arXiv subjects

Eun-Ah Kim

Publications and source records attributed to Eun-Ah Kim.

At least 37 records · Page 2Linked to original sources

arXiv2024

Hamiltonian-reconstruction distance as a success metric for the Variational Quantum Eigensolver

The Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm for quantum simulation that can be run on near-term quantum hardware. A challenge in VQE -- as well as any other heuristic algorithm for finding ground states of Hamiltonians -- is to know how close the algorithm's output solution is to the true ground state, when the true ground state and ground-state energy are unknown. This is especially important in iterative algorithms, such as VQE, where one wants to avoid erroneous early termination. Recent developments in Hamiltonian reconstruction -- the inference of a Hamiltonian given an eigenstate -- give a metric can be used to assess the quality of a variational solution to a Hamiltonian-eigensolving problem. This metric can assess the proximity of the variational solution to the ground state without any knowledge of the true ground state or ground-state energy. In numerical simulations and in demonstrations on a cloud-based trapped-ion quantum computer, we show that for examples of both one-dimensional transverse-field-Ising (11 qubits) and two-dimensional J1-J2 transverse-field-Ising (6 qubits) spin problems, the Hamiltonian-reconstruction distance gives a helpful indication of whether VQE has yet found the ground state or not. Our experiments included cases where the energy plateaus as a function of the VQE iteration, which could have resulted in erroneous early stopping of the VQE algorithm, but where the Hamiltonian-reconstruction distance correctly suggests to continue iterating. We find that the Hamiltonian-reconstruction distance has a useful correlation with the fidelity between the VQE solution and the true ground state. Our work suggests that the Hamiltonian-reconstruction distance may be a useful tool for assessing success in VQE, including on noisy quantum processors in practice.

quant-ph↗

arXiv2024

Machine learning reveals features of spinon Fermi surface

With rapid progress in simulation of strongly interacting quantum Hamiltonians, the challenge in characterizing unknown phases becomes a bottleneck for scientific progress. We demonstrate that a Quantum-Classical hybrid approach (QuCl) of mining sampled projective snapshots with interpretable classical machine learning can unveil signatures of seemingly featureless quantum states. The Kitaev-Heisenberg model on a honeycomb lattice under external magnetic field presents an ideal system to test QuCl, where simulations have found an intermediate gapless phase (IGP) sandwiched between known phases, launching a debate over its elusive nature. We use the correlator convolutional neural network, trained on labeled projective snapshots, in conjunction with regularization path analysis to identify signatures of phases. We show that QuCl reproduces known features of established phases. Significantly, we also identify a signature of the IGP in the spin channel perpendicular to the field direction, which we interpret as a signature of Friedel oscillations of gapless spinons forming a Fermi surface. Our predictions can guide future experimental searches for spin liquids.

cond-mat.str-el↗

arXiv2024

Dominant 1/3-filling Correlated Insulator States and Orbital Geometric Frustration in Twisted Bilayer Graphene

Geometric frustration is a phenomenon in a lattice system where not all interactions can be satisfied, the simplest example being antiferromagnetically coupled spins on a triangular lattice. Frustrated systems are characterized by their many nearly degenerate ground states, leading to non-trivial phases such as spin ice and spin liquids. To date most studies are on geometric frustration of spins; much less explored is orbital geometric frustration. For electrons in twisted bilayer graphene (tBLG) at denominator 3 fractional filling, Coulomb interactions and the Wannier orbital shapes are predicted to strongly constrain spatial charge ordering, leading to geometrically frustrated ground states that produce a new class of correlated insulators (CIs). Here we report the observation of dominant denominator 3 fractional filling insulating states in large angle tBLG; these states persist in magnetic fields and display magnetic ordering signatures and tripled unit cell reconstruction. These results are in agreement with a strong-coupling theory of symmetry-breaking of geometrically frustrated fractional states.

cond-mat.str-el↗

arXiv2024

Bragg glass signatures in Pd$_x$ErTe$_3$ with X-ray diffraction Temperature Clustering (X-TEC)

