arXiv subjects

Lode Pollet

Publications and source records attributed to Lode Pollet.

At least 55 records · Page 3Linked to original sources

arXiv2021

Revealing the Phase Diagram of Kitaev Materials by Machine Learning: Cooperation and Competition between Spin Liquids

Kitaev materials are promising materials for hosting quantum spin liquids and investigating the interplay of topological and symmetry-breaking phases. We use an unsupervised and interpretable machine-learning method, the tensorial-kernel support vector machine, to study the honeycomb Kitaev-$Γ$ model in a magnetic field. Our machine learns the global classical phase diagram and the associated analytical order parameters, including several distinct spin liquids, two exotic $S_3$ magnets, and two modulated $S_3 \times Z_3$ magnets. We find that the extension of Kitaev spin liquids and a field-induced suppression of magnetic order already occur in the large-$S$ limit, implying that critical parts of the physics of Kitaev materials can be understood at the classical level. Moreover, the two $S_3 \times Z_3$ orders are induced by competition between Kitaev and $Γ$ spin liquids and feature a different type of spin-lattice entangled modulation, which requires a matrix description instead of scalar phase factors. Our work provides a direct instance of a machine detecting new phases and paves the way towards the development of automated tools to explore unsolved problems in many-body physics.

cond-mat.str-el↗

arXiv2020

The view of TK-SVM on the phase hierarchy in the classical kagome Heisenberg antiferromagnet

We illustrate how the tensorial kernel support vector machine (TK-SVM) can probe the hidden multipolar orders and emergent local constraint in the classical kagome Heisenberg antiferromagnet. We show that TK-SVM learns the finite-temperature phase diagram in an unsupervised way. Moreover, in virtue of its strong interpretability, it identifies the tensorial quadrupolar and octupolar orders, which define a biaxial $D_{3h}$ spin nematic, and the local constraint that underlies the selection of coplanar states. We then discuss the disorder hierarchy of the phases, which can be inferred from both the analytical order parameters and a SVM bias parameter. For completeness we mention that the machine also picks up the leading $\sqrt{3} \times \sqrt{3}$ correlations in the dipolar channel at very low temperature, which are however weak compared to the quadrupolar and octupolar orders. Our work shows how TK-SVM can facilitate and speed up the analysis of classical frustrated magnets.

cond-mat.str-el↗

arXiv2020

Z2 parton phases in the mixed-dimensional $t-J_z$ model

We study the interplay of spin- and charge degrees of freedom in a doped Ising antiferromagnet, where the motion of charges is restricted to one dimension. The phase diagram of this mixed-dimensional $t - J_z$ model can be understood in terms of spin-less chargons coupled to a Z2 lattice gauge field. The antiferromagnetic couplings give rise to interactions between Z2 electric field lines which, in turn, lead to a robust stripe phase at low temperatures. At higher temperatures, a confined meson-gas phase is found for low doping whereas at higher doping values, a robust deconfined chargon-gas phase is seen which features hidden antiferromagnetic order. We confirm these phases in quantum Monte Carlo simulations. Our model can be implemented and its phases detected with existing technology in ultracold atom experiments. The critical temperature for stripe formation with a sufficiently high hole concentration is around the spin-exchange energy $J_z$, i.e., well within reach of current experiments.

cond-mat.str-el↗

arXiv2019

Identification of hidden order and emergent constraints in frustrated magnets using tensorial kernel methods

Machine-learning techniques have proved successful in identifying ordered phases of matter. However, it remains an open question how far they can contribute to the understanding of phases without broken symmetry, such as spin liquids. Here we demonstrate how a machine learning approach can automatically learn the intricate phase diagram of a classical frustrated spin model. The method we employ is a support vector machine equipped with a tensorial kernel and a spectral graph analysis which admits its applicability in an effectively unsupervised context. Thanks to the interpretability of the machine we are able to infer, in closed form, both order parameter tensors of phases with broken symmetry, and the local constraints which signal an emergent gauge structure, and so characterize classical spin liquids. The method is applied to the classical XXZ model on the pyrochlore lattice where it distinguishes---among others---between a hidden biaxial spin nematic phase and several different classical spin liquids. The results are in full agreement with a previous analysis by Taillefumier \emph{et al.} [Phys. Rev. X 7, 041057 (2017)], but go further by providing a systematic hierarchy between disordered regimes, and establishing the physical relevance of the susceptibilities associated with the local constraints. Our work paves the way for the search of new orders and spin liquids in generic frustrated magnets.

cond-mat.str-el↗

arXiv2019

Constrained Random Phase Approximation of the effective Coulomb interaction in lattice models of twisted bilayer graphene

