arXiv subjects

Geoffrey Ji

Publications and source records attributed to Geoffrey Ji.

12 recordsLinked to original sources

arXiv2022

Frustration- and doping-induced magnetism in a Fermi-Hubbard simulator

Geometrical frustration in strongly correlated systems can give rise to a plethora of novel ordered states and intriguing magnetic phases, such as quantum spin liquids. Promising candidate materials for such phases can be described by the Hubbard model on an anisotropic triangular lattice, a paradigmatic model capturing the interplay between strong correlations and magnetic frustration. However, the fate of frustrated magnetism in the presence of itinerant dopants remains unclear, as well as its connection to the doped phases of the square Hubbard model. Here we investigate the local spin order of a Hubbard model with controllable frustration and doping, using ultracold fermions in anisotropic optical lattices continuously tunable from a square to a triangular geometry. At half-filling and strong interactions $U/t \sim 9$, we observe at the single-site level how frustration reduces the range of magnetic correlations and drives a transition from a collinear N\'eel antiferromagnet to a short-range correlated 120$^{\circ}$ spiral phase. Away from half-filling, the triangular limit shows enhanced antiferromagnetic correlations on the hole-doped side and a reversal to ferromagnetic correlations at particle dopings above 20%, hinting at the role of kinetic magnetism in frustrated systems. This work paves the way towards exploring possible chiral ordered or superconducting phases in triangular lattices and realizing t-t' square lattice Hubbard models that may be essential to describe superconductivity in cuprate materials.

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↗

arXiv2021

Coupling a mobile hole to an antiferromagnetic spin background: Transient dynamics of a magnetic polaron

Understanding the interplay between charge and spin and its effects on transport is a ubiquitous challenge in quantum many-body systems. In the Fermi-Hubbard model, this interplay is thought to give rise to magnetic polarons, whose dynamics may explain emergent properties of quantum materials such as high-temperature superconductivity. In this work, we use a cold-atom quantum simulator to directly observe the formation dynamics and subsequent spreading of individual magnetic polarons. Measuring the density- and spin-resolved evolution of a single hole in a 2D Hubbard insulator with short-range antiferromagnetic correlations reveals fast initial delocalization and a dressing of the spin background, indicating polaron formation. At long times, we find that dynamics are slowed down by the spin exchange time, and they are compatible with a polaronic model with strong density and spin coupling. Our work enables the study of out-of-equilibrium emergent phenomena in the Fermi-Hubbard model, one dopant at a time.

cond-mat.quant-gas↗

arXiv2020

Correlator Convolutional Neural Networks: An Interpretable Architecture for Image-like Quantum Matter Data

Machine learning models are a powerful theoretical tool for analyzing data from quantum simulators, in which results of experiments are sets of snapshots of many-body states. Recently, they have been successfully applied to distinguish between snapshots that can not be identified using traditional one and two point correlation functions. Thus far, the complexity of these models has inhibited new physical insights from this approach. Here, using a novel set of nonlinearities we develop a network architecture that discovers features in the data which are directly interpretable in terms of physical observables. In particular, our network can be understood as uncovering high-order correlators which significantly differ between the data studied. We demonstrate this new architecture on sets of simulated snapshots produced by two candidate theories approximating the doped Fermi-Hubbard model, which is realized in state-of-the art quantum gas microscopy experiments. From the trained networks, we uncover that the key distinguishing features are fourth-order spin-charge correlators, providing a means to compare experimental data to theoretical predictions. Our approach lends itself well to the construction of simple, end-to-end interpretable architectures and is applicable to arbitrary lattice data, thus paving the way for new physical insights from machine learning studies of experimental as well as numerical data.

cond-mat.str-el↗

arXiv2019

String patterns in the doped Hubbard model

Understanding strongly correlated quantum many-body states is one of the most difficult challenges in modern physics. For example, there remain fundamental open questions on the phase diagram of the Hubbard model, which describes strongly correlated electrons in solids. In this work we realize the Hubbard Hamiltonian and search for specific patterns within the individual images of many realizations of strongly correlated ultracold fermions in an optical lattice. Upon doping a cold-atom antiferromagnet we find consistency with geometric strings, entities that may explain the relationship between hole motion and spin order, in both pattern-based and conventional observables. Our results demonstrate the potential for pattern recognition to provide key insights into cold-atom quantum many-body systems.

cond-mat.quant-gas↗

arXiv2018

Classifying Snapshots of the Doped Hubbard Model with Machine Learning

Quantum gas microscopes for ultracold atoms can provide high-resolution real-space snapshots of complex many-body systems. We implement machine learning to analyze and classify such snapshots of ultracold atoms. Specifically, we compare the data from an experimental realization of the two-dimensional Fermi-Hubbard model to two theoretical approaches: a doped quantum spin liquid state of resonating valence bond type, and the geometric string theory, describing a state with hidden spin order. This approach considers all available information without a potential bias towards one particular theory by the choice of an observable and can therefore select the theory which is more predictive in general. Up to intermediate doping values, our algorithm tends to classify experimental snapshots as geometric-string-like, as compared to the doped spin liquid. Our results demonstrate the potential for machine learning in processing the wealth of data obtained through quantum gas microscopy for new physical insights.

cond-mat.quant-gas↗

arXiv2018

Quantum state engineering of a Hubbard system with ultracold fermions

Accessing new regimes in quantum simulation requires the development of new techniques for quantum state preparation. We demonstrate the quantum state engineering of a strongly correlated many-body state of the two-component repulsive Fermi-Hubbard model on a square lattice. Our scheme makes use of an ultralow entropy doublon band insulator created through entropy redistribution. After isolating the band insulator, we change the underlying potential to expand it into a half-filled system. The final many-body state realized shows strong antiferromagnetic correlations and a temperature below the exchange energy. We observe an increase in entropy, which we find is likely caused by the many-body physics in the last step of the scheme. This technique is promising for low-temperature studies of cold-atom-based lattice models.

