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Annabelle Bohrdt

Publications and source records attributed to Annabelle Bohrdt.

At least 73 records · Page 4Linked to original sources
arXiv2023

Formation of stripes in a mixed-dimensional cold-atom Fermi-Hubbard system

The relation between d-wave superconductivity and stripes is fundamental to the understanding of ordered phases in cuprates. While experimentally both phases are found in close proximity, numerical studies on the related Fermi-Hubbard model have long been investigating whether stripes precede, compete or coexist with superconductivity. Such stripes are characterised by interleaved charge and spin density wave ordering where fluctuating lines of dopants separate domains of opposite antiferromagnetic order. Here we show first signatures of stripes in a cold-atom Fermi-Hubbard quantum simulator. By engineering a mixed-dimensional system, we increase their typical energy scales to the spin exchange energy, enabling us to access the interesting crossover temperature regime where stripes begin to form. We observe extended, attractive correlations between hole dopants and find an increased probability to form larger structures akin to stripes. In the spin sector, we study correlation functions up to third order and find results consistent with stripe formation. These higher-order correlation measurements pave the way towards an improved microscopic understanding of the emergent properties of stripes and their relation to other competing phases. More generally, our approach has direct relevance for newly discovered high-temperature superconducting materials in which mixed dimensions play an essential role.

cond-mat.quant-gas↗
arXiv2023

Feshbach hypothesis of high-Tc superconductivity in cuprates

Resonant interactions associated with the emergence of a bound state constitute one of the cornerstones of modern many-body physics, ranging from Kondo physics, BEC-BCS crossover, to tunable interactions at Feshbach resonances in ultracold atoms or 2D semiconductors. Here we present a Feshbach perspective on the origin of strong pairing in Fermi-Hubbard type models. We perform a theoretical analysis of interactions between charge carriers in doped Mott insulators, modeled by a near-resonant two-channel scattering problem, and find strong evidence for Feshbach-type interactions in the $d_{x^2-y^2}$ channel that can support strong pairing, consistent with the established phenomenology of cuprates. Existing experimental and numerical results on hole-doped cuprates lead us to conjecture the existence of a light, long-lived, low-energy excited state of two holes with bipolaron character in these systems, which enables near-resonant interactions and can thus provide a microscopic foundation for theories of high-temperature superconductivity involving strong attraction, as assumed e.g. in BEC-BCS crossover scenarios. To put our theory to a direct test we suggest to use coincidence angle-resolved photoemission spectroscopy (cARPES), pair-tunneling measurements or less direct pump-probe experiments. The emergent Feshbach resonance we propose could also underlie superconductivity in other doped antiferromagnetic Mott insulators, as recently proposed for bilayer nickelates, highlighting its potential as a unifying strong-coupling pairing mechanism rooted in quantum magnetism.

cond-mat.str-el↗
arXiv2023

Feshbach resonance in a strongly repulsive bilayer model: a possible scenario for bilayer nickelate superconductors

Since the discovery of superconductivity in cuprate materials, the minimal ingredients for high-T$_c$ superconductivity have been an outstanding puzzle. Motivated by the recently discovered nickelate bilayer superconductor La$_3$Ni$_2$O$_3$ under pressure, we study a minimal bilayer model, in which, as in La$_3$Ni$_2$O$_3$, inter- and intralayer magnetic interactions but no interlayer hopping are present: a mixed-dimensional (mixD) $t-J$ model. In the setting of a mixD ladder, we show that the system exhibits a crossover associated with a Feshbach resonance: from a closed-channel dominated regime of tightly bound bosonic pairs of holes to an open-channel dominated regime of spatially more extended Cooper pairs. The crossover can be tuned by varying doping, or by a nearest-neighbor Coulomb repulsion $V$ that we include in our model. Using density matrix renormalization group (DMRG) simulations and analytical descriptions of both regimes, we find that the ground state is a Luther-Emery liquid, competing with a density wave of tetraparton plaquettes at commensurate filling $δ=0.5$ at large repulsion, and exhibits a pairing dome where binding is facilitated by doping. Our observations can be understood in terms of pairs of correlated spinon-chargon excitations constituting the open channel, which are subject to attractive interactions mediated by the closed channel of tightly bound chargon-chargon pairs. When the closed channel is lowered in energy by doping or tuning $V$, a Feshbach resonance is realized, associated with a dome in the binding energy. Our predictions can be directly tested in state-of-the art quantum simulators, and we argue that the pairing mechanism we describe may be realized in the nickelate bilayer superconductor La$_3$Ni$_2$O$_3$.

