arXiv subjects

Annabelle Bohrdt

Publications and source records attributed to Annabelle Bohrdt.

At least 37 records · Page 2Linked to original sources

arXiv2025

Two-dopant origin of competing stripe and pair formation in Hubbard and $t$-$J$ models

Understanding the physics of the two-dimensional Hubbard model is widely believed to be a key step in achieving a full understanding of high-$T_\mathrm{c}$ cuprate superconductors. In recent years, progress has been made by large-scale numerical simulations at finite doping and, on the other hand, by microscopic theories able to capture the physics of individual charge carriers. In this work, we study single pairs of dopants in a cylindrical system using the density-matrix renormalization group algorithm. We identify two coexisting charge configurations that couple to the spin environment in different ways: A tightly bound configuration featuring (next-)nearest-neighbor pairs and a stripe-like configuration of dopants on opposite sides of the cylinder, accompanied by a spin domain wall. Thus, we establish that the interplay between stripe order and uniform pairing, central to the models' phases at finite doping, has its origin at the single-pair level. By interpolating between the Hubbard and the related $t$-$J$ model, we are able to quantitatively understand discrepancies in the pairing properties of the two models through the three-site hopping term usually omitted from the $t$-$J$ Hamiltonian. This term is closely related to a next-nearest-neighbor tunneling $t'$, which we observe to upset the balance between the competing stripe and pair states on the two-dopant level.

cond-mat.str-el↗

arXiv2025

Simulating the two-dimensional $t-J$ model at finite doping with neural quantum states

Simulating large, strongly interacting fermionic systems remains a major challenge for existing numerical methods. In this work, we introduce Gutzwiller projected hidden fermion determinant states (G-HFDS) to simulate the strongly interacting limit of the Fermi-Hubbard model, namely the $t$-$J$ model, across the entire doping regime. We demonstrate that the G-HFDS achieve energies competitive with matrix product states (MPS) on lattices as large as $10 \times 10$ sites while using several orders of magnitude fewer parameters, suggesting the potential for efficient application to even larger system sizes. This remarkable efficiency enables us to probe low-energy physics across the full doping range, providing new insights into the competition between kinetic and magnetic interactions and the nature of emergent quasiparticles. Starting from the low-doping regime, where magnetic polarons dominate the low energy physics, we track their evolution with increasing doping and different next-nearest neighbor hopping amplitudes through analyses of spin and polaron correlation functions as well as the Fermi surface. Our findings demonstrate the potential of determinant-based neural quantum states with inherent fermionic sign structure, opening the way for simulating large-scale fermionic systems at any particle filling.

cond-mat.str-el↗

arXiv2025

Towards effective models for low-dimensional cuprates: From ground state Hamiltonian reconstruction to spectral functions

Understanding which minimal effective model captures the essential physics of cuprates is a key step towards unraveling the mechanism behind high-$T_c$ superconductivity. Recent measurements of the dynamical spin structure factor (DSF) in cuprate ladder compounds have indicated the presence of a large effective attraction in the single-band Hubbard model, possibly mediated by phonons. Here, we demonstrate that similar DSF features can also be captured by $t$-$J$ descriptions with or even without any attractive term. Motivated by this observation, we systematically investigate the strength and origin of different contributions to the single-band Hamiltonians by downfolding either from the three-band Emery model or the electron-phonon coupled Hubbard-Holstein model. For one-dimensional systems, we find that the extended versions of both single-band descriptions can reproduce the experimentally observed DSF signatures. Finally, we extend our analysis to two dimensions by comparing two-hole correlation functions for the different single-band models. Our results provide new insights into the long-standing question of which single-band Hamiltonian can capture the essential physics of cuprates.

cond-mat.str-el↗

arXiv2025

Machine learning applications in cold atom quantum simulators

As ultracold atom experiments become highly controlled and scalable quantum simulators, they require sophisticated control over high-dimensional parameter spaces and generate increasingly complex measurement data that need to be analyzed and interpreted efficiently. Machine learning (ML) techniques have been established as versatile tools for addressing these challenges, offering strategies for data interpretation, experimental control, and theoretical modeling. In this review, we provide a perspective on how machine learning is being applied across various aspects of quantum simulation, with a focus on cold atomic systems. Emphasis is placed on practical use cases -- from classifying many-body phases to optimizing experimental protocols and representing quantum states -- highlighting the specific contexts in which different ML approaches prove effective. Rather than presenting algorithmic details, we focus on the physical insights enabled by ML and the kinds of problems in quantum simulation where these methods offer tangible benefits.