The Bragg glass phase is a nearly perfect crystal with glassy features predicted to occur in vortex lattices and charge density wave systems in the presence of disorder. Detecting it has been challenging despite its sharp theoretical definition in terms of diverging correlation lengths. Here, we present evidence supporting a Bragg glass phase in the systematically disordered charge density wave material PdxErTe3. We do this using comprehensive x-ray data and a machine learning analysis tool called X-ray temperature clustering, or X-TEC. We establish a diverging correlation length in samples with moderate intercalation over a wide temperature range. To enable this analysis, we introduced a high-throughput measure of inverse correlation length that we call peak spread. The detection of Bragg glass order and the resulting phase diagram advance our understanding of the complex interplay between disorder and fluctuations significantly. Moreover, the use of our analysis technique to target fluctuations through a high-throughput measure of peak spread can revolutionize the study of fluctuations in scattering experiments.

cond-mat.str-el↗

arXiv2024

Quantum Melting of Generalized Wigner Crystals in Transition Metal Dichalcogenide Moiré Systems

Generalized Wigner Crystal (GWC) is a novel quantum phase of matter driven by further-range interaction at fractional fillings of a lattice. The role of further range interaction as the driver for the incompressible state is akin to Wigner crystal. On the other hand, the significant role of commensurate filling is akin to the Mott insulator. Recent progress in simulator platforms presents unprecedented opportunities to investigate quantum melting in the strongly interacting regime through synergy between theory and experiments. However, the earlier theory literature presents diverging predictions. We study the quantum freezing of GWC through large-scale density matrix renormalization group simulations of a triangular lattice extended Hubbard model. We find a single first-order phase transition between the Fermi liquid and the $\sqrt{3}\times\sqrt{3}$ GWC state. The GWC state shows long-range antiferromagnetic $120^\circ$ N{é}el order. Our results present the simplest answers to the question of the quantum phase transition into the GWC phase and the properties of the GWC phase.

cond-mat.str-el↗

arXiv2023

Realizing a tunable honeycomb lattice in ABBA-stacked twisted double bilayer WSe$_2$

The ideal honeycomb lattice, featuring sublattice and SU(2) spin rotation symmetries, is a fundamental model for investigating quantum matters with topology and correlations. With the rise of the moiré-based design of model systems, realizing a tunable and symmetric honeycomb lattice system with a narrow bandwidth can open access to new phases and insights. We propose the ABBA-stacked twisted double bilayer WSe$_2$ as a realistic and tunable platform for reaching this goal. Adjusting the twist angle allows the bandwidth and the ratio between hopping parameters of different ranges to be tuned. Moreover, the system's small bandwidth and spin rotation symmetry enable effective control of the electronic structure through an in-plane magnetic field. We construct an extended Hubbard model for the system to demonstrate this tunability and explore possible ordered phases using the Hartree-Fock approximation. We find that at a hole filling of $ν= 2$ (two holes per moiré unit cell), an in-plane magnetic field of a few Tesla can ``dope" the system from a semimetal to a metal. Interactions then drive an instability towards a canted antiferromagnetic insulator ground state. Additionally, we observe a competing insulating phase with sublattice charge polarization. Finally, we discuss the experimental signatures of these novel insulating phases.

cond-mat.str-el↗

arXiv2023

Materials Expert-Artificial Intelligence for Materials Discovery

The advent of material databases provides an unprecedented opportunity to uncover predictive descriptors for emergent material properties from vast data space. However, common reliance on high-throughput ab initio data necessarily inherits limitations of such data: mismatch with experiments. On the other hand, experimental decisions are often guided by an expert's intuition honed from experiences that are rarely articulated. We propose using machine learning to "bottle" such operational intuition into quantifiable descriptors using expertly curated measurement-based data. We introduce "Materials Expert-Artificial Intelligence" (ME-AI) to encapsulate and articulate this human intuition. As a first step towards such a program, we focus on the topological semimetal (TSM) among square-net materials as the property inspired by the expert-identified descriptor based on structural information: the tolerance factor. We start by curating a dataset encompassing 12 primary features of 879 square-net materials, using experimental data whenever possible. We then use Dirichlet-based Gaussian process regression using a specialized kernel to reveal composite descriptors for square-net topological semimetals. The ME-AI learned descriptors independently reproduce expert intuition and expand upon it. Specifically, new descriptors point to hypervalency as a critical chemical feature predicting TSM within square-net compounds. Our success with a carefully defined problem points to the "machine bottling human insight" approach as promising for machine learning-aided material discovery.