Recent experiments on twisted bilayer graphene show the urgent need for establishing a low-energy lattice model for the system. We use the constrained random phase approximation to study the interaction parameters of such models taking into account screening from the moire bands left outside the model space. Based on an atomic-scale tight-binding model, we develop a numerically tractable approximation to the polarization function and study its behavior for different twist angles. We find that the polarization has three different momentum regimes. For small momenta, the polarization is quadratic, leading to a linear dielectric function expected for a two-dimensional dielectric material. For large momenta, the polarization becomes independent of the twist angle and approaches that of uncoupled graphene layers. In the intermediate momentum regime, the dependence on the twist-angle is strong. Close to the largest magic angle the dielectric function peaks at a momentum of $~1/(4 \: nm)$ attaining values of 25, meaning very strong screening at intermediate distances. We also calculate the effective screened Coulomb interaction in real space and give estimates for the on-site and extended interaction terms for the recently developed hexagonal-lattice model. For free-standing TBG the effective interaction decays slower than $1/r$ at intermediate distances $r$, while it remains essentially unscreened at large enough $r$.

cond-mat.str-el↗

arXiv2019

Learning multiple order parameters with interpretable machines

Machine-learning techniques are evolving into a subsidiary tool for studying phase transitions in many-body systems. However, most studies are tied to situations involving only one phase transition and one order parameter. Systems that accommodate multiple phases of coexisting and competing orders, which are common in condensed matter physics, remain largely unexplored from a machine-learning perspective. In this paper, we investigate multiclassification of phases using support vector machines (SVMs) and apply a recently introduced kernel method for detecting hidden spin and orbital orders to learn multiple phases and their analytical order parameters. Our focus is on multipolar orders and their tensorial order parameters whose identification is difficult with traditional methods. The importance of interpretability is emphasized for physical applications of multiclassification. Furthermore, we discuss an intrinsic parameter of SVM, the bias, which allows for a special interpretation in the classification of phases, and its utility in diagnosing the existence of phase transitions. We show that it can be exploited as an efficient way to explore the topology of unknown phase diagrams where the supervision is entirely delegated to the machine.

cond-mat.stat-mech↗

arXiv2019

Probing hidden spin order with interpretable machine learning

The search of unconventional magnetic and nonmagnetic states is a major topic in the study of frustrated magnetism. Canonical examples of those states include various spin liquids and spin nematics. However, discerning their existence and the correct characterization is usually challenging. Here we introduce a machine-learning protocol that can identify general nematic order and their order parameter from seemingly featureless spin configurations, thus providing comprehensive insight on the presence or absence of hidden orders. We demonstrate the capabilities of our method by extracting the analytical form of nematic order parameter tensors up to rank 6. This may prove useful in the search for novel spin states and for ruling out spurious spin liquid candidates.

cond-mat.stat-mech↗

arXiv2018

Polaron mobility in the "beyond quasiparticles" regime

In a number of physical situations, from polarons to Dirac liquids and to non-Fermi liquids, one encounters the "beyond quasiparticles" regime, in which the inelastic scattering rate exceeds the thermal energy of quasiparticles. Transport in this regime cannot be described by the kinetic equation. We employ the Diagrammatic Monte Carlo method to study the mobility of a Fröhlich polaron in this regime and discover a number of non-perturbative effects: a strong violation of the Mott-Ioffe-Regel criterion at intermediate and strong couplings, a mobility minimum at $T \sim Ω$ in the strong-coupling limit ($Ω$ is the optical mode frequency), a substantial delay in the onset of an exponential dependence of the mobility for $T<Ω$ at intermediate coupling, and complete smearing of the Drude peak at strong coupling. These effects should be taken into account when interpreting mobility data in materials with strong electron-phonon coupling.

cond-mat.str-el↗

arXiv2018

Strong randomness criticality in the scratched-XY model

We study the finite-temperature superfluid transition in a modified two-dimensional (2D) XY model with power-law distributed "scratch"-like bond disorder. As its exponent decreases, the disorder grows stronger and the mechanism driving the superfluid transition changes from conventional vortex-pair unbinding to a strong randomness criticality (termed scratched-XY criticality) characterized by a non-universal jump of the superfluid stiffness. The existence of the scratched-XY criticality at finite temperature and its description by an asymptotically exact semi-renormalization group theory, previously developed for the superfluid-insulator transition in one-dimensional disordered quantum systems, is numerically proven by designing a model with minimal finite size effects. Possible experimental implementations are discussed.

