Single-particle Hopping Research Articles

Mixtures of ultracold atomic gases in optical lattices with nonzero pair or counterflow hopping

We study the critical behavior of a mixture of two species of lattice bosons described by the extended Bose–Hubbard model. Our goal is to analyze in which conditions exotic orderings like pair superfluid or counterflow superfluid could be detected. We use a numerical method based on mean field approximation to calculate the phase diagram of the system, along with particle density, and order parameter profiles in selected multicritical points. We observe that the phase diagram becomes significantly renormalized in the presence of pair flow or counterflow. Furthermore, a critical particle density emerges, which isolates a new region of the phase diagram, in which the exotic order parameter exists for any value of single-particle hopping.

Majorana zero modes in fermionic wires coupled by Aharonov-Bohm cages

We devise a number-conserving scheme for the realization of Majorana zero modes in an interacting fermionic ladder coupled by Aharonov-Bohm cages. The latter provide an efficient mechanism to cancel single-particle hopping by destructive interference. The crucial parity symmetry in each wire is thus encoded in the geometry of the setup, in particular, its translation invariance. A generic nearest-neighbor interaction generates the desired correlated hopping of pairs. We exhibit the presence of an extended topological region in parameter space, first in a simplified effective model via bosonization techniques, and subsequently in a larger parameter regime with matrix-product-states numerical simulations. We demonstrate the adiabatic connection to previous models, including exactly solvable ones, and we briefly comment on possible experimental realizations in synthetic quantum platforms, like cold atomic samples.

Majorana edge modes in a spinful-particle conserving model

We show the presence of Majorana edge modes in an interacting fermionic ladder with spin in a number-conserved setting. The interchain single-particle hopping is suppressed and only a pair hopping is present between the different chains of the ladder. Additionally, the hopping along the chains is spin imbalanced and a transverse magnetic field is applied breaking time-reversal invariance. We study the robustness of the topological phase with respect to an on-site interaction between the spin-up and spin-down fermions and the spin-dependent imbalance of the hopping. The main result of the present work is that the topological phase survives for a finite region in the parameter space in the presence of interactions. The localized Majorana edge modes seem to be more stable in the case when the on-site interaction is an attraction.

Collective dynamics in a glass-former with Mari-Kurchan interactions.

We numerically study the equilibrium relaxation dynamics of a two-dimensional Mari-Kurchan glass model. The tree-like structure of particle interactions forbids both nontrivial structural motifs and the emergence of a complex free-energy landscape leading to a thermodynamic glass transition, while the finite-dimensional nature of the model prevents the existence of a mode-coupling singularity. Nevertheless, the equilibrium relaxation dynamics is shown to be in excellent agreement with simulations performed in conventional glass-formers. Averaged time correlation functions display a phenomenology typical of supercooled liquids, including the emergence of an excess signal in relaxation spectra at intermediate frequencies. We show that this evolution is accompanied by strong signatures of collective and heterogeneous dynamics that cannot be interpreted in terms of single particle hopping and emerge from dynamic facilitation. Our study demonstrates that an off-lattice interacting particle model with extremely simple structural correlations displays quantitatively realistic glassy dynamics.

Single Particle Hopping as an Indicator for Evaluating Electrocatalysts.

The design and screening of electrocatalysts for gas evolution reactions suffer from little understanding of multiphase processes at the electrode-electrolyte interface. Due to the complexity of the multiphase interface, it is still a great challenge to capture gas evolution dynamics under operando conditions to precisely portray the intrinsic catalytic performance of the interface. Here, we establish a single particle imaging method to real-time monitor a potential-dependent vertical motion or hopping of electrocatalysts induced by electrogenerated gas nanobubbles. The hopping feature of a single particle is closely correlated with intrinsic activities of electrocatalysts and thus is developed as an indicator to evaluate gas evolution performance of various electrocatalysts. This optical indicator diminishes interference from heterogeneous morphologies, non-Faradaic processes, and parasitic side reactions that are unavoidable in conventional electrochemical measurements, therefore enabling precise evaluation and high-throughput screening of catalysts for gas evolution systems.