cond-mat.quant-gas↗

arXiv2017

Parton theory of magnetic polarons: Mesonic resonances and signatures in dynamics

When a mobile hole is moving in an anti-ferromagnet it distorts the surrounding Neel order and forms a magnetic polaron. Such interplay between hole motion and anti-ferromagnetism is believed to be at the heart of high-Tc superconductivity in cuprates. We study a single hole described by the t-Jz model with Ising interactions between the spins in 2D. This situation can be experimentally realized in quantum gas microscopes. When the hole hopping is much larger than couplings between the spins, we find strong evidence that magnetic polarons can be understood as bound states of two partons, a spinon and a holon carrying spin and charge quantum numbers respectively. We introduce a microscopic parton description which is benchmarked by comparison with results from advanced numerical simulations. Using this parton theory, we predict a series of excited states that are invisible in the spectral function and correspond to rotational excitations of the spinon-holon pair. This is reminiscent of mesonic resonances observed in high-energy physics, which can be understood as rotating quark antiquark pairs. We also apply the strong coupling parton theory to study far-from equilibrium dynamics of magnetic polarons observable in current experiments with ultracold atoms. Our work supports earlier ideas that partons in a confining phase of matter represent a useful paradigm in condensed-matter physics and in the context of high-Tc superconductivity. While direct observations of spinons and holons in real space are impossible in traditional solid-state experiments, quantum gas microscopes provide a new experimental toolbox. We show that, using this platform, direct observations of partons in and out-of equilibrium are possible. Extensions of our approach to the t-J model are also discussed. Our predictions in this case are relevant to current experiments with quantum gas microscopes for ultracold atoms.

cond-mat.quant-gas↗

arXiv2017

Site-resolved measurement of the spin-correlation function in the Hubbard model

Exotic phases of matter can emerge from strong correlations in quantum many-body systems. Quantum gas microscopy affords the opportunity to study these correlations with unprecedented detail. Here we report site-resolved observations of antiferromagnetic correlations in a two-dimensional, Hubbard-regime optical lattice and demonstrate the ability to measure the spin-correlation function over any distance. We measure the in-situ distributions of the particle density and magnetic correlations, extract thermodynamic quantities from comparisons to theory, and observe statistically significant correlations over three lattice sites. The temperatures that we reach approach the limits of available numerical simulations. The direct access to many-body physics at the single-particle level demonstrated by our results will further our understanding of how the interplay of motion and magnetism gives rise to new states of matter.

cond-mat.quant-gas↗

arXiv2016

Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms

Many exotic phenomena in strongly correlated electron systems emerge from the interplay between spin and motional degrees of freedom. For example, doping an antiferromagnet gives rise to interesting phases including pseudogap states and high-temperature superconductors. A promising route towards achieving a complete understanding of these materials begins with analytic and computational analysis of simplified models. Quantum simulation has recently emerged as a complementary approach towards understanding these models. Ultracold fermions in optical lattices offer the potential to answer open questions on the low-temperature regime of the doped Hubbard model, which is thought to capture essential aspects of the cuprate superconductor phase diagram but is numerically intractable in that parameter regime. A new perspective is afforded by quantum gas microscopy of fermions, which allows readout of magnetic correlations at the site-resolved level. Here we report the realization of an antiferromagnet in a repulsively interacting Fermi gas on a 2D square lattice of approximately 80 sites. Using site-resolved imaging, we detect (finite-size) antiferromagnetic long-range order (LRO) through the development of a peak in the spin structure factor and the divergence of the correlation length that reaches the size of the system. At our lowest temperature of T/t = 0.25(2) we find strong order across the entire sample. Our experimental platform enables doping away from half filling, where pseudogap states and stripe ordering are expected, but theoretical methods become numerically intractable. In this regime we find that the antiferromagnetic LRO persists to hole dopings of about 15%, providing a guideline for computational methods. Our results demonstrate that quantum gas microscopy of ultracold fermions in optical lattices can now address open questions on the low-temperature Hubbard model.

cond-mat.quant-gas↗

arXiv2016

Site-resolved imaging of a fermionic Mott insulator

The complexity of quantum many-body systems originates from the interplay of strong interactions, quantum statistics, and the large number of quantum-mechanical degrees of freedom. Probing these systems on a microscopic level with single-site resolution offers important insights. Here we report site-resolved imaging of two-component fermionic Mott insulators, metals, and band insulators using ultracold atoms in a square lattice. For strong repulsive interactions we observe two-dimensional Mott insulators containing over 400 atoms. For intermediate interactions, we observe a coexistence of phases. From comparison to theory we find trap-averaged entropies per particle of $1.0\,k_{\mathrm{B}}$. In the band-insulator we find local entropies as low as $0.5\,k_{\mathrm{B}}$. Access to local observables will aid the understanding of fermionic many-body systems in regimes inaccessible by modern theoretical methods.

cond-mat.quant-gas↗

arXiv2011

Electron shielding of vortons in high-density quark matter

We consider the the effect of the electron cloud about a vorton in the CFL-$K^0$ high-density phase by numerically solving the ultrarelativistic Thomas-Fermi equation about a toroidal charge. Including electrons removes the electric monopole contribution to the energy, and noticeably decreases the equilibrium radius of these stable vortex loops.

nucl-th↗