Quantum simulation of the Hubbard model with ultracold fermions in optical lattices

Tarruell, Leticia; Sanchez-Palencia, Laurent

doi:10.1016/j.crhy.2018.10.013

Cited by 147 publications

(101 citation statements)

References 184 publications

(283 reference statements)

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“…[45,46], and it is being directly realized with fermionic atoms in optical lattices, see, e.g., Refs. [7,47,48]. It is defined by the Hubbard Hamiltonian Figure 1.…”

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confidence: 99%

Achieving the Scaling Limit for Nonequilibrium Green Functions Simulations

2020

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The dynamics of strongly correlated fermions following an external excitation reveals extremely rich collective quantum effects. Examples are fermionic atoms in optical lattices, electrons in correlated materials, and dense quantum plasmas. Presently, the only quantum-dynamics approach that rigorously describes these processes in two and three dimensions is nonequilibrium Green functions (NEGF). However, NEGF simulations are computationally expensive due to their T 3 scaling with the simulation duration T . Recently, T 2 scaling was achieved with the generalized Kadanoff-Baym ansatz (GKBA), for second order Born (SOA) selfenergies, which has substantially extended the scope of NEGF simulations. Here we demonstrate that GKBA-NEGF simulations can be performed with order T 1 scaling, both for SOA and GW selfenergies, and point out the remarkable capabilities of this approach.

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“…[45,46], and it is being directly realized with fermionic atoms in optical lattices, see, e.g., Refs. [7,47,48]. It is defined by the Hubbard Hamiltonian Figure 1.…”

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confidence: 99%

Achieving the Scaling Limit for Nonequilibrium Green Functions Simulations

2020

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“…We discuss the challenges, define both digital and analog quantum simulators, and list the demanding conditions they require. We also provide a brief account of the contributions gathered in the dossier on Quantum Simulation of the Comptes-Rendus de Physique of the French Academy of Sciences [1,2,3,4,5,6]. The latter completes excellent reviews that appeared previously, see for instance Refs.…”

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confidence: 77%

Quantum simulation: From basic principles to applications

Sanchez-Palencia

2018

Comptes Rendus. Physique

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Envisioned by Richard Feynman in the early 1980s, quantum simulation has received dramatic impetus thanks to the development of a variety of plateforms able to emulate a wide class of quantum Hamiltonians. During the past decade, most of the quantum simulators have implemented rather well-known models, hence permitting a direct comparison with theoretical calculations and a precise benchmarking of their reliability. The field has now reached a maturity such that one can address difficult problems, which cannot be solved efficiently using classical algorithms. These advances provide unprecedented opportunities to explore previously unreachable fields, test theoretical predictions, and inspire novel approaches.This contribution is an elementary introduction to quantum simulation. We discuss the challenges, define both digital and analog quantum simulators, and list the demanding conditions they require. We also provide a brief account of the contributions gathered in the dossier on Quantum Simulation of the Comptes-Rendus de Physique of the French Academy of Sciences [1,2,3,4,5,6]. The latter completes excellent reviews that appeared previously, see for instance Refs. [7,8,9,10,11,12,13,14].Universal models and the role of simulations in many-body physics Understanding the behavior of macroscopic quantum systems is a major challenge of modern physics. The basic laws of low-energy physics are by now quite well known at the microscopic, say atomic, scale. Conversely, many fundamental questions remain open, and even debated, about the collective dynamics at the macroscopic scale. By "macroscopic scale", here we mean systems made up of a huge number of constituents, or degrees of freedom, say 10 6 , 10 23 , or even more, as relevant in condensed matter physics or in astrophysics, for instance. Such huge systems cannot be treated exactly, be it a the classical level and, even worse, at the quantum level. Yet, it is the main outcome of the thermodynamic approach that the collective behavior of a macroscopic system can drastically differ from that of its elementary constituents. For instance, the elementary interactions between the H 2 O molecules are fundamentally unchanged when a water bucket turns from the liquid phase to the solid phase at zero degree Celsius. Similarly, the interactions between the microscopic magnetic moments do not show any brutal change when a magnetic material gets magnetized underneath the Curie temperature. Hence, the dramatic effects observed in macroscopic systems are governed by largescale instabilities, without obvious counterparts at the microscopic level. This observation takes a universal character, summarized in the celebrated motto "More is Different" [15]. Such so-called emerging phenomena also appear in quantum systems, where new effects that are impossible in the classical world show up below some critical temperature or at zero temperature when some interaction parameter passes through a critical value. Celebrated examples include the superfluid Λ transition in helium or super-cond...

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“…The driven dynamical quasicondensation outlined is realizable in a standard optical lattice experiment with feasible lattice parameters [59,[93][94][95]. To illustrate this we consider the well studied case of fermionic K 40 in an undriven 3D optical lattice potential.…”

Section: Cold-atom Implementationmentioning

confidence: 99%

“…17 are t = 0.03E R ≈ 0.6kHz for nearest-neighbour hopping between A and B sites, t = 7 × 10 −4 E R ≈ 0.01kHz for next-nearestneighbour hopping, and t = 1.2 × 10 −4 E R ≈ 0.002kHz for the hopping across neighbouring one dimensional channels of between A and B sites. The on-site Hubbard interaction is U ≈ 48g/λ 3 L where g/(hλ 3 L ) = 4πa sh 2 /m a hλ 3 L ≈ 0.1kHz using the s-wave scattering cross section a s which is 118 Bohr radii for K 40 [94,95]. The interaction strength U can be independently tuned via a Feshbach resonance.…”

Section: (A18)mentioning

confidence: 99%

Controllable finite-momenta dynamical quasicondensation in the periodically driven one-dimensional Fermi-Hubbard model

Cook

Clark

2020

Phys. Rev. A

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In the strongly interacting limit of the Hubbard model localized double-occupancies form effective hardcore bosonic excitations, called a doublons, which are long-lived due to energy conservation. Using timedependent density-matrix renormalisation group we investigate numerically the dynamics of doublons arising from the sudden expansion of a spatially confined band-insulating state in one spatial dimension. By analysing the occupation scaling of the natural orbitals within the many-body state, we show that doublons dynamically quasicondense at the band edges, consistent with the spontaneous emergence of an η-quasicondensate. Building on this, we study the effect of periodically driving the system during the expansion. Floquet analysis reveals that doublon-hopping and doublon-repulsion are strongly renormalised by the drive, breaking the η−SU(2) symmetry of the Hubbard model. Numerical simulation of the driven expansion dynamics demonstrate that the momentum in which doublons quasicondense can be controlled by the driving amplitude. These results point to new pathways for engineering non-equilibrium condensates in fermionic cold-atom experiments and are potentially relevant to driven solid-state systems.

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Quantum simulation of the Hubbard model with ultracold fermions in optical lattices

Cited by 147 publications

References 184 publications

Achieving the Scaling Limit for Nonequilibrium Green Functions Simulations

Achieving the Scaling Limit for Nonequilibrium Green Functions Simulations

Quantum simulation: From basic principles to applications

Controllable finite-momenta dynamical quasicondensation in the periodically driven one-dimensional Fermi-Hubbard model

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