cond-mat.quant-gas↗

arXiv2025

Realization of a doped quantum antiferromagnet with dipolar tunnelings in a Rydberg tweezer array

Doping an antiferromagnetic Mott insulator is central to our understanding of a variety of phenomena in strongly-correlated electrons, including high-temperature superconductors. To describe the competition between tunneling $t$ of hole dopants and antiferromagnetic (AFM) spin interactions $J$, theoretical and numerical studies often focus on the paradigmatic $t$-$J$ model, and the direct analog quantum simulation of this model in the relevant regime of high-particle density has long been sought. Here, we realize a doped quantum antiferromagnet with next-nearest neighbour (NNN) tunnelings $t'$ and hard-core bosonic holes using a Rydberg tweezer platform. We utilize coherent dynamics between three Rydberg levels, encoding spins and holes, to implement a tunable bosonic $t$-$J$-$V$ model allowing us to study previously inaccessible parameter regimes. We observe dynamical phase separation between hole and spin domains for $|t/J|\ll 1$, and demonstrate the formation of repulsively bound hole pairs in a variety of spin backgrounds. The interference between NNN tunnelings $t'$ and perturbative pair tunneling gives rise to light and heavy pairs depending on the sign of $t$. Using the single-site control allows us to study the dynamics of a single hole in 2D square lattice (anti)ferromagnets. The model we implement extends the toolbox of Rydberg tweezer experiments beyond spin-1/2 models to a larger class of $t$-$J$ and spin-$1$ models.

quant-ph↗

arXiv2025

Neural quantum states for emitter dynamics in waveguide QED

Quantum emitters coupled to one-dimensional waveguides constitute a paradigmatic quantum-optical platform for exploring collective phenomena in open quantum many-body systems. For appropriately spaced emitters, they realize the Dicke model, whose characteristic permutation symmetry allows for efficient exact solutions featuring superradiance. When the emitters are arbitrarily spaced, however, this symmetry is lost and general analytical solutions are no longer available. In this work, we introduce a novel numerical method to study the dynamics of such systems by extending the time-dependent neural quantum state (t-NQS) framework to open quantum systems. We benchmark our approach across a range of waveguide QED settings and compare its performance with tensor-network calculations. Our results demonstrate that the t-NQS approach is competitive with other numerical methods and highlight the potential of t-NQSs for studying open quantum many-body systems out of equilibrium.

quant-ph↗

arXiv2025

Geometric orthogonal metals: Hidden antiferromagnetism and pseudogap from fluctuating stripes

One of the key features of hole-doped cuprates is the presence of an extended pseudogap phase, whose microscopic origin has been the subject of intense investigation since its discovery and is believed to be crucial for understanding high-temperature superconductivity. Various explanations have been proposed for the pseudogap, including links to symmetry-breaking orders such as stripes or pairing, and the emergence of novel fractionalized Fermi liquid (FL*) and orthogonal metal (OM) phases. The topological nature of FL* and OM phases has been identified as scenarios compatible with a small Fermi surface without symmetry breaking, as suggested experimentally. With recent experimental and numerical studies supporting an intricate relationship between stripe order and the pseudogap phase, we here propose an alternative scenario: an orthogonal metal with a geometric origin (GOM) driven by fluctuating domain walls. The essential mechanism behind our proposal is hidden order, where the proliferation of domain walls stabilized by charge fluctuations obscures the underlying long-range antiferromagnetic order in real-space, but order is preserved in the reference frame of the background spins. As a result, well-defined fermionic quasiparticles in the form of magnetic polarons exist, which couple to $\mathbb{Z}_2$ topological excitations of the domain wall string-net condensate in the ground state and constitute a small Fermi surface. At a critical doping value, we argue that hidden order is lost, driving a transition to a regular Fermi liquid at a hidden quantum critical point (hQCP) featuring quantum critical transport properties. Our GOM framework establishes a deep connection between the antiferromagnetic, stripe, and pseudogap phases, and suggests a possible unification of superconductivity in (electron and hole) doped cuprates and heavy fermion compounds.