Many-body energy invariant for T -linear resistivity

The description of dynamics of strongly correlated quantum matter is a challenge, particularly in physical situations where a quasiparticle description is absent. In such situations, however, the many-body Kubo formula from linear response theory, involving matrix elements of the current operator computed with many-body wavefunctions, remains valid. Working directly in the many-body Hilbert space and not making any reference to quasiparticles (or lack thereof), we address the puzzle of linear in temperature ($T$-linear) resistivity seen in non-Fermi liquid phases that occur in several strongly correlated condensed matter systems. We derive a simple criterion for the occurrence of $T$-linear resistivity based on an analysis of the contributions to the many-body Kubo formula, determined by an energy invariant "$f$-function" involving current matrix elements and energy eigenvalues that describes the DC conductivity of the system in the microcanonical ensemble. Using full diagonalization, we test this criterion for the $f$-function in the spinless nearest neighbor Hubbard model and in a system of Sachdev-Ye-Kitaev dots coupled by weak single particle hopping. We also study the $f$-function for the spin conductivity in the 2D Heisenberg model and arrive at similar conclusions. Our work suggests that a general principle, formulated in terms of many-body Hilbert space concepts, is at the core of the occurrence of $T$-linear resistivity in a wide range of systems, and precisely translates $T$-linear resistivity into a notion of energy scale invariance far beyond what is typically associated with quantum critical points.

Kinetic formation of trimers and multimers in a spinless fermionic chain

We study a chain of spinless fermions with a multimer hopping term which kinematically favors the formation of multimers and competes with single-particle hopping. We argue that this model generically stabilizes two different multimer phases, as well as intermediate phases where the free-fermion and multimer fluids coexist and do not spatially separate. Using density-matrix renormalization group techniques, we establish the phase diagram of the model in the case of trimers. For one of the intermediate phases, hybridization between the fermions and trimers liquids does occur and the onset of their correlations is well captured by a generalized BCS-like ansatz. The case of tetramers is finally addressed.

Constructing Hubbard models for the hydrogen chain using sliced-basis density matrix renormalization group

Sliced-basis DMRG(sb-DMRG) is used to simulate a chain of hydrogen atoms and to construct low-energy effective Hubbard-like models. The downfolding procedure first involves a change of basis to a set of atom-centered Wannier functions constructed from the natural orbitals of the exact DMRG one-particle density matrix. The Wannier function model is then reduced to a fewer-parameter Hubbard-like model, whose parameters are determined by minimizing the expectation value of the Wannier Hamiltonian in the ground state of the Hubbard Hamiltonian. This indirect variational procedure not only yields compact and simple models for the hydrogen chain, but also allows us to explore the importance of constraints in the effective Hamiltonian, such as the restricting the range of the single-particle hopping and two-particle interactions, and to assess the reliability of more conventional downfolding. The entanglement entropy for a model's ground state, cut in the middle, is an important property determining the ability of DMRG and tensor networks to simulate the model, and we study its variation with the range of the interactions. Counterintuitively, we find that shorter ranged interactions often have larger entanglement.

Quantum dot-like plasmonic modes in twisted bilayer graphene supercells

We derive a material-realistic real-space many-body Hamiltonian for twisted bilayer graphene from first principles, including both single-particle hopping terms for p z electrons and their long-range Coulomb interaction. By disentangling low- and high-energy subspaces of the electronic dispersion, we are able to utilize state-of-the-art constrained random phase approximation calculations to reliably describe the non-local background screening from the high-energy s, p x , and p y electron states which we find to be independent of the bilayer stacking and thus of the twisting angle. The twist-dependent low-energy screening from p z states is subsequently added to obtain a full screening model. We use this modeling scheme to study plasmons in electron-doped twisted bilayer graphene supercells. We find that the finite system size yields discretized plasmonic levels, which are controlled by the system size, doping level, and twisting angle. This tunability together with atomic-like charge distributions of some of the excitations renders these plasmonic excitations remarkably similar to the electronic states in electronic quantum dots. To emphasize this analogy in the following we refer to these supercells as plasmonic quantum dots. Based on a careful comparison to pristine AB-stacked bilayer graphene plasmons, we show that two kinds of plasmonic excitations arise, which differ in their layer polarization. Depending on this layer polarization the resulting plasmonic quantum dot states are either significantly or barely dependent on the twisting angle. Due to their tunability and their coupling to light, these plasmonic quantum dots form a versatile and promising platform for tailored light-matter interactions.