cond-mat.str-el↗
arXiv2023

Neural network approach to quasiparticle dispersions in doped antiferromagnets

Numerically simulating spinful, fermionic systems is of great interest from the perspective of condensed matter physics. However, the exponential growth of the Hilbert space dimension with system size renders an exact parameterization of large quantum systems prohibitively demanding. This is a perfect playground for neural networks, owing to their immense representative power that often allows to use only a fraction of the parameters that are needed in exact methods. Here, we investigate the ability of neural quantum states (NQS) to represent the bosonic and fermionic $t-J$ model - the high interaction limit of the Fermi-Hubbard model - on different 1D and 2D lattices. Using autoregressive recurrent neural networks (RNNs) with 2D tensorized gated recurrent units, we study the ground state representations upon doping the half-filled system with holes. Moreover, we present a method to calculate dispersion relations from the neural network state representation, applicable to any neural network architecture and any lattice geometry, that allows to infer the low-energy physics from the NQS. To demonstrate our approach, we calculate the dispersion of a single hole in the $t-J$ model on different 1D and 2D square and triangular lattices. Furthermore, we analyze the strengths and weaknesses of the RNN approach for fermionic systems, pointing the way for an accurate and efficient parameterization of fermionic quantum systems using neural quantum states.

cond-mat.str-el↗
arXiv2023

Adaptive Quantum State Tomography with Active Learning

Recently, tremendous progress has been made in the field of quantum science and technologies: different platforms for quantum simulation as well as quantum computing, ranging from superconducting qubits to neutral atoms, are starting to reach unprecedentedly large systems. In order to benchmark these systems and gain physical insights, the need for efficient tools to characterize quantum states arises. The exponential growth of the Hilbert space with system size renders a full reconstruction of the quantum state prohibitively demanding in terms of the number of necessary measurements. Here we propose and implement an efficient scheme for quantum state tomography using active learning. Based on a few initial measurements, the active learning protocol proposes the next measurement basis, designed to yield the maximum information gain. We apply the active learning quantum state tomography scheme to reconstruct different multi-qubit states with varying degree of entanglement as well as to ground states of the XXZ model in 1D and a kinetically constrained spin chain. In all cases, we obtain a significantly improved reconstruction as compared to a reconstruction based on the exact same number of measurements and measurement configurations, but with randomly chosen basis configurations. Our scheme is highly relevant to gain physical insights in quantum many-body systems as well as for benchmarking and characterizing quantum devices, e.g. for quantum simulation, and paves the way for scalable adaptive protocols to probe, prepare, and manipulate quantum systems.

quant-ph↗
arXiv2023

Detecting Hidden Order in Fractional Chern Insulators

Topological phase transitions go beyond Ginzburg and Landau's paradigm of spontaneous symmetry breaking and occur without an associated local order parameter. Instead, such transitions can be characterized by the emergence of non-local order parameters, which require measurements on extensively many particles simultaneously - an impossible venture in real materials. On the other hand, quantum simulators have demonstrated such measurements, making them prime candidates for an experimental confirmation of non-local topological order. Here, building upon the recent advances in preparing few-particle fractional Chern insulators using ultracold atoms and photons, we propose a realistic scheme for detecting the hidden off-diagonal long-range order (HODLRO) characterizing Laughlin states. Furthermore, we demonstrate the existence of this hidden order in fractional Chern insulators, specifically for the $ν=\frac{1}{2}$-Laughlin state in the isotropic Hofstadter-Bose-Hubbard model. This is achieved by large-scale numerical density matrix renormalization group (DMRG) simulations based on matrix product states, for which we formulate an efficient sampling procedure providing direct access to HODLRO in close analogy to the proposed experimental scheme. We confirm the characteristic power-law scaling of HODLRO, with an exponent $\frac{1}ν = 2$, and show that its detection requires only a few thousand snapshots. This makes our scheme realistically achievable with current technology and paves the way for further analysis of non-local topological orders, e.g. in topological states with non-Abelian anyonic excitations.