cond-mat.mtrl-sci↗

arXiv2023

Frustrated charge order and cooperative distortions in ScV6Sn6

Here we study the stability of charge order in the kagome metal ScV6Sn6. Synchrotron x-ray diffraction measurements reveal high-temperature, short-range charge correlations at the wave vectors along q=(1/3,1/3,1/2) whose inter-layer correlation lengths diverge upon cooling. At the charge order transition, this divergence is interrupted and long-range order freezes in along q=(1/3,1/3,1/3), as previously reported, while disorder enables the charge correlations to persist at the q=(1/3,1/3,1/2) wave vector down to the lowest temperatures measured. Both short-range and long-range charge correlations seemingly arise from the same instability and both are rapidly quenched upon the introduction of larger Y ions onto the Sc sites. Our results validate the theoretical prediction of the primary lattice instability at q=(1/3,1/3,1/2), and we present a heuristic picture for viewing the frustration of charge order in this compound.

cond-mat.str-el↗

arXiv2023

Fractionalization in Fractional Correlated Insulating States at $n\pm 1/3$ filled twisted bilayer graphene

Fractionalization without time-reversal symmetry breaking is a long-sought-after goal in the study of correlated phenomena. The earlier proposal of correlated insulating states at $n \pm 1/3$ filling in twisted bilayer graphene and recent experimental observations of insulating states at those fillings strongly suggest that moiré graphene systems provide a new platform to realize time-reversal symmetric fractionalized states. However, the nature of fractional excitations and the effect of quantum fluctuation on the fractional correlated insulating states are unknown. We show that excitations of the fractional correlated insulator phases in the strong coupling limit carry fractional charges and exhibit fractonic restricted mobility. Upon introduction of quantum fluctuations, the resonance of ``lemniscate" structured operators drives the system into ``quantum lemniscate liquid (QLL)" or ``quantum lemniscate solid (QLS)". We find an emergent $U(1)\times U(1)$ 1-form symmetry unifies distinct motions of the fractionally charged excitations in the strong coupling limit and in the QLL phase while providing a new mechanism for fractional excitations in two-dimension. We predict emergent Luttinger liquid behavior upon dilute doping in the strong coupling limit due to restricted mobility and discuss implications at a general $n \pm 1/3$ filling.

cond-mat.str-el↗

arXiv2023

Domain-dependent surface adhesion in twisted few-layer graphene: Platform for moiré-assisted chemistry

Twisted van der Waals multilayers are widely regarded as a rich platform to access novel electronic phases, thanks to the multiple degrees of freedom such as layer thickness and twist angle that allow control of their electronic and chemical properties. Here, we propose that the stacking domains that form naturally due to the relative twist between successive layers act as an additional "knob" for controlling the behavior of these systems, and report the emergence and engineering of stacking domain-dependent surface chemistry in twisted few-layer graphene. Using mid-infrared near-field optical microscopy and atomic force microscopy, we observe a selective adhesion of metallic nanoparticles and liquid water at the domains with rhombohedral stacking configurations of minimally twisted double bi- and tri-layer graphene. Furthermore, we demonstrate that the manipulation of nanoparticles located at certain stacking domains can locally reconfigure the moiré superlattice in their vicinity at the μm-scale. In addition, we report first-principles simulations of the energetics of adhesion of metal atoms and water molecules on the stacking domains in an attempt to elucidate the origin of the observed selective adhesion. Our findings establish a new approach to controlling moiré-assisted chemistry and nanoengineering.

cond-mat.mtrl-sci↗

arXiv2023

Quantum Phases of Transition Metal Dichalcogenide Moiré Systems

Moiré systems provide a rich platform for studies of strong correlation physics. Recent experiments on hetero-bilayer transition metal dichalcogenide (TMD) Moiré systems are exciting in that they manifest a relatively simple model system of an extended Hubbard model on a triangular lattice. Inspired by the prospect of the hetero-TMD Moiré system's potential as a solid-state-based quantum simulator, we explore the extended Hubbard model on the triangular lattice using the density matrix renormalization group (DMRG). Specifically, we explore the two-dimensional phase space of the kinetic energy relative to the interaction strength $t/U$ and the further-range interaction strength $V_1/U$. We find competition between Fermi fluid, chiral spin liquid, spin density wave, and charge density wave. In particular, our finding of the optimal further-range interaction for the chiral correlation presents a tantalizing possibility.

cond-mat.str-el↗

arXiv2023

Structural evolution of the kagome superconductors $A$V$_3$Sb$_5$ ($A$ = K, Rb, and Cs) through charge density wave order

