Direct observation of incommensurate magnetism in Hubbard chains

Salomon, Guillaume; Koepsell, Joannis; Vijayan, Jayadev; Hilker, Timon A.; Nespolo, Jacopo; Pollet, Lode; Bloch, Immanuel; Groß, Christian

doi:10.1038/s41586-018-0778-7

Cited by 87 publications

(92 citation statements)

References 38 publications

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“…Modelling and simulating such systems can in some instances only be achieved through the use of engineered, controllable systems that operate in the quantum regime [1]. Efforts to build quantum simulators have already demonstrated great promise at this early stage [10], mainly led by the ultracold atom community [11][12][13][14][15][16][17]. More broadly, quantum simulations of many-body fermionic systems have been carried out in a range of experimental systems such as quantum dot lattices [18], dopant atoms [19], superconducting circuits [20] and trapped ions [21].…”

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confidence: 99%

Nagaoka ferromagnetism observed in a quantum dot plaquette

Dehollain

Mukhopadhyay

Michal

et al. 2020

Nature

112

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Engineered, highly-controllable quantum systems hold promise as simulators of emergent physics beyond the capabilities of classical computers [1]. An important problem in many-body physics is itinerant magnetism, which originates purely from long-range interactions of free electrons and whose existence in real systems has been subject to debate for decades [2,3]. Here we use a quantum simulator consisting of a four-site square plaquette of quantum dots [4] to demonstrate Nagaoka ferromagnetism [5]. This form of itinerant magnetism has been rigorously studied theoretically [6][7][8][9] but has remained unattainable in experiment. We load the plaquette with three electrons and demonstrate the predicted emergence of spontaneous ferromagnetic correlations through pairwise measurements of spin. We find the ferromagnetic ground state is remarkably robust to engineered disorder in the on-site potentials and can induce a transition to the low-spin state by changing the plaquette topology to an open chain. This demonstration of Nagaoka ferromagnetism highlights that quantum simulators can be used to study physical phenomena that have not yet been observed in any system before. The work also constitutes an important step towards large-scale quantum dot simulators of correlated electron systems.The potential impact of discovering and understanding exotic forms of magnetism and superconductivity is one of the largest motivations for research in condensedmatter physics. These quantum mechanically governed effects result from the strong correlations that arise between interacting electrons. Modelling and simulating such systems can in some instances only be achieved through the use of engineered, controllable systems that operate in the quantum regime [1]. Efforts to build quantum simulators have already demonstrated great promise at this early stage [10], mainly led by the ultracold atom * These authors contributed equally to this work. † e-mail: l.m.k.vandersypen@tudelft.nl community [11-17]. More broadly, quantum simulations of many-body fermionic systems have been carried out in a range of experimental systems such as quantum dot lattices [18], dopant atoms [19], superconducting circuits [20] and trapped ions [21]. Electrostatically defined semiconductor quantum dots [22][23][24] have been proposed as excellent candidates for quantum simulations [25][26][27]. Their ability to reach thermal energies far below the hopping and on-site interaction energies enable access to previously unexplored material phases. Quantum dot systems have already achieved success in realising simulations of Mott-insulator physics in linear arrays [28]. Additionally, the feasibility to extend these systems into 2D lattices has recently been demonstrated [4,[29][30][31][32], including the ability to perform measurements of spin correlations [4]. As a result, quantum dot systems are now prime candidates for exploring how superconductivity and magnetism emerge in strongly-correlated electron systems [33][34][35].The emergence of magnetism in purely i...

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confidence: 99%

Nagaoka ferromagnetism observed in a quantum dot plaquette

Dehollain

Mukhopadhyay

Michal

et al. 2020

Nature

112

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“…After solving the dynamics governed by the periodic Hamiltonian, the time-evolution in the original frame can be simply mapped back by applying the inverse of the unitary. The underlying idea -albeit with site-dependent instead of time-dependent unitaries -has been employed to study spiral magnetism in doped Hubbard models in the context of high-temperature cuprate superconductors [30][31][32] and with recent cold atom experiments [33]. For coplanar spirals the Hubbard model in the spin rotated frame becomes translationally invariant efficiently treatable via Bloch waves even for incommensurate spirals.…”

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confidence: 99%

Floquet time spirals and stable discrete-time quasicrystals in quasiperiodically driven quantum many-body systems