cond-mat.stat-mech↗

arXiv2018

Stochastic lists: Sampling multi-variable functions with population methods

We introduce the method of stochastic lists to deal with a multi-variable positive function, defined by a self-consistent equation, typical for certain problems in physics and mathematics. In this approach, the function's properties are represented statistically by lists containing a large collection of sets of coordinates (or "walkers") that are distributed according to the function's value. The coordinates are generated stochastically by the Metropolis algorithm and may replace older entries according to some protocol. While stochastic lists offer a solution to the impossibility of efficiently computing and storing multi-variable functions without a systematic bias, extrapolation in the inverse of the number of walkers is usually difficult, even though in practice very good results are found already for short lists. This situation is reminiscent of diffusion Monte Carlo, and is hence generic for all population-based methods. We illustrate the method by computing the lowest-order vertex corrections in Hedin's scheme for the Fröhlich polaron and the ground state energy and wavefunction of the Heisenberg model in two dimensions.

cond-mat.stat-mech↗

arXiv2018

Self-energy functional theory with symmetry breaking for disordered lattice bosons

We extend the self-energy functional theory (SFT) to the case of interacting lattice bosons in the presence of symmetry breaking and quenched disorder. The self-energy functional we derive depends only on the self-energies of the disorder-averaged propagators, allowing for the construction of general non-perturbative approximations. Using a simple single-site reference system with only three variational parameters, we are able to reproduce numerically exact quantum Monte Carlo (QMC) results on local observables of the Bose-Hubbard model with box disorder with high accuracy. At strong interactions, the phase boundaries are reproduced qualitatively but shifted with respect to the ones observed with QMC due to the extremely low condensate fraction in the superfluid phase. Deep in the strongly-disordered weakly-interacting regime, the simple reference system employed is insufficient and no stationary solutions can be found within its restricted variational subspace. By systematically analyzing thermodynamical observables and the spectral function, we find that the strongly-interacting Bose glass is characterized by different regimes, depending on which local occupations are activated as a function of the disorder strength. We find that the particles delocalize into isolated superfluid lakes over a strongly localized background around maximally-occupied sites whenever these sites are particularly rare. Our results indicate that the transition from the Bose glass to the superfluid phase around unit filling at strong interactions is driven by the percolation of superfluid lakes which form around doubly occupied sites.

cond-mat.quant-gas↗

arXiv2018

Quasi-one-dimensional Hall physics in the Harper-Hofstadter-Mott model

We study the ground-state phase diagram of the strongly interacting Harper-Hofstadter-Mott model at quarter flux on a quasi-one-dimensional lattice consisting of a single magnetic flux quantum in $y$-direction. In addition to superfluid phases with various density patterns, the ground-state phase diagram features quasi-one-dimensional analogues of fractional quantum Hall phases at fillings $ν=1/2$ and $3/2$, where the latter is only found thanks to the hopping anisotropy and the quasi-one-dimensional geometry. At integer fillings - where in the full two-dimensional system the ground-state is expected to be gapless - we observe gapped non-degenerate ground-states: At $ν=1$ it shows an odd 'fermionic' Hall conductance, while the Hall response at $ν=2$ consists of the transverse transport of a single particle-hole pair, resulting in a net zero Hall conductance. The results are obtained by exact diagonalization and in the reciprocal mean-field approximation.

cond-mat.quant-gas↗

arXiv2018

Direct observation of incommensurate magnetism in Hubbard chains

The interplay between magnetism and doping is at the origin of exotic strongly correlated electronic phases and can lead to novel forms of magnetic ordering. One example is the emergence of incommensurate spin-density waves with a wave vector that does not match the reciprocal lattice. In one dimension this effect is a hallmark of Luttinger liquid theory, which also describes the low energy physics of the Hubbard model. Here we use a quantum simulator based on ultracold fermions in an optical lattice to directly observe such incommensurate spin correlations in doped and spin-imbalanced Hubbard chains using fully spin and density resolved quantum gas microscopy. Doping is found to induce a linear change of the spin-density wave vector in excellent agreement with Luttinger theory predictions. For non-zero polarization we observe a decrease of the wave vector with magnetization as expected from the Heisenberg model in a magnetic field. We trace the microscopic origin of these incommensurate correlations to holes, doublons and excess spins which act as delocalized domain walls for the antiferromagnetic order. Finally, when inducing interchain coupling we observe fundamentally different spin correlations around doublons indicating the formation of a magnetic polaron.

cond-mat.quant-gas↗

arXiv2018

Full and unbiased solution of the Dyson-Schwinger equation in the functional integro-differential representation