The kagome superconductors KV$_3$Sb$_5$, RbV$_3$Sb$_5$, and CsV$_3$Sb$_5$ are known to display charge density wave (CDW) order which impacts the topological characteristics of their electronic structure. Details of their structural ground states and how they evolve with temperature are revealed here using single crystal X-ray crystallographic refinements as a function of temperature, carried out with synchrotron radiation. The compounds KV$_3$Sb$_5$ and RbV$_3$Sb$_5$ present 2$\times$2$\times$2 superstructures in the $Fmmm$ space group with a staggered tri-hexagonal deformation of vanadium layers. CsV$_3$Sb$_5$ displays more complex structural evolution, whose details have been unravelled by applying machine learning methods to the scattering data. Upon cooling through the CDW transition, CsV$_3$Sb$_5$ displays a staged progression of ordering from a 2$\times$2$\times$1 supercell and a 2$\times$2$\times$2 supercell into a final 2$\times$2$\times$4 supercell that persists to $T$ = 11 K and exhibits an average structure where vanadium layers display both tri-hexagonal and Star of David patterns of deformations. Diffraction from CsV$_3$Sb$_5$ under pulsed magnetic fields up to $μ_0H$ = 28 T suggest the real component of the CDW state is insensitive to external magnetic fields.

cond-mat.supr-con↗

arXiv2022

High-Throughput $\textit{Ab Initio}$ Design of Atomic Interfaces using InterMatch

Forming a hetero-interface is a materials-design strategy that can access an astronomically large phase space. However, the immense phase space necessitates a high-throughput approach for optimal interface design. Here we introduce a high-throughput computational framework, InterMatch, for efficiently predicting charge transfer, strain, and superlattice structure of an interface by leveraging the databases of individual bulk materials. Specifically, the algorithm reads in the lattice vectors, density of states, and the stiffness tensors for each material in their isolated form from the Materials Project. From these bulk properties, InterMatch estimates the interfacial properties. We benchmark InterMatch predictions for the charge transfer against experimental measurements and supercell density-functional theory calculations. We then use InterMatch to predict promising interface candidates for doping transition metal dichalcogenide MoSe$_2$. Finally, we explain experimental observation of factor of 10 variation in the supercell periodicity within a few microns in graphene/$α$-RuCl$_3$ by exploring low energy superlattice structures as a function of twist angle using InterMatch. We anticipate our open-source InterMatch algorithm accelerating and guiding ever-growing interfacial design efforts. Moreover, the interface database resulting from the InterMatch searches presented in this paper can be readily accessed through https://contribs.materialsproject.org/projects/intermatch/ .

cond-mat.mtrl-sci↗

arXiv2022

Graph gauge theory of mobile non-Abelian anyons in a qubit stabilizer code

Stabilizer codes allow for non-local encoding and processing of quantum information. Deformations of stabilizer surface codes introduce new and non-trivial geometry, in particular leading to emergence of long sought after objects known as projective Ising non-Abelian anyons. Braiding of such anyons is a key ingredient of topological quantum computation. We suggest a simple and systematic approach to construct effective unitary protocols for braiding, manipulation and readout of non-Abelian anyons and preparation of their entangled states. We generalize the surface code to a more generic graph with vertices of degree 2, 3 and 4. Our approach is based on the mapping of the stabilizer code defined on such a graph onto a model of Majorana fermions charged with respect to two emergent gauge fields. One gauge field is akin to the physical magnetic field. The other one is responsible for emergence of the non-Abelian anyonic statistics and has a purely geometric origin. This field arises from assigning certain rules of orientation on the graph known as the Kasteleyn orientation in the statistical theory of dimer coverings. Each 3-degree vertex on the graph carries the flux of this "Kasteleyn" field and hosts a non-Abelian anyon. In our approach all the experimentally relevant operators are unambiguously fixed by locality, unitarity and gauge invariance. We illustrate the power of our method by making specific prescriptions for experiments verifying the non-Abelian statistics.

quant-ph↗

arXiv2022

Unsupervised learning of two-component nematicity from STM data on magic angle bilayer graphene

