Suppression of the critical temperature for superfluidity near the Mott transition

Trotzky, Stefan; Pollet, Lode; Gerbier, Fabrice; Schnorrberger, U.; Bloch, Immanuel; Prokof’ev, Nikolay; Svistunov, Boris; Troyer, Matthias

doi:10.1038/nphys1799

Cited by 202 publications

(363 citation statements)

References 52 publications

(82 reference statements)

Supporting

Mentioning

340

Contrasting

Order By: Relevance

“…Since the Bose-Hubbard model does not suffer from a sign problem, it can also be simulated on a classical computer. Using quantum Monte Carlo, in this way the quantum simulator has been accurately validated in comparison to the cold atoms experiments [33]. Thus it has been demonstrated explicitly that accurate quantitative experimental control of the theoretical Bose-Hubbard model has indeed been achieved.…”

Section: Introductionmentioning

confidence: 93%

Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories

2013

View full text Add to dashboard Cite

Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, Abelian U(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev's toric code is a Z(2) lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non-Abelian SU(3) gauge theory of the strong interactions between quarks and gluons, is nonperturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer from the notorious sign problem, they open the door to studies of the real-time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories suggests itself for quantum simulation, which should allow us to address very challenging problems, ranging from confinement and deconfinement, or chiral symmetry breaking and its restoration at finite baryon density, to color superconductivity and the real-time evolution of heavy-ion collisions, first in simpler model gauge theories and ultimately in QCD.

show abstract

Section: Introductionmentioning

confidence: 93%

Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories

2013

View full text Add to dashboard Cite

show abstract

“…The optical lattice is realized with counter-propagating laser beams, whose intensity determines the amplitude for hopping between neighboring lattice sites. The quantum simulation has been validated in comparison with accurate quantum Monte Carlo simulations [25], which are possible because the Bose-Hubbard model does not suffer from a sign problem. The next challenge in this field is to quantum simulate the fermionic Hubbard model, in order to decide whether it can describe high-temperature superconductivity.…”

Section: Introductionmentioning

confidence: 99%

Towards quantum simulating QCD

Wiese

2014

Nuclear Physics A

103

View full text Add to dashboard Cite

Quantum link models provide an alternative non-perturbative formulation of Abelian and non-Abelian lattice gauge theories. They are ideally suited for quantum simulation, for example, using ultracold atoms in an optical lattice. This holds the promise to address currently unsolvable problems, such as the real-time and high-density dynamics of strongly interacting matter, first in toy-model gauge theories, and ultimately in QCD.

show abstract

“…and simulation for the fermionic Hubbard model similar to what has previously been done for bosons 13 .…”

mentioning

confidence: 99%

“…In experiments, a Mott insulating phase has been realized 8,9 , and the detection of a Néel state seems feasible in the not too distant future. Progress in simulation methods 10,11 13 .Even more intriguing physics than in the Hubbard model is expected in shallow optical lattices, where-in analogy to materials-a rich variety of phases is expected as the bandgap closes and multi-band and orbital effects become important. Although shallow lattices are easy to achieve experimentally by reducing the laser amplitude, they pose a challenge to theoretical treatments.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Density functional theory for atomic Fermi gases

et al. 2012

View full text Add to dashboard Cite

The interplay between interaction and inhomogeneity for electrons in solids generates many interesting phenomena, including insulating and metallic behaviour, magnetism, superconductivity, quantum criticality and more exotic phases 1 . Many of the same phenomena appear in ultracold fermionic atoms in optical lattices 2 , which provide clean, controlled and tunable 'quantum simulators' to explore the intriguing physics of fermionic systems. Although density functional theory 3-5 (DFT) is widely used to calculate material properties 6 , it has not yet been applied to cold atomic gases in optical lattices. Here we present a new density functional for short-range interactions (as opposed to Coulomb interactions of electrons), which renders DFT suitable for atomic Fermi gases. This grants us access to an extensive toolset, previously developed for materials simulations, to calculate the static and dynamic properties of atomic Fermi gases in optical lattices and external potentials. Ultracold atom quantum simulators can in turn be used to explore limitations of DFT functionals, and to further improve hybrid functionals, thus forming a bridge between materials simulations and atomic physics.Ultracold atomic gases have several advantages over materials for systematically exploring fermionic quantum systems. In materials, strong interactions go hand in hand with increasing localization of electrons as one moves from weakly correlated materials with s and p electrons to transition metal compounds with d electrons, and lanthanides and actinides with even more localized f orbitals. In contrast, all relevant parameters can be almost arbitrarily changed for fermionic gases in optical lattices: increasing the intensity of the optical lattice tunes continuously from shallow lattices with extended wave functions to deep lattices with almost localized Wannier functions, and the band structure can be further modified by changing the laser wave form. The strength of the inter-atomic interactions can independently be varied by tuning an external magnetic field across Feshbach resonances 7 . This facilitates a controlled realization of intriguing quantum phenomena in fermionic systems, and the systematic exploration of interaction and localization effects. The simplicity of atomic gases, the absence of core electrons and the ability to realize strongly interacting systems already in the lowest band makes optical lattice systems also much easier to treat from a theoretical point of view, avoiding the need for expensive all-electron calculations including the core electrons or the use of less reliable pseudopotentials incorporating their effects.So far, the experimental and theoretical focus has been on deep optical lattices, which are described well by single-band Hubbard models and where exciting progress has been achieved. In experiments, a Mott insulating phase has been realized 8,9 , and the detection of a Néel state seems feasible in the not too distant future. Progress in simulation methods 10,11 13 .Even more intriguing physics...

show abstract

Suppression of the critical temperature for superfluidity near the Mott transition

Cited by 202 publications

References 52 publications

Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories

Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories

Towards quantum simulating QCD

Density functional theory for atomic Fermi gases

Contact Info

Product

Resources

About