We provide a full and unbiased solution to the Dyson-Schwinger equation illustrated for $ϕ^4$ theory in 2D. It is based on an exact treatment of the functional derivative $\partial Γ/ \partial G$ of the 4-point vertex function $Γ$ with respect to the 2-point correlation function $G$ within the framework of the homotopy analysis method (HAM) and the Monte Carlo sampling of rooted tree diagrams. The resulting series solution in deformations can be considered as an asymptotic series around $G=0$ in a HAM control parameter $c_0G$, or even a convergent one up to the phase transition point if shifts in $G$ can be performed (such as by summing up all ladder diagrams). These considerations are equally applicable to fermionic quantum field theories and offer a fresh approach to solving integro-differential equations.

cond-mat.stat-mech↗

arXiv2018

Lecture notes on Diagrammatic Monte Carlo for the Fröhlich polaron

These notes are intended as a detailed discussion on how to implement the diagrammatic Monte Carlo method for a physical system which is technically simple and where it works extremely well, namely the Fröhlich polaron problem. Sampling schemes for the Green function as well as the self-energy in the bare and skeleton (bold) expansion are disclosed in full detail. We discuss the Monte Carlo updates, possible implementations in terms of common data structures, as well as techniques on how to perform the Fourier transforms for functions with discontinuities. Control over the variety of parameters, especially in the bold scheme, is demonstrated. Sample codes are made available online along with extensive documentation. Towards the end, we discuss various extensions of the method and their applications. After working through these notes, the reader will be well equipped to explore the richness of the diagrammatic Monte Carlo method for quantum many-body systems.

cond-mat.stat-mech↗

arXiv2018

Generic first-order phase transitions between isotropic and orientational phases with polyhedral symmetries

Polyhedral nematics are examples of exotic orientational phases that possess a complex internal symmetry, representing highly non-trivial ways of rotational symmetry breaking, and are subject to current experimental pursuits in colloidal and molecular systems. The classification of these phases has been known for a long time, however, their transitions to the disordered isotropic liquid phase remain largely unexplored, except for a few symmetries. In this work, we utilize a recently introduced non-Abelian gauge theory to explore the nature of the underlying nematic-isotropic transition for all three-dimensional polyhedral nematics. The gauge theory can readily be applied to nematic phases with an arbitrary point-group symmetry, including those where traditional Landau methods and the associated lattice models may become too involved to implement owing to a prohibitive order-parameter tensor of high rank or (the absence of) mirror symmetries. By means of exhaustive Monte Carlo simulations, we find that the nematic-isotropic transition is generically first-order for all polyhedral symmetries. Moreover, we show that this universal result is fully consistent with our expectation from a renormalization group approach, as well as with other lattice models for symmetries already studied in the literature. We argue that extreme fine tuning is required to promote those transitions to second order ones. We also comment on the nature of phase transitions breaking the $O(3)$ symmetry in general cases.

cond-mat.stat-mech↗

arXiv2017

Spin and Charge Resolved Quantum Gas Microscopy of Antiferromagnetic Order in Hubbard Chains

The repulsive Hubbard Hamiltonian is one of the foundational models describing strongly correlated electrons and is believed to capture essential aspects of high temperature superconductivity. Ultracold fermions in optical lattices allow for the simulation of the Hubbard Hamiltonian with a unique control over kinetic energy, interactions and doping. A great challenge is to reach the required low entropy and to observe antiferromagnetic spin correlations beyond nearest neighbors, for which quantum gas microscopes are ideal. Here we report on the direct, single-site resolved detection of antiferromagnetic correlations extending up to three sites in spin-$1/2$ Hubbard chains, which requires an entropy well below $s^*=\ln(2)$. Finally, the simultaneous detection of spin and density opens the route towards the study of the interplay between magnetic ordering and doping in various dimensions.

cond-mat.quant-gas↗

arXiv2017

The anisotropic Harper-Hofstadter-Mott model: competition between condensation and magnetic fields

We derive the reciprocal cluster mean-field method to study the strongly-interacting bosonic Harper-Hofstadter-Mott model. The system exhibits a rich phase diagram featuring band insulating, striped superfluid, and supersolid phases. Furthermore, for finite hopping anisotropy we observe gapless uncondensed liquid phases at integer fillings, which are analyzed by exact diagonalization. The liquid phases at fillings 1 and 3 exhibit the same band fillings as the fermionic integer quantum Hall effect, while the phase at filling 2 is CT-symmetric with zero charge response. We discuss how these phases become gapped on a quasi-one-dimensional cylinder, leading to a quantized Hall response, which we characterize by introducing a suitable measure for non-trivial many-body topological properties. Incompressible metastable states at fractional filling are also observed, indicating competing fractional quantum Hall phases. The combination of reciprocal cluster mean-field and exact diagonalization yields a promising method to analyze the properties of bosonic lattice systems with non-trivial unit cells in the thermodynamic limit.

cond-mat.quant-gas↗