cond-mat.str-el↗

arXiv2025

Magnetic polarons at finite temperature: One-hole spectroscopy study

The physics of strongly correlated fermions described by Hubbard or $t$-$J$ models in the underdoped regime -- relevant for high-temperature superconductivity in cuprate compounds -- remains a subject of ongoing debate. In particular, the nature of charge carriers in this regime is poorly understood, in part due to the unusual properties of their spectral function. In this Letter, we present unbiased numerical results for the one-hole spectral function in a $t$-$J$ model at finite temperatures. Our study provides valuable insights into the underlying physics of magnetic (or spin-) polaron formation in a doped antiferromagnet (AFM). For example, we find how the suppression of spectral weight outside the magnetic Brillouin zone -- a precursor of Fermi arc formation -- disappears with increasing temperature, revealing nearly-deconfined spinon excitations of the undoped AFM. The pristine setting we consider can be directly explored using quantum simulators. Our calculations demonstrate that coherent quasiparticle peaks associated with magnetic polarons can be observed up to temperatures $T>J$ above the spin-exchange $J$, routinely obtained in such experiments. This paves the way for future studies of the fate of magnetic polarons in the pseudogap phase.

cond-mat.str-el↗

arXiv2025

Finite-temperature real-time properties of magnetic polarons in two-dimensional quantum antiferromagnets

Due to significant progress in quantum gas microscopy in recent years, there is a rapidly growing interest in real-space properties of single mobile dopands created in correlated antiferromagnetic (AFM) Mott insulators. However, a detailed numerical description remains challenging, even for simple toy models. As a consequence, previous numerical simulations for large systems were largely limited to $T=0$. To provide guidance for cold-atom experiments, numerical calculations at finite temperature are required. Here, we numerically study the real-time properties of a single mobile hole in the 2D $t$-$J$ model at finite temperature and draw a comparison to features observed at $T=0$. We find that a three-stage process of hole motion, which was reported at $T=0$, is valid even at finite temperature. However, already at low temperatures, the average hole velocity at long times is not simply proportional to the spin coupling, contrary to the $T=0$ behavior. Comparing our finite-temperature numerical results with the experimental data from quantum gas microscopy we find a qualitative disagreement: in experiment, hole spreading speeds up with increasing $J/t$, while in our numerics it slows down. The latter is consistent with the numerical findings previously reported at $T=0$.

cond-mat.quant-gas↗

arXiv2025

Transformer neural networks and quantum simulators: a hybrid approach for simulating strongly correlated systems

Owing to their great expressivity and versatility, neural networks have gained attention for simulating large two-dimensional quantum many-body systems. However, their expressivity comes with the cost of a challenging optimization due to the in general rugged and complicated loss landscape. Here, we present a hybrid optimization scheme for neural quantum states (NQS), involving a data-driven pretraining with numerical or experimental data and a second, Hamiltonian-driven optimization stage. By using both projective measurements from the computational basis as well as expectation values from other measurement configurations such as spin-spin correlations, our pretraining gives access to the sign structure of the state, yielding improved and faster convergence that is robust w.r.t. experimental imperfections and limited datasets. We apply the hybrid scheme to the ground state search for the 2D transverse field Ising model and dipolar XY model on $6\times 6$ and $10\times 10$ square lattices with a patched transformer wave function, using numerical data as well as experimental data from a programmable Rydberg quantum simulator [Chen et al., Nature 616 (2023)], and show that the information from a second measurement basis highly improves the performance. Our work paves the way for a reliable and efficient optimization of neural quantum states.

cond-mat.dis-nn↗

arXiv2025

Emergent spinon-holon Feshbach resonance in a doped Majumdar-Ghosh model

Experimental and numerical spectroscopy have revealed rich physics in antiferromagnets, in particular in frustrated and doped systems. The Majumdar-Ghosh (MG) model has an analytically known spin-disordered ground state of dimerized singlets as a result of magnetic frustration. Here we study the single-hole angle-resolved photoemission spectrum (ARPES) of a doped MG model, where we introduce a spin-hole interaction that is experimentally accessible with ultracold molecules. We report a bound spinon-holon ground state and clear signatures of a spinon-holon molecule state and polarons in the ARPES spectrum at different magnetizations. Moreover, we find signatures of an emergent Feshbach resonance with tunable interactions associated with the unbinding of the spinon and the holon. Our results provide new insights into the physics of dopants in frustrated $t$-$J$ models and establish the latter as a new platform for studies of emergent few-body phenomena.