Moiré materials such as magic angle twisted bilayer graphene (MATBG) exhibit remarkable phenomenology, but present significant challenges for certain experimental methods, particularly scanning probes such as scanning tunneling microscopy (STM). Typical STM studies that can image tens of thousands of atomic unit cells can image roughly ten moiré cells, making data analysis statistically fraught. Here, we propose a method to mitigate this problem by aggregating STM conductance data from several bias voltages, and then using the unsupervised machine learning method of gaussian mixture model clustering to draw maximal insight from the resulting dataset. We apply this method, using as input coarse-grained bond variables respecting the point group symmetry, to investigate nematic ordering tendencies in MATBG for both charge neutral and hole-doped samples. For the charge-neutral dataset, the clustering reveals the surprising coexistence of multiple types of nematicity that are unrelated by symmetry, and therefore generically nondegenerate. By contrast, the clustering in the hole doped data is consistent with long range order of a single type. Beyond its value in analyzing nematicity in MATBG, our method has the potential to enhance understanding of symmetry breaking and its spatial variation in a variety of moiré materials.

cond-mat.str-el↗

arXiv2021

Strange Metals from Melting Correlated Insulators in Twisted Bilayer Graphene

Even as the understanding of the mechanism behind correlated insulating states in magic-angle twisted bilayer graphene converges towards various kinds of spontaneous symmetry breaking, the metallic "normal state" above the insulating transition temperature remains mysterious, with its excessively high entropy and linear-in-temperature resistivity. In this work, we focus on the effects of fluctuations of the order-parameters describing correlated insulating states at integer fillings of the low-energy flat bands on charge transport. Motivated by the observation of heterogeneity in the order-parameter landscape at zero magnetic field in certain samples, we conjecture the existence of frustrating extended range interactions in an effective Ising model of the order-parameters on a triangular lattice. The competition between short-distance ferromagnetic interactions and frustrating extended range antiferromagnetic interactions leads to an emergent length scale that forms stripe-like mesoscale domains above the ordering transition. The gapless fluctuations of these heterogeneous configurations are found to be responsible for the linear-in-temperature resistivity as well as the enhanced low temperature entropy. Our insights link experimentally observed linear-in-temperature resistivity and enhanced entropy to the strength of frustration, or equivalently, to the emergence of mesoscopic length scales characterizing order-parameter domains.

cond-mat.str-el↗

arXiv2021

Machine learning discovery of new phases in programmable quantum simulator snapshots

Machine learning has recently emerged as a promising approach for studying complex phenomena characterized by rich datasets. In particular, data-centric approaches lend to the possibility of automatically discovering structures in experimental datasets that manual inspection may miss. Here, we introduce an interpretable unsupervised-supervised hybrid machine learning approach, the hybrid-correlation convolutional neural network (Hybrid-CCNN), and apply it to experimental data generated using a programmable quantum simulator based on Rydberg atom arrays. Specifically, we apply Hybrid-CCNN to analyze new quantum phases on square lattices with programmable interactions. The initial unsupervised dimensionality reduction and clustering stage first reveals five distinct quantum phase regions. In a second supervised stage, we refine these phase boundaries and characterize each phase by training fully interpretable CCNNs and extracting the relevant correlations for each phase. The characteristic spatial weightings and snippets of correlations specifically recognized in each phase capture quantum fluctuations in the striated phase and identify two previously undetected phases, the rhombic and boundary-ordered phases. These observations demonstrate that a combination of programmable quantum simulators with machine learning can be used as a powerful tool for detailed exploration of correlated quantum states of matter.

quant-ph↗

arXiv2021

Melting of generalized Wigner crystals in transition metal dichalcogenide heterobilayer Moiré systems

Moiré superlattice systems such as transition metal dichalcogenide heterobilayers have garnered significant recent interest due to their promising utility as tunable solid state simulators. Recent experiments on a WSe$_2$/WS$_2$ heterobilayer detected incompressible charge ordered states that one can view as generalized Wigner crystals. The tunability of the hetero-TMD Moiré system presents an opportunity to study the rich set of possible phases upon melting these charge-ordered states. Here we use Monte Carlo simulations to study these intermediate phases in between incompressible charge-ordered states in the strong coupling limit. We find two distinct stripe solid states to be each preceded by distinct types of nematic states. In particular, we discover microscopic mechanisms that stabilize each of the nematic states, whose order parameter transforms as the two-dimensional $E$ representation of the Moiré lattice point group. Our results provide a testable experimental prediction of where both types of nematic occur, and elucidate the microscopic mechanism driving their formation.

cond-mat.str-el↗