cond-mat.quant-gas↗
arXiv2023

Enhancing variational Monte Carlo using a programmable quantum simulator

Programmable quantum simulators based on Rydberg atom arrays are a fast-emerging quantum platform, bringing together long coherence times, high-fidelity operations, and large numbers of interacting qubits deterministically arranged in flexible geometries. Today's Rydberg array devices are demonstrating their utility as quantum simulators for studying phases and phase transitions in quantum matter. In this paper, we show that unprocessed and imperfect experimental projective measurement data can be used to enhance in silico simulations of quantum matter, by improving the performance of variational Monte Carlo simulations. As an example, we focus on data spanning the disordered-to-checkerboard transition in a $16 \times 16$ square lattice array [S. Ebadi et al. Nature 595, 227 (2021)] and employ data-enhanced variational Monte Carlo to train powerful autoregressive wavefunction ansätze based on recurrent neural networks (RNNs). We observe universal improvements in the convergence times of our simulations with this hybrid training scheme. Notably, we also find that pre-training with experimental data enables relatively simple RNN ansätze to accurately capture phases of matter that are not learned with a purely variational training approach. Our work highlights the promise of hybrid quantum--classical approaches for large-scale simulation of quantum many-body systems, combining autoregressive language models with experimental data from existing quantum devices.

cond-mat.quant-gas↗
arXiv2023

Dichotomy of heavy and light pairs of holes in the $t-J$ model

A key step in unraveling the mysteries of materials exhibiting unconventional superconductivity is to understand the underlying pairing mechanism. While it is widely agreed upon that the pairing glue in many of these systems originates from antiferromagnetic spin correlations, a microscopic description of pairs of charge carriers remains lacking. Here we use state-of-the art numerical methods to probe the internal structure and dynamical properties of pairs of charge carriers in quantum antiferromagnets in four-legged cylinders. Exploiting the full momentum resolution in our simulations, we are able to distinguish two qualitatively different types of bound states: a highly mobile, meta-stable pair, which has a dispersion proportional to the hole hopping $t$, and a heavy pair, which can only move due to spin exchange processes and turns into a flat band in the Ising limit of the model. Understanding the pairing mechanism can on the one hand pave the way to boosting binding energies in related models, and on the other hand enable insights into the intricate competition of various phases of matter in strongly correlated electron systems.

cond-mat.str-el↗
arXiv2023

Fluctuation based interpretable analysis scheme for quantum many-body snapshots

Microscopically understanding and classifying phases of matter is at the heart of strongly-correlated quantum physics. With quantum simulations, genuine projective measurements (snapshots) of the many-body state can be taken, which include the full information of correlations in the system. The rise of deep neural networks has made it possible to routinely solve abstract processing and classification tasks of large datasets, which can act as a guiding hand for quantum data analysis. However, though proven to be successful in differentiating between different phases of matter, conventional neural networks mostly lack interpretability on a physical footing. Here, we combine confusion learning with correlation convolutional neural networks, which yields fully interpretable phase detection in terms of correlation functions. In particular, we study thermodynamic properties of the 2D Heisenberg model, whereby the trained network is shown to pick up qualitative changes in the snapshots above and below a characteristic temperature where magnetic correlations become significantly long-range. We identify the full counting statistics of nearest neighbor spin correlations as the most important quantity for the decision process of the neural network, which go beyond averages of local observables. With access to the fluctuations of second-order correlations -- which indirectly include contributions from higher order, long-range correlations -- the network is able to detect changes of the specific heat and spin susceptibility, the latter being in analogy to magnetic properties of the pseudogap phase in high-temperature superconductors. By combining the confusion learning scheme with transformer neural networks, our work opens new directions in interpretable quantum image processing being sensible to long-range order.

cond-mat.quant-gas↗
arXiv2023

Realistic scheme for quantum simulation of $\mathbb{Z}_2$ lattice gauge theories with dynamical matter in $(2+1)$D

Gauge fields coupled to dynamical matter are ubiquitous in many disciplines of physics, ranging from particle to condensed matter physics, but their implementation in large-scale quantum simulators remains challenging. Here we propose a realistic scheme for Rydberg atom array experiments in which a $\mathbb{Z}_2$ gauge structure with dynamical charges emerges on experimentally relevant timescales from only local two-body interactions and one-body terms in two spatial dimensions. The scheme enables the experimental study of a variety of models, including $(2+1)$D $\mathbb{Z}_2$ lattice gauge theories coupled to different types of dynamical matter and quantum dimer models on the honeycomb lattice, for which we derive effective Hamiltonians. We discuss ground-state phase diagrams of the experimentally most relevant effective $\mathbb{Z}_2$ lattice gauge theories with dynamical matter featuring various confined and deconfined, quantum spin liquid phases. Further, we present selected probes with immediate experimental relevance, including signatures of disorder-free localization and a thermal deconfinement transition of two charges.