Hybridization of Bogoliubov Quasiparticles between Adjacent CuO_{2} Layers in the Triple-Layer Cuprate Bi_{2}Sr_{2}Ca_{2}Cu_{3}O_{10+δ} Studied by Angle-Resolved Photoemission Spectroscopy.

Hybridization of Bogoliubov quasiparticles (BQPs) between the CuO_{2} layers in the triple-layer cuprate high-temperature superconductor Bi_{2}Sr_{2}Cu_{2}Cu_{3}O_{10+δ} is studied by angle-resolved photoemission spectroscopy (ARPES). In the superconducting state, an anticrossing gap opens between the outer- and inner-BQP bands, which we attribute primarily to interlayer single-particle hopping with possible contributions from interlayer Cooper pairing. We find that the d-wave superconducting gap of both BQP bands smoothly develops with momentum without an abrupt jump in contrast to a previous ARPES study. Hybridization between the BQPs also gradually increases in going from the off nodal to the antinodal region, which is explained by the momentum dependence of the interlayer single-particle hopping. As possible mechanisms for the enhancement of the superconducting transition temperature, the hybridization between the BQPs as well as the combination of phonon modes of the triple CuO_{2} layers and spin fluctuations represented by a four-well model are discussed.

Spin-orbit-coupling-driven superfluid states in optical lattices at zero and finite temperatures

We investigate the quantum phase transitions of a two-dimensional Bose-Hubbard model in the presence of a Rashba spin-orbit coupling with and without thermal fluctuations. The interplay of single-particle hopping, strength of spin-orbit coupling, and interspin interaction leads to superfluid phases with distinct properties. With interspin interactions weaker than intraspin interactions, the spin-orbit coupling induces two finite-momentum superfluid phases. One of them is a phase-twisted superfluid that exists at low hopping strengths and reduces the domain of insulating phases. At comparatively higher hopping strengths, there is a transition from the phase-twisted to a finite momenta stripe superfluid. With interspin interactions stronger than the intraspin interactions, the system exhibits phase-twisted to ferromagnetic phase transition. At finite temperatures, the thermal fluctuations destroy the phase-twisted superfluidity and lead to a wide region of normal-fluid states. These findings can be observed in recent quantum gas experiments with spin-orbit coupling in optical lattices.

Charge and heat transport through quantum dots with local and correlated-hopping interactions

The transport properties of junctions composed of a central region tunnel-coupled to external electrodes are frequently studied within the single-impurity Anderson model with Hubbard on-site interaction. In the present work, we supplement the model with an important ingredient, namely the charge-bond interaction, also known as correlated or assisted hopping. Correlated hopping enters the second-quantised Hamiltonian, written in the Wannier representation, as an off-diagonal many-body term. Using the equation of motion technique, we study the effect of the correlated hopping on the spectral and transport characteristics of a two-terminal quantum dot. Two different Green functions (GFs) appear: one of them describes the spectral properties of the quantum dot, the other the transport properties of the system. The calculation of the transport GF requires the knowledge of the spectral one. We use decoupling procedures similar to those which properly describe the standard Anderson model within the Kondo regime and outside of it. For an arbitrary ratio $x$ between the amplitudes of correlated and single-particle hopping terms, the transport GF fulfils the $x \leftrightarrow 2-x$ symmetry of the model. The average occupation of the dot also obeys this symmetry, albeit the spectral function of the quantum dot, calculated within an analogous decoupling scheme as for the transport GF, does not. We identify the physical reason for this behavior, and propose a way to cure it. Since the correlated-hopping term breaks the particle-hole symmetry of the model and modifies all transport characteristics of the system, the detailed knowledge of its influence on measurable characteristics is a prerequisite for its experimental detection. Simple, experimentally feasible methods are proposed.

