Observation of spatial charge and spin correlations in the 2D Fermi-Hubbard model

Cheuk, Lawrence; Nichols, Matthew; Lawrence, Katherine R.; Okan, Melih; Zhang, Hao; Khatami, Ehsan; Trivedi, Nandini; Paiva, Thereza; Rigol, Marcos; Zwierlein, Martin

doi:10.1126/science.aag3349

Cited by 350 publications

(370 citation statements)

References 48 publications

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“…Seminal efforts are underway in the control of artificial quantum systems, that can be made to emulate the underlying Fermi-Hubbard models [5, 6, 7, 8,9,10,11]. Electrostatically confined conduction band electrons define interacting quantum coherent spin and charge degrees of freedom that allow all-electrical pure-state initialisation and readily adhere to an engineerable Fermi-Hubbard Hamiltonian [12,13,14,15,16,17,18,19,20,21,22,23].…”

Section: Introductionmentioning

confidence: 99%

“…Although the potential of such correlated-electron phases for realizing novel electronic and magnetic properties has prompted quantum simulation efforts across multiple platforms [5,6,7,8,9,10,24,25], experimental correlations are often limited in span and strength due to the residual entropy of the initialized system [8,9,10]. Furthermore, scaling to similarly homogeneous but larger system sizes is not always straightforward [5,7,8,9,10,11,25]. Semiconductor quantum dots form a scalable platform that is naturally described by a Fermi-Hubbard model in the low-temperature, strong-interaction regime, when cooled down to dilution temperatures [12,13,15,14,16].…”

Section: Introductionmentioning

confidence: 99%

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Quantum simulation of a Fermi–Hubbard model using a semiconductor quantum dot array

Hensgens

Fujita

Janssen

et al. 2017

Nature

323

329

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Interacting fermions on a lattice can develop strong quantum correlations, which lie at the heart of the classical intractability of many exotic phases of matter [1, 2, 3, 4]. Seminal efforts are underway in the control of artificial quantum systems, that can be made to emulate the underlying Fermi-Hubbard models [5, 6, 7, 8,9,10,11]. Electrostatically confined conduction band electrons define interacting quantum coherent spin and charge degrees of freedom that allow all-electrical pure-state initialisation and readily adhere to an engineerable Fermi-Hubbard Hamiltonian [12,13,14,15,16,17,18,19,20,21,22,23]. Until now, however, the substantial electrostatic disorder inherent to solid state has made attempts at emulating Fermi-Hubbard physics on solid-state platforms few and far between [24,25]. Here, we show that for gate-defined quantum dots, this disorder can be suppressed in a controlled manner. Novel insights and a newly developed semi-automated and scalable toolbox allow us to homogeneously and independently dial in the electron filling and nearest-neighbour tunnel coupling. Bringing these ideas and tools to fruition, we realize the first detailed characterization of the collective Coulomb blockade transition [26], which is the finite-size analogue of the interaction-driven Mott metal-to-insulator transition [1]. As automation and device fabrication of semiconductor quantum dots continue to improve, the ideas presented here show how quantum dots can be used to investigate the physics of ever more complex many-body states.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum simulation of a Fermi–Hubbard model using a semiconductor quantum dot array

Hensgens

Fujita

Janssen

et al. 2017

Nature

323

329

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“…Already, Mott-insulating phases and short-range antiferromagnetic correlations have been observed, but temperatures were too high to create an antiferromagnet [12][13][14][15]. A new perspective is afforded by quantum gas microscopy [16][17][18][19][20][21][22][23][24][25][26][27][28], which allows readout of magnetic correlations at the site-resolved level [25][26][27][28]. Here we report the realization of an antiferromagnet in a repulsively interacting Fermi gas on a 2D square lattice of approximately 80 sites.…”

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confidence: 99%

A cold-atom Fermi–Hubbard antiferromagnet

Mazurenko

Chiu

et al. 2017

Nature

751

689

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Many exotic phenomena in strongly correlated electron systems emerge from the interplay between spin and motional degrees of freedom [1, 2]. For example, doping an antiferromagnet gives rise to interesting phases including pseudogap states and high-temperature superconductors [3]. 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 [4][5][6][7][8]. Ultracold fermions in optical lattices offer the potential to answer open questions on the lowtemperature regime of the doped Hubbard model [9][10][11], which is thought to capture essential aspects of the cuprate superconductor phase diagram but is numerically intractable in that parameter regime. Already, Mott-insulating phases and short-range antiferromagnetic correlations have been observed, but temperatures were too high to create an antiferromagnet [12][13][14][15]. A new perspective is afforded by quantum gas microscopy [16][17][18][19][20][21][22][23][24][25][26][27][28], which allows readout of magnetic correlations at the site-resolved level [25][26][27][28]. 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, where the staggered magnetization approaches the ground-state value. 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.The Hubbard Hamiltonian is a fundamental model for spinful lattice electrons describing a competition between kinetic energy t and interaction energy U [29]. In the limiting case of half-filling (average one particle per site) and dominant interactions (U/t 1) the Hubbard model maps to the Heisenberg model [1]. There, the exchange energy J = 4t 2 /U can give rise to antiferromagnetically ordered states at low temperatures [30]. This order persists for all finite U/t, where charge fluctuations reduce the ordering strength [31]. Away from half-filling, the coupling between motional and spin degrees of freedom is expected to give rise to a rich many-body phase diagram (see Fig. 1a), which is challenging to understand theoretically due to the fermion sign problem [32]. Even so, in the thermodynamic limit com...

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“…Experimental methods for realizing the Hubbard Hamiltonian have also been developed in the ultracold gas community [3][4][5]. Especially, the recent development of the fermionic quantum gas microscopes provides an interesting platform for observing magnetic order [6][7][8][9][10][11][12][13][14][15], although further advances are needed to reach the possible superconducting phases.…”

Section: Introductionmentioning

confidence: 99%

Dynamical mean-field theory study of stripe order and d -wave superconductivity in the two-dimensional Hubbard model

Vanhala

Törmä

2018

Phys. Rev. B

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We use cellular dynamical mean-field theory with extended unit cells to study the ground state of the two-dimensional repulsive Hubbard model at finite doping. We calculate the energy of states where d-wave superconductivity coexists with spatially nonuniform magnetic and charge order and find that they are energetically favored in a large doping region as compared to the uniform solution. We also study the spatial form of the density and the superconducting and magnetic order parameters at different doping values.

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Observation of spatial charge and spin correlations in the 2D Fermi-Hubbard model

Cited by 350 publications

References 48 publications

Quantum simulation of a Fermi–Hubbard model using a semiconductor quantum dot array

Quantum simulation of a Fermi–Hubbard model using a semiconductor quantum dot array

A cold-atom Fermi–Hubbard antiferromagnet

Dynamical mean-field theory study of stripe order and d -wave superconductivity in the two-dimensional Hubbard model

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