cond-mat.quant-gas↗
arXiv2023

Robust quantum many-body scars in lattice gauge theories

Quantum many-body scarring is a paradigm of weak ergodicity breaking arising due to the presence of special nonthermal many-body eigenstates that possess low entanglement entropy, are equally spaced in energy, and concentrate in certain parts of the Hilbert space. Though scars have been shown to be intimately connected to gauge theories, their stability in such experimentally relevant models is still an open question, and it is generally considered that they exist only under fine-tuned conditions. In this work, we show through Krylov-based time-evolution methods how quantum many-body scars can be made robust in the presence of experimental errors through utilizing terms linear in the gauge-symmetry generator or a simplified pseudogenerator in $\mathrm{U}(1)$ and $\mathbb{Z}_2$ lattice gauge theories. Our findings are explained by the concept of quantum Zeno dynamics. Our experimentally feasible methods can be readily implemented in existing large-scale ultracold-atom quantum simulators and setups of Rydberg atoms with optical tweezers.

cond-mat.quant-gas↗
arXiv2023

Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics

Preparing finite temperature states in quantum simulators of spin systems, such as trapped ions or Rydberg atoms in optical tweezers, is challenging due to their almost perfect isolation from the environment. Here, we show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality and equivalent to the one in Lu, Banuls and Cirac, PRX Quantum 2, 020321 (2021). It consists of classical importance sampling of initial states and a measurement of the Loschmidt echo with a quantum simulator. We use the method as a quantum-inspired classical algorithm and simulate the protocol with matrix product states to analyze the requirements on a quantum simulator. This way, we show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators. We propose a concrete measurement protocol for the Loschmidt echo and discuss the influence of measurement noise, dephasing, as well as state preparation and measurement errors. We argue that the algorithm is robust against those imperfections under realistic conditions.

quant-ph↗
arXiv2023

Ferromagnetism and Skyrmions in the Hofstadter-Fermi-Hubbard Model

Strongly interacting fermionic systems host a variety of interesting quantum many-body states with exotic excitations. For instance, the interplay of strong interactions and the Pauli exclusion principle can lead to Stoner ferromagnetism, but the fate of this state remains unclear when kinetic terms are added. While in many lattice models the fermions' dispersion results in delocalization and destabilization of the ferromagnet, flat bands can restore strong interaction effects and ferromagnetic correlations. To reveal this interplay, here we propose to study the Hofstadter-Fermi-Hubbard model using ultracold atoms. We demonstrate, by performing large-scale DMRG simulations, that this model exhibits a lattice analog of the quantum Hall ferromagnet at magnetic filling factor $ν=1$. We reveal the nature of the low energy spin-singlet states around $ν\approx1$ and find that they host quasi-particles and quasi-holes exhibiting spin-spin correlations reminiscent of skyrmions. Finally, we predict the breakdown of flat-band ferromagnetism at large fields. Our work paves the way towards experimental studies of lattice quantum Hall ferromagnetism, including prospects to study many-body states of interacting skyrmions and explore the relation to high-$T_{\rm c}$ superconductivity.

cond-mat.quant-gas↗
arXiv2022

Particle zoo in a doped spin chain: Correlated states of mesons and magnons

It is a widely accepted view that the interplay of spin- and charge-degrees of freedom in doped antiferromagnets (AFMs) gives rise to the rich physics of high-temperature superconductors. Nevertheless, it remains unclear how effective low-energy degrees of freedom and the corresponding field theories emerge from microscopic models, including the $t-J$ and Hubbard Hamiltonians. A promising view comprises that the charge carriers have a rich internal parton structure on intermediate scales, but the interplay of the emergent partons with collective magnon excitations of the surrounding AFM remains unexplored. Here we study a doped one-dimensional spin chain in a staggered magnetic field and demonstrate that it supports a zoo of various long-lived excitations. These include magnons; mesonic pairs of spinons and chargons, along with their ro-vibrational excitations; and tetra-parton bound states of mesons and magnons. We identify these types of quasiparticles in various spectra using DMRG simulations. Moreover, we introduce a strong-coupling theory describing the polaronic dressing and molecular binding of mesons to collective magnon excitations. The effective theory can be solved by standard tools developed for polaronic problems, and can be extended to study similar physics in two-dimensional doped AFMs in the future. Experimentally, the doped spin-chain in a staggered field can be directly realized in quantum gas microscopes.

