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arXiv:2209.08815 · Physical review. B./Physical review. B

Genuine multipartite entanglement in a one-dimensional Bose-Hubbard model with frustrated hopping

Sudipto Singha Roy, Leon Carl, Philipp Hauke

Published Nov 29, 2022• 11 citations
arXivHTMLPDF

Abstract

Frustration and quantum entanglement are two exotic quantum properties in quantum many-body systems. However, despite several efforts, an exact relationship between them remains elusive. In this work, we explore the relationship between frustration and quantum entanglement in a physical model describing strongly correlated ultracold bosonic atoms in optical lattices. In particular, we consider the one-dimensional Bose-Hubbard model comprising both nearest-neighbor (${t}_{1}$) and frustrated next-nearest neighbor (${t}_{2}$) hoppings and examine how the interplay of on-site interaction ($U$) and hoppings results in different quantum correlations dominating the ground state of the system. We then analyze the behavior of quantum entanglement in the model. In particular, we compute genuine multipartite entanglement as quantified through the generalized geometric measure and make a comparative study with bipartite entanglement and other relevant order parameters. We observe that genuine multipartite entanglement has a very rich behavior throughout the considered parameter regime and frustration does not necessarily favor generating a high amount of it. Moreover, we show that in the region with strong quantum fluctuations, the particles remain highly delocalized in all momentum modes and share a very low amount of both bipartite and multipartite entanglement. Our work illustrates the necessity to give separate attention to dominating ordering behavior and quantum entanglement in the ground state of strongly correlated systems.