2019

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We analyse quasi-periodically driven quantum systems that can be mapped exactly to periodically driven ones and find Floquet Time Spirals in analogy with spatially incommensurate spiral magnetic states. Generalising the mechanism to many-body systems we discover that a form of discrete time-translation symmetry breaking can also occur in quasi-periodically driven systems. We construct a discrete time quasi-crystal stabilised by many-body localisation. Crucially, it persists also under perturbations that break the equivalence with periodic systems. As such it provides evidence of a stable quasi-periodically driven many-body quantum system which does not heat up to the featureless infinite temperature state.The dynamics of a quantum system governed by a generic time-dependent Hamiltonian is generally hard to analyse because to reach a certain point in time the entire history of evolution is required. Hence, simulations quickly become computationally unfeasible, especially for many-body systems. There are some exceptions such as periodically driven (PD) systems, i.e. whose Hamiltonian is periodic in time H(t + T ) = H(t), for which Floquet theory significantly reduces the effort to simulate the dynamics by decomposing the wave function to Floquet modes periodic over one time period T up to phases. PD systems are of immense recent interest as they have been exploited extensively for engineering sought after Hamiltonians [1-5], controlling quantum systems [6][7][8][9][10][11][12][13][14]and realising non-equilibrium quantum phases [15][16][17]. For instance, the proper combination of periodic driving and many-body localisaton [18] gave birth to the discovery of discrete time crystals (DTCs) [19][20][21][22][23][24][25][26], a new quantum phase with broken discrete time translation symmetry.Here, we address the intriguing question whether quasi-periodically driven (QPD) quantum systems can show features similar to time-crystalline behaviour of periodically driven ones? Normally it is expected -apart for special integrable systems with momentum conservation [27] -that QPD systems generically heat up to featureless infinite-temperature states [28,29]. Hence, a related important question we address is whether there are interacting QPD quantum systems with a stable nontrivial steady state? Of course, generally such questions are hard to answer because Floquet theory, which provides an elegant framework for the analysis of PD quantum systems normally does not generalise to aperiodic time-dependencies. Here, we address the above questions by studying a class of QPD systems which can be efficiently treated within Floquet theory. This allows us to find QPD steady states with time-crystalline behaviour at special fine-tuned points whose stability to generic perturbations is studied with exact diagonalisation.The main idea is that special cases of originally QPD Hamiltonian H can be mapped exactly to a periodic(a) (b) Δθ 2Δθ FIG. 1. (a) Mapping a quasi-periodic magnetic spiral to a periodic ferromagnet. (b)Illustration of the tw...

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“…(3) and(8) we have ρ(k) = 1/2π andκ(k) = −2 cos k − µ − 2u − H. Together with Eq. (5) and the definitions(14) they imply that in phase II v c = 2 sin(πn) and v s = 0.…”

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confidence: 69%

“…Ultracold fermions in optical lattices provide realizations of the Hubbard model in a very clean environment with a high degree of control over temperature, chemical potential, on-site repulsion, tunneling amplitude and even dimensionality. Very recently, experimental realizations of the repulsive one-dimensional (1D) Hubbard model were reported together with observations of antiferromagnetic spin correlations [6,7], incommensurate magnetism [8] and measurement of non-equilibrium transport properties [9]. The many-body physics of 1D systems presents features which distinguish them from their higher-dimensional counterparts.…”

Section: Introductionmentioning

confidence: 99%

Quantum critical behavior and thermodynamics of the repulsive one-dimensional Hubbard model in a magnetic field

2020

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Even though the Hubbard model is one of the most fundamental models of highly correlated electrons, analytical and numerical data describing its thermodynamics at nonzero magnetization are relatively scarce. We present a detailed investigation of the thermodynamic properties for the one dimensional repulsive Hubbard model in the presence of an arbitrary magnetic field for all values of the filling fraction and temperatures as low as T ∼ 0.005 t. Our analysis is based on the system of integral equations derived in the quantum transfer matrix framework. We determine the critical exponents of the quantum phase transitions and also provide analytical derivations for some of the universal functions characterizing the thermodynamics in the vicinities of the quantum critical points. Extensive numerical data for the specific heat, susceptibility, compressibility, and entropy are reported. The experimentally relevant double occupancy presents an interesting doubly nonmonotonic temperature dependence at intermediate values of the interaction strength and also at large repulsion and magnetic fields close to the critical value. The susceptibility in zero magnetic field has a logarithmic singularity at low temperatures for all filling factors similar to the behavior of the same quantity in the XXX spin chain. We determine the density profiles for a harmonically trapped system and show that while the total density profile seems to depend mainly on the value of chemical potential at the center of the trap the distribution of phases in the inhomogeneous system changes dramatically as we increase the magnetic field.

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Direct observation of incommensurate magnetism in Hubbard chains

Cited by 87 publications

References 38 publications

Nagaoka ferromagnetism observed in a quantum dot plaquette

Nagaoka ferromagnetism observed in a quantum dot plaquette

Floquet time spirals and stable discrete-time quasicrystals in quasiperiodically driven quantum many-body systems

Quantum critical behavior and thermodynamics of the repulsive one-dimensional Hubbard model in a magnetic field

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