiral states are
not stabilized in the Heisenberg model with nearest-neighbor super-exchange
couplings, and the Dirac state corresponds to the lowest-energy Ansatz within
this family of variational wave functions. Our results support the idea that
spinons with a gapless conical spectrum coexist with gapless monopole
excitations, even for the spin-1/2 case.
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The Transformer architecture has become the state-of-art model for natural
language processing tasks and, more recently, also for computer vision tasks,
thus defining the Vision Transformer (ViT) architecture. The key feature is the
ability to describe long-range correlations among the elements of the input
sequences, through the so-called self-attention mechanism. Here, we propose an
adaptation of the ViT architecture with complex parameters to define a new
class of variational neural-network states for quantum many-body systems, the
ViT wave function. We apply this idea to the one-dimensional $J_1$-$J_2$
Heisenberg model, demonstrating that a relatively simple parametrization gets
excellent results for both gapped and gapless phases. In this case, excellent
accuracies are obtained by a relatively shallow architecture, with a single
layer of self-attention, thus largely simplifying the original architecture.
Still, the optimization of a deeper structure is possible and can be used for
more challenging models, most notably highly-frustrated systems in two
dimensions. The success of the ViT wave function relies on mixing both local
and global operations, thus enabling the study of large systems with high
accuracy.
"Static and dynamical signatures of Dzyaloshinskii-Moriya interactions in the Heisenberg model on the kagome lattice"
Francesco Ferrari, Sen Niu, Juraj Hasik, Yasir Iqbal, Didier Poilblanc et al.
SciPost Phys. 14, 139 (2023)
Motivated by recent experiments on Cs$_2$Cu$_3$SnF$_{12}$ and
YCu$_{3}$(OH)$_{6}$Cl$_{3}$, we consider the ${S=1/2}$ Heisenberg model on the
kagome lattice with nearest-neighbor super-exchange $J$ and (out-of-plane)
Dzyaloshinskii-Moriya interaction $J_D$, which favors (in-plane) ${\bf
Q}=(0,0)$ magnetic order. By using both variational Monte Carlo (based upon
Gutzwiller-projected fermionic wave functions) and tensor-network approaches
(built from infinite projected-entangled pair/simplex states), we show that the
ground state develops a finite magnetization for $J_D/J \gtrsim 0.03 - 0.04$,
while the gapless spin liquid remains stable for smaller values of the
Dzyaloshinskii-Moriya interaction. The relatively small value of $J_D/J$ for
which magnetic order sets in is particularly relevant for the interpretation of
low-temperature behaviors of kagome antiferromagnets, including
ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$. In addition, we assess the spin dynamical
structure factors and the corresponding low-energy spectrum, by using the
variational Monte Carlo technique. The existence of a continuum of excitations
above the magnon modes is reported within the magnetically ordered phase,
similarly to what has been detected by inelastic neutron scattering on
Cs$_{2}$Cu$_{3}$SnF$_{12}$.
"A Jastrow wave function for the spin-1 Heisenberg chain: the string order revealed by the mapping to the classical Coulomb gas"
Davide Piccioni, Christian Apostoli, Federico Becca, Guglielmo Mazzola, Alberto Parola et al.
Phys. Rev. B 108, 104417 (2023)
We show that a two-body Jastrow wave function is able to capture the
ground-state properties of the $S=1$ antiferromagnetic Heisenberg chain with
the single-ion anisotropy term, in both the topological and trivial phases.
Here, the optimized Jastrow pseudo potential assumes a very simple form in
Fourier space, i.e., $v_{q} \approx 1/q^2$, which is able to give rise to a
finite string-order parameter in the topological regime. The results are
analysed by using an exact mapping from the quantum expectation values over the
variational state to the classical partition function of the one-dimensional
Coulomb gas of particles with charge $q=\pm 1$. Here, two phases are present at
low temperatures: the first one is a diluted gas of dipoles (bound states of
particles with opposite charges), which are randomly oriented (describing the
trivial phase); the other one is a dense liquid of dipoles, which are aligned
thanks to the residual dipole-dipole interactions (describing the topological
phase, with the finite string order being related to the dipole alignment). Our
results provide an insightful interpretation of the ground-state nature of the
spin-1 antiferromagnetic Heisenberg model.