Bad metallic transport in geometrically frustrated models

We study the transport properties for a family of geometrically frustrated models on the triangular lattice with an interaction scale far exceeding the single-particle bandwidth. Starting from the interaction-only limit, which can be solved exactly, we analyze the transport and thermodynamic behavior as a function of filling and temperature at the leading non-trivial order in the single-particle hopping. Over a broad range of intermediate temperatures, we find evidence of a dc resistivity scaling linearly with temperature and with typical values far exceeding the quantum of resistance, $h/e^2$. At a sequence of commensurate fillings, the bad-metallic regime eventually crosses over into interaction induced insulating phases in the limit of low temperatures. We discuss the relevance of our results to experiments in cold-atom and moir\'e heterostructure based platforms.

Exploring universal and nonuniversal regimes of trimers from three-body interactions in one-dimensional lattices

We investigate the formation of trimers in an infinite one-dimensional lattice model of hard-core particles with single-particle hopping $t$ and and nearest-neighbour two-body $U$ and three-body $V$ interactions of relevance to Rydberg atoms and polar molecules. For sufficiently attractive $U\leq-2t$ and positive $V>0$ a large trimer is stabilized, which persists as $V\rightarrow \infty$, while both attractive $U\leq0$ and $V\leq0$ bind a small trimer. The excited state above this small trimer is also bound and has a large extent; its behavior as $V\rightarrow -\infty$ resembles that of the large ground-state trimer. These large bound states appear to admit a continuum description. Furthermore, we find that in the limit $V>>t$, $U<-2t$ the bound-state behavior qualitatively evolves with larger $|U|$ from a state described by the scattering of three far separated particles to a state of a compact dimer scattering with a single particle.

Pair hopping in systems of strongly interacting hard-core bosons

We have used the Stochastic Series Expansion quantum Monte Carlo method to study interacting hard-core bosons on the square lattice, with pair-hopping processes supplementing the standard single-particle hopping. Such pair hopping arises in effective models for frustrated quantum magnets. Our goal is to investigate the effects of the pair hopping process on the commonly observed superfluid, insulating (Mott), and super-solid ground-state phases in the standard hard-core boson model with various interaction terms. The model is specifically motivated by the observation of finite dispersion of 2-magnon bound states in neutron diffraction experiments SrCu$_2$(BO$_3$)$_2$. Our results show that the pair hopping has different effects on Mott phases at different filling fractions, "melting" them at different critical pair-hopping amplitudes. Thus, it appears that pair hopping may have an important role in determining which out of a potentially large number of Mott phases (stabilized by details of the charge-diagonal interaction terms) actually survive the totality of quantum fluctuations present.

Realization of density-dependent Peierls phases to engineer quantized gauge fields coupled to ultracold matter

Gauge fields that appear in models of high-energy and condensed matter physics are dynamical quantum degrees of freedom due to their coupling to matter fields. Since the dynamics of these strongly correlated systems is hard to compute, it was proposed to implement this basic coupling mechanism in quantum simulation platforms with the ultimate goal to emulate lattice gauge theories. Here, we realize the fundamental ingredient for a density-dependent gauge field acting on ultracold fermions in an optical lattice by engineering non-trivial Peierls phases that depend on the site occupations. We propose and implement a Floquet scheme that relies on breaking time-reversal symmetry (TRS) by driving the lattice simultaneously at two frequencies which are resonant with the onsite interactions. This induces density-assisted tunnelling processes that are controllable in amplitude and phase. We demonstrate techniques in a Hubbard dimer to quantify the amplitude and to directly measure the Peierls phase with respect to the single-particle hopping. The tunnel coupling features two distinct regimes as a function of the modulation amplitudes, which can be characterised by a $\mathbb{Z}_2$-invariant. Moreover, we provide a full tomography of the winding structure of the Peierls phase around a Dirac point that appears in the driving parameter space.