DOI
10.1103/physrevb.106.195158

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Frustration and quantum entanglement are two exotic quantum properties in quantum many-body systems. However, despite several efforts, an exact relationship between them remains elusive. In this work, we explore the relationship between frustration and quantum entanglement in a physical model describing strongly correlated ultracold bosonic atoms in optical lattices. In particular, we consider the one-dimensional Bose-Hubbard model comprising both nearest-neighbor (t1{t}_{1}t1​) and frustrated next-nearest neighbor (t2{t}_{2}t2​) hoppings and examine how the interplay of on-site interaction (UUU) and hoppings results in different quantum correlations dominating the ground state of the system. We then analyze the behavior of quantum entanglement in the model. In particular, we compute genuine multipartite entanglement as quantified through the generalized geometric measure and make a comparative study with bipartite entanglement and other relevant order parameters. We observe that genuine multipartite entanglement has a very rich behavior throughout the considered parameter regime and frustration does not necessarily favor generating a high amount of it. Moreover, we show that in the region with strong quantum fluctuations, the particles remain highly delocalized in all momentum modes and share a very low amount of both bipartite and multipartite entanglement. Our work illustrates the necessity to give separate attention to dominating ordering behavior and quantum entanglement in the ground state of strongly correlated systems.
The study of geometrically frustrated many-body quantum systems is of central importance to uncover novel quantum mechanical effects. We design a scheme where ultracold bosons trapped in a one-dimensional state-dependent optical lattice are modeled by a frustrated Bose-Hubbard Hamiltonian. A derivation of the Hamiltonian parameters based on Cesium atoms, further show large tunability of contact and nearest-neighbor interactions. For pure contact repulsion, we discover the presence of two phases peculiar to frustrated quantum magnets: the bond-order-wave insulator with broken inversion symmetry and a chiral superfluid. When the nearest-neighbor repulsion becomes sizable, a further density-wave insulator with broken translational symmetry can appear. We show that the phase transition between the two spontaneously symmetry-broken phases is continuous, thus representing a one-dimensional deconfined quantum critical point not captured by the Landau-Ginzburg-Wilson symmetry-breaking paradigm. Our results provide a solid ground to unveil the novel quantum physics induced by the interplay of nonlocal interactions, geometrical frustration, and quantum fluctuations.
The Hubbard model underlies our understanding of strongly correlated materials. Whereas its standard form only comprises interactions between particles at the same lattice site, extending it to encompass long-range interactions is predicted to profoundly alter the quantum behavior of the system. We realize the extended Bose-Hubbard model for an ultracold gas of strongly magnetic erbium atoms in a three-dimensional optical lattice. Controlling the orientation of the atomic dipoles, we reveal the anisotropic character of the onsite interaction and hopping dynamics and their influence on the superfluid-to-Mott insulator quantum phase transition. Moreover, we observe nearest-neighbor interactions, a genuine consequence of the long-range nature of dipolar interactions. Our results lay the groundwork for future studies of exotic many-body quantum phases.
We investigate the behavior of entanglement in the ground state of a doped one-dimensional lattice, where the particles interact via the quantum t-J model, which can be obtained from the Hubbard Hamiltonian with large onsite interactions. For different values of the electron concentration, the rich phase diagram exhibits both polynomial and exponential decay of bipartite quantum entanglement, with increasing lattice distance. This respectively characterizes the properties of the Luttinger liquid and the electron-hole phase separation regions of the phase diagram. Interestingly, at low electron concentration, where the spin-gap opens, the ground state turns out to be a long-ranged resonating valence bond gas. We observe that the phase diagram remains qualitatively unchanged even when additional next-nearest-neighbor spin couplings are introduced, though the phase boundaries are dependent on the relative strength between the nearest and next-nearest neighbor interactions, which the decay patterns of entanglement can capture. A key finding of the study relates to the genuine multipartite entanglement of the ground state of the model at low electron densities. We observe that for fixed values of the electron density, multipartite entanglement remains immutable under perturbative or sudden changes of system parameters, a phenomenon termed as adiabatic freezing. The phenomenon is absent in the anisotropic undoped limit of the system. It is to be noted that multipartite entanglement, in general, is sensitive to external perturbation, as observed in several systems, and hitherto, no freezing behavior has been reported.
The Hubbard model underlies our understanding of strongly correlated materials. Whereas its standard form only comprises interactions between particles at the same lattice site, extending it to encompass long-range interactions is predicted to profoundly alter the quantum behavior of the system. We realize the extended Bose-Hubbard model for an ultracold gas of strongly magnetic erbium atoms in a three-dimensional optical lattice. Controlling the orientation of the atomic dipoles, we reveal the anisotropic character of the onsite interaction and hopping dynamics and their influence on the superfluid-to-Mott insulator quantum phase transition. Moreover, we observe nearest-neighbor interactions, a genuine consequence of the long-range nature of dipolar interactions. Our results lay the groundwork for future studies of exotic many-body quantum phases.
A system of ultracold atoms in an optical lattice provides a powerful platform for quantum simulation. In our laboratory, we use a quantum gas microscope to tune lattice parameters not only in a global scale but also at the level of individual sites. This allows us to control and detect the quantum state of interacting many-body systems as well as to engineer a broad class of Hamiltonians with high fidelity. Leveraging this versatility, we can realize several types of strongly correlated bosonic systems, which present intriguing behaviors and implement novel phases of matter. Analyzing snapshots of the atomic distribution with single-site resolution, we measure correlations and entanglement within these systems to reveal their main features, including non-equilibrium dynamics and quantum phase transitions. In this thesis, I present the works performed by our team for four different types of systems. First of all, I briefly introduce the behavior of a 1D disordered system in the critical regime between the thermal and the many-body-localized phases. In particular, we discuss what happens when a disordered and a non-disordered region are coupled via a single site. We find evidence for accelerated transport of thermal inclusion into the localized region, which shows the existence of a quantum avalanche, i.e. thermalization via accelerated transport throughout the localized system. In the second part, we realize a fractional quantum Hall state using an artificial gauge field, by implementing an adiabatic preparation protocol. We identify a topological phase transition in our system and characterize several key physical features expected for a Laughlin state by measuring density correlations and Hall conductivity. The next topic of this thesis relates to quantum magnetism. Mapping nearest hopping in a tilted optical lattice to spin flips, we realize a finite one-dimensional chain of 1/2-spins with closed boundary conditions. We perform an in-depth investigation on behaviors shown across the quantum phase transition between paramagnetic and antiferromagnetic ground states, including the evolution of the magnetization and Néel order parameter. Also, we find evidence for quantum superposition at the many-body level as a result of geometric frustration. In the last chapter, I report the experimental realization of a novel dipolar Bose-Hubbard Hamiltonian, based on a strongly tilted lattice system. When the tilt becomes the dominant energy scale, the Hamiltonian is fragmented, and the system behaves in a way that conserves dipole moment. Starting from a 1D chain of unity filled sites, we generate individual dipolar and anti-dipolar excitations at desired pinpoints. We observe quantum walks of these dipolar quasi-particles as well as their scattering dynamics, which allows us to study this new type of Hamiltonian using a bottom-up approach.
We investigate the behavior of genuine multiparticle entanglement, as quantified by the generalized geometric measure, in gapless-to-gapped quantum transitions of one- and two-dimensional quantum spin models. The investigations are performed in the exactly solvable one-dimensional XYXYXY models, as well as two-dimensional frustrated J1−−J2{J}_{1}--{J}_{2}J1​−−J2​ models, including the Shastry-Sutherland model. The generalized geometric measure shows nonmonotonic features near such transitions in the frustrated quantum systems. We also compare the features of the generalized geometric measure near the quantum critical points with the same for measures of bipartite quantum correlations. The multipartite quantum correlation measure turns out to be a better indicator of quantum critical points than the bipartite measures, especially for two-dimensional models.