cond-mat.str-el↗
arXiv2022

Pairing of holes by confining strings in antiferromagnets

In strongly correlated quantum materials, the behavior of charge carriers is dominated by strong electron-electron interactions. These can lead to insulating states with spin order, and upon doping to competing ordered states including unconventional superconductivity. The underlying pairing mechanism remains poorly understood however, even in strongly simplified theoretical models. Recent advances in quantum simulation allow to study pairing in paradigmatic settings, e.g. in the $t-J$ and $t-J_z$ Hamiltonians. Even there, the most basic properties of paired states of only two dopants, such as their dispersion relation and excitation spectra, remain poorly studied in many cases. Here we provide new analytical insights into a possible string-based pairing mechanism of mobile holes in an antiferromagnet. We analyze an effective model of partons connected by a confining string and calculate the spectral properties of bound states. Our model is equally relevant for understanding Hubbard-Mott excitons consisting of a bound doublon-hole pair or confined states of dynamical matter in lattice gauge theories, which motivates our study of different parton statistics. Although an accurate semi-analytic estimation of binding energies is challenging, our theory provides a detailed understanding of the internal structure of pairs. For example, in a range of settings we predict heavy states of immobile pairs with flat-band dispersions -- including for the lowest-energy $d$-wave pair of fermions. Our findings shed new light on the long-standing question about the origin of pairing and competing orders in high-temperature superconductors.

cond-mat.str-el↗
arXiv2022

Snapshot-based detection of $\frac{1}{2}$-Laughlin states: coupled chains and central charge

Experimental realizations of topologically ordered states of matter, such as fractional quantum Hall states, with cold atoms are now within reach. In particular, optical lattices provide a promising platform for the realization and characterization of such states, where novel detection schemes enable an unprecedented microscopic understanding. Here we show that the central charge can be directly measured in current cold atom experiments using the number entropy as a proxy for the entanglement entropy. We perform density-matrix renormalization-group simulations of Hubbard-interacting bosons on coupled chains subject to a magnetic field with $α=\frac{1}{4}$ flux quanta per plaquette. Tuning the inter-chain hopping, we find a transition from a trivial quasi-one dimensional phase to the topologically ordered Laughlin state at magnetic filling factor $ν=\frac{1}{2}$ for systems of three or more chains. We resolve the transition using the central charge, on-site correlations, momentum distributions and the many-body Chern number. Additionally, we propose a scheme to experimentally estimate the central charge from Fock basis snapshots. The model studied here is experimentally realizable with existing cold atom techniques and the proposed observables pave the way for the detection and classification of a larger class of interacting topological states of matter.

cond-mat.quant-gas↗
arXiv2022

Characterizing Topological Excitations of a Long-Range Heisenberg Model with Trapped Ions

Realizing and characterizing interacting topological phases in synthetic quantum systems is a formidable challenge. Here, we propose a Floquet protocol to realize the antiferromagnetic Heisenberg model with power-law decaying interactions. Based on analytical and numerical arguments, we show that this model features a quantum phase transition from a liquid to a valence bond solid that spontaneously breaks lattice translational symmetry and is reminiscent of the Majumdar-Ghosh state. The different phases can be probed dynamically by measuring the evolution of a fully dimerized state. We moreover introduce an interferometric protocol to characterize the topological excitations and the bulk topological invariants of the interacting many-body system.

cond-mat.quant-gas↗
arXiv2022

Schrieffer-Wolff Transformations for Experiments: Dynamically Suppressing Virtual Doublon-Hole Excitations in a Fermi-Hubbard Simulator

In strongly interacting systems with a separation of energy scales, low-energy effective Hamiltonians help provide insights into the relevant physics at low temperatures. The emergent interactions in the effective model are mediated by virtual excitations of high-energy states: For example, virtual doublon-hole excitations in the Fermi-Hubbard model mediate antiferromagnetic spin-exchange interactions in the derived effective model, known as the $t-J-3s$ model. Formally this procedure is described by performing a unitary Schrieffer-Wolff basis transformation. In the context of quantum simulation, it can be advantageous to consider the effective model to interpret experimental results. However, virtual excitations such as doublon-hole pairs can obfuscate the measurement of physical observables. Here we show that quantum simulators allow one to access the effective model even more directly by performing measurements in a rotated basis. We propose a protocol to perform a Schrieffer-Wolff transformation on Fermi-Hubbard low-energy eigenstates (or thermal states) to dynamically prepare approximate $t-J-3s$ model states using fermionic atoms in an optical lattice. Our protocol involves performing a linear ramp of the optical lattice depth, which is slow enough to eliminate the virtual doublon-hole fluctuations but fast enough to freeze out the dynamics in the effective model. We perform a numerical study using exact diagonalization and find an optimal ramp speed for which the state after the lattice ramp has maximal overlap with the $t-J-3s$ model state. We compare our numerics to experimental data from our Lithium-6 fermionic quantum gas microscope and show a proof-of-principle demonstration of this protocol. More generally, this protocol can be beneficial to studies of effective models by enabling the suppression of virtual excitations in a wide range of quantum simulation experiments.

cond-mat.quant-gas↗