Many-body localization due to correlated disorder in Fock space

In presence of strong enough disorder one dimensional systems of interacting spinless fermions at non-zero filling factor are known to be in a many body localized phase. When represented in Fock space, the Hamiltonian of such a system looks like that of a single particle hopping on a Fock lattice in the presence of a random disordered potential. The coordination number of the Fock lattice increases linearly with the system size L in 1D. Thus in the thermodynamic limit, the disordered interacting problem in 1D maps on to an Anderson model with infinite coordination number. Despite this, this system displays localization which appears counterintuitive. A close observation of the on-site disorders on the Fock lattice reveals a large degree of correlation among them as they are derived from an exponentially smaller number of on-site disorders in real space. This indicates that the correlations between the on-site disorders on a Fock lattice has a strong effect on the localization properties of the corresponding many-body system. In this work we perform a systematic quantitative exploration of the nature of correlations of the Fock space potential required for localization. Without changing the typical strength of the on-site disorders in Fock lattice we show that changing the correlation strength can induce thermalization or localization in systems. From among the various functional forms of correlations we study through exact diagonalization, we find that only the linear variation of correlations with Hamming distance in Fock space is able to drive a thermal-MBL phase transition where the transition is driven by the correlation strength. Systems with the other forms of correlations we study are found to be ergodic.

Floquet Mechanism for Non-Abelian Fractional Quantum Hall States.

Three-body correlations, which arise between spin-polarized electrons in the first excited Landau level, are believed to play a key role in the emergence of enigmatic non-Abelian fractional quantum Hall (FQH) effects. Inspired by recent advances in Floquet engineering, we investigate periodic driving of anisotropic two-body interactions as a route for controllably creating and tuning effective three-body interactions in the FQH regime. We develop an analytic formalism to describe this Floquet-FQH protocol, which is distinct from previous approaches that instead focus on band structure engineering via modulation of single-particle hopping terms. By systematically analyzing the resulting interactions using generalized pseudopotentials, we show that our Floquet-FQH approach leads to repulsive as well as attractive three-body interactions that are highly tunable and support a variety of non-Abelian multicomponent FQH states. Finally, we propose an implementation of the protocol in optically dressed ultracold polar molecules with modulated Rabi frequencies.

Dimensional crossover in the quasi-one-dimensional superconductor Tl2Mo6Se6

Long-range order in quasi-one-dimensional (q1D) arrays of superconducting nanowires is established via a dimensional crossover from a fluctuating 1D regime to a phase-coherent 3D ground state. If a homogeneous crystalline superconductor exhibits sufficiently high uniaxial anisotropy, a similar 1D$\rightarrow$3D crossover has been predicted to occur, provided that single-particle hopping transverse to the 1D axis is absent in the normal state. Here we present magnetic penetration depth and electrical transport data in single crystals of q1D Tl$_2$Mo$_6$Se$_6$, which reveal a 1D$\rightarrow$3D superconducting dimensional crossover. Both experimental techniques uncover multiple energy scales within the superconducting transition, which describe a sequence of fluctuating regimes. As the temperature is reduced below $T_{ons}=$~6.7~K, 1D pairing fluctuations are replaced by 1D phase slips below $T_p\sim$~5.9~K. These give way to 3D phase fluctuations below $T_{ab}=$~4.9~K, prior to dimensional crossover at $T_{x2}\sim$~4.4~K. The electrical resistivity below $T_{ab}$ is quantitatively consistent with the establishment of phase coherence through gradual binding of Josephson vortex strings to form 3D loops. An anomalously low superfluid density persist down to $\sim$3~K before rising steeply --- in agreement with a theoretical model for crossovers in q1D superconductors, and suggesting that a small population of unbound, weakly-pinned vortices survives below the crossover. The observation of a dimensional crossover within the superconducting state has important consequences for the low-temperature normal state in Tl$_2$Mo$_6$Se$_6$ and similar q1D metals, which may exhibit one-dimensional behavior over far greater temperature ranges than band structure calculations suggest.

Sliding states of a soft-colloid cluster crystal: Cluster versus single-particle hopping.

We study a two-dimensional model for interacting colloidal particles which displays spontaneous clustering. Within this model we investigate the competition between the pinning to a periodic corrugation potential and a sideways constant pulling force which would promote a sliding state. For a few sample particle densities and amplitudes of the periodic corrugation potential we investigate the depinning from the statically pinned to the dynamically sliding regime. This sliding state exhibits the competition between a dynamics where entire clusters are pulled from a minimum to the next and a dynamics where single colloids or smaller groups leave a cluster and move across the corrugation energy barrier to join the next cluster downstream in the force direction. Both kinds of sliding states can occur either coherently across the entire sample or asynchronously: the two regimes result in different average mobilities. Finite temperature tends to destroy separate sliding regimes, generating a smoother dependence of the mobility on the driving force.