cond-mat.str-el↗

arXiv2025

Autoregressive neural quantum states of Fermi Hubbard models

Neural quantum states (NQS) have emerged as a powerful ansatz for variational quantum Monte Carlo studies of strongly-correlated systems. Here, we apply recurrent neural networks (RNNs) and autoregressive transformer neural networks to the Fermi-Hubbard and the (non-Hermitian) Hatano-Nelson-Hubbard models in one and two dimensions. In both cases, we observe that the convergence of the RNN ansatz is challenged when increasing the interaction strength. We present a physically-motivated and easy-to-implement strategy for improving the optimization, namely, by ramping of the model parameters. Furthermore, we investigate the advantages and disadvantages of the autoregressive sampling property of both network architectures. For the Hatano-Nelson-Hubbard model, we identify convergence issues that stem from the autoregressive sampling scheme in combination with the non-Hermitian nature of the model. Our findings provide insights into the challenges of the NQS approach and make the first step towards exploring strongly-correlated electrons using this ansatz.

cond-mat.str-el↗

arXiv2024

Many-body dynamics with explicitly time-dependent neural quantum states

Simulating the dynamics of many-body quantum systems is a significant challenge, especially in higher dimensions where entanglement grows rapidly. Neural quantum states (NQS) offer a promising tool for representing quantum wavefunctions, but their application to time evolution faces scaling challenges. We introduce the time-dependent neural quantum state (t-NQS), a novel approach incorporating explicit time dependence into the neural network ansatz. This framework optimizes a single, time-independent set of parameters to solve the time-dependent Schrödinger equation across an entire time interval. We detail an autoregressive, attention-based transformer architecture and techniques for extending the model's applicability. To benchmark and demonstrate our method, we simulate quench dynamics in the 2D transverse field Ising model and the time-dependent preparation of the 2D antiferromagnetic state in a Heisenberg model, demonstrating state of the art performance, scalability, and extrapolation to unseen intervals. These results establish t-NQS as a powerful framework for exploring quantum dynamics in strongly correlated systems.

quant-ph↗

arXiv2024

Kinetic magnetism and stripe order in the antiferromagnetic bosonic ${t-J}$ model

Unraveling the microscopic mechanisms governing the physics of doped quantum magnets is key to advancing our understanding of strongly correlated quantum matter. Quantum simulation platforms, e.g., ultracold atoms in optical lattices or tweezer arrays, provide a powerful tool to investigate the interplay between spin and charge motion in microscopic detail. Here, in a new twist, we disentangle the role of particle statistics from the physics of strong correlations by exploring the strong coupling limit of doped \emph{bosonic} quantum magnets, specifically the antiferromagnetic (AFM) bosonic $t-J$ model. Using large-scale density matrix renormalization group (DMRG) calculations, we map out the phase diagram on the 2D square lattice at finite doping. In the low-doping regime, bosonic holes form partially-filled stripes, akin to those observed in high-$T_c$ cuprates. As doping increases, a transition occurs to a partially-polarized ferromagnetic (FM) phase, driven by the motion of mobile bosonic charge carriers forming Nagaoka polarons. At high doping or large $t/J$, the system evolves into a fully-polarized ferromagnet. These findings shed new light on the role of particle statistics in strongly correlated many-body systems, revealing connections to stripe formation and the physics of kinetic (i.e., Nagaoka-type) ferromagnetism. Our results may be realized in state-of-the-art quantum simulation platforms with bosonic quantum gas microscopes and Rydberg atom tweezer arrays, paving the way for future experimental studies of doped bosonic quantum magnets.

cond-mat.quant-gas↗

arXiv2024

Microscopy of bosonic charge carriers in staggered magnetic fields

The interplay of spin and charge degrees of freedom is believed to underlie various unresolved phenomena in strongly correlated systems. Quantum simulators based on neutral atoms provide an excellent testbed for investigating such phenomena and resolving their microscopic origins. Up to now, the majority of experimental and theoretical studies has focused on systems with fermionic exchange statistics. Here we expand the existing cold atom toolbox through the use of negative temperature states, enabling us to realize an antiferromagnetic, bosonic $t-J$ model in two spatial dimensions, subject to a strong staggered magnetic field in a quantum gas microscope. Through comparison of the spreading dynamics of a single hole in a Néel versus a spin-polarized initial state, we establish the relevance of memory effects resulting from the buildup of strong spin-charge correlations in the dynamics of charge carriers in antiferromagnets. We further numerically predict rich dynamics of pairs of doped holes, which we demonstrate to be bound by a similar memory effect, while their center-of-mass can expand freely. Our work paves the way for the systematic exploration of the effect of antiferromagnetic spin ordering on the properties of individual charge carriers as well as finite doping phases: Our study demonstrates that the staggered field can be used to single out the effect of antiferromagnetism and holds the prospect to prepare low-temperature states in the near future.