"Non-equilibrium dynamics of dipolar polarons"
Artem G. Volosniev, Giacomo Bighin, Luis Santos, Luis A. Peña Ardila
SciPost Phys. 15, 232 (2023)
We study the out-of-equilibrium quantum dynamics of dipolar polarons, i.e.,
impurities immersed in a dipolar Bose-Einstein condensate, after a quench of
the impurity-boson interaction. We show that the dipolar nature of the
condensate and of the impurity results in anisotropic relaxation dynamics, in
particular, anisotropic dressing of the polaron. More relevantly for cold-atom
setups, quench dynamics is strongly affected by the interplay between dipolar
anisotropy and trap geometry. Our findings pave the way for simulating
impurities in anisotropic media utilizing experiments with dipolar mixtures.
"Catalyzation of supersolidity in binary dipolar condensates"
D. Scheiermann, L. A. Peña Ardila, T. Bland, R. N. Bisset, L. Santos
Phys. Rev. A 107, L021302 (2023)
Breakthrough experiments have newly explored the fascinating physics of
dipolar quantum droplets and supersolids. The recent realization of dipolar
mixtures opens further intriguing possibilities. We show that under rather
general conditions, the presence of a second component catalyzes droplet
nucleation and supersolidity in an otherwise unmodulated condensate. Droplet
catalyzation in miscible mixtures, which may occur even for a surprisingly
small impurity doping, results from a local roton instability triggered by the
doping-dependent modification of the effective dipolar strength. The
catalyzation mechanism may trigger the formation of a two-fluid supersolid,
characterized by a generally different superfluid fraction of each component,
which opens intriguing possibilities for the future study of spin physics in
dipolar supersolids.
"Many-body bound states and induced interactions of charged impurities in a bosonic bath"
G. E. Astrakharchik, L. A. Peña Ardila, K. Jachymski, A. Negretti
Nature communications 14, 1647 (2023)
Induced interactions and bound states of charge carriers immersed in a
quantum medium are crucial for the investigation of quantum transport.
Ultracold atom-ion systems can provide a convenient platform for studying this
problem. Here, we investigate the static properties of one and two ionic
impurities in a bosonic bath using quantum Monte Carlo methods. We identify
three bipolaronic regimes depending on the strength of the atom-ion potential
and the number of its two-body bound states: a perturbative regime resembling
the situation of a pair of neutral impurities, a non-perturbative regime that
loses the quasi-particle character of the former, and a many-body bound state
regime that can arise only in the presence of a bound state in the two-body
potential. We further reveal strong bath-induced interactions between the two
ionic polarons. Our findings show that numerical simulations are indispensable
for describing highly correlated impurity models.
"Probing the graphene/substrate interaction by electron tunneling decay"
Virginia Carnevali, Alessandro Sala, Pietro Biasin, Mirco Panighel, Giovanni Comelli et al.
Carbon (2023)
The electronic properties of graphene can be modified by the local
interaction with a selected metal substrate. To probe this effect, Scanning
Tunneling Microscopy is widely employed, particularly by means of local
measurement via lock-in amplifier of the differential conductance and of the
field emission resonance. In this article we propose an alternative, reliable
method of probing the graphene/substrate interaction that is readily available
to any STM apparatus. By testing the tunneling current as function of the
tip/sample distance on nanostructured graphene on Ni(100), we demonstrate that
I(z) spectroscopy can be quantitatively compared with Density Functional Theory
calculations and can be used to assess the nature of the interaction between
graphene and substrate. This method can expand the capabilities of standard STM
systems to study graphene/substrate complexes, complementing standard
topographic probing with spectroscopic information.