cond-mat.quant-gas↗

arXiv2024

Neural Network Quantum States for the Interacting Hofstadter Model with Higher Local Occupations and Long-Range Interactions

Due to their immense representative power, neural network quantum states (NQS) have gained significant interest in current research. In recent advances in the field of NQS, it has been demonstrated that this approach can compete with state-of-the-art numerical techniques, making NQS a compelling alternative, in particular for the simulation of large, two-dimensional quantum systems. In this study, we show that recurrent neural network (RNN) wave functions can be employed to study systems relevant to current research in quantum many-body physics. Specifically, we employ a 2D tensorized gated RNN to explore the bosonic Hofstadter model with a variable local Hilbert space cut-off and long-range interactions. At first, we benchmark the RNN-NQS for the Hofstadter-Bose-Hubbard (HBH) Hamiltonian on a square lattice. We find that this method is, despite the complexity of the wave function, capable of efficiently identifying and representing most ground state properties. Afterwards, we apply the method to an even more challenging model for current methods, namely the Hofstadter model with long-range interactions. This model describes Rydberg-dressed atoms on a lattice subject to a synthetic magnetic field. We study systems of size up to $12 \times 12$ sites and identify three different regimes by tuning the interaction range and the filling fraction $ν$. In addition to phases known from the HBH model at short-ranged interaction, we observe bubble crystals and Wigner crystals for long-ranged interactions. Especially interesting is the evidence of a bubble crystal phase on a lattice, as this gives experiments a starting point for the search of clustered liquid phases, possibly hosting non-Abelian anyon excitations. In our work we show that NQS are an efficient and reliable simulation method for quantum systems, which are the subject of current research.

cond-mat.dis-nn↗

arXiv2024

Spin exchange-enabled quantum simulator for large-scale non-Abelian gauge theories

A central requirement for the faithful implementation of large-scale lattice gauge theories (LGTs) on quantum simulators is the protection of the underlying gauge symmetry. Recent advancements in the experimental realizations of large-scale LGTs have been impressive, albeit mostly restricted to Abelian gauge groups. Guided by this requirement for gauge protection, we propose an experimentally feasible approach to implement large-scale non-Abelian $\mathrm{SU}(N)$ and $\mathrm{U}(N)$ LGTs with dynamical matter in $d+1$D, enabled by two-body spin-exchange interactions realizing local emergent gauge-symmetry stabilizer terms. We present two concrete proposals for $2+1$D $\mathrm{SU}(2)$ and $\mathrm{U}(2)$ LGTs, including dynamical bosonic matter and induced plaquette terms, that can be readily implemented in current ultracold-molecule and next-generation ultracold-atom platforms. We provide numerical benchmarks showcasing experimentally accessible dynamics, and demonstrate the stability of the underlying non-Abelian gauge invariance. We develop a method to obtain the effective gauge-invariant model featuring the relevant magnetic plaquette and minimal gauge-matter coupling terms. Our approach paves the way towards near-term realizations of large-scale non-Abelian quantum link models in analog quantum simulators.

cond-mat.quant-gas↗

arXiv2024

Robust stripes in the mixed-dimensional $t-J$ model

Microscopically understanding competing orders in strongly correlated systems is a key challenge in modern quantum many-body physics. For example, the origin of stripe order and its relation to pairing in the Fermi-Hubbard model remains one of the central questions, and may help to understand the origin of high-temperature superconductivity in cuprates. Here, we analyze stripe formation in the doped mixed-dimensional (mixD) variant of the $t-J$ model, where charge carriers are restricted to move only in one direction, whereas magnetic SU(2) interactions are two-dimensional. Using the density matrix renormalization group at finite temperature, we find a stable vertical stripe phase in the absence of pairing, featuring incommensurate magnetic order and long-range charge density wave profiles over a wide range of dopings. We find high critical temperatures on the order of the magnetic coupling $\sim J/2$, hence being within reach of current quantum simulators. Snapshots of the many-body state, accessible to quantum simulators, reveal hidden spin correlations in the mixD setting, whereby antiferromagnetic correlations are enhanced when considering purely the magnetic background. The proposed model can be viewed as realizing a parent Hamiltonian of the stripe phase, whose hidden spin correlations lead to the predicted resilience against quantum and thermal fluctuations.

cond-mat.quant-gas↗