Simulating lattice gauge theories within quantum technologies

Bañuls, Mari Carmen; Blatt, R.; Catani, Jacopo; Celi, Alessio; Cirac, J. Ignacio; Dalmonte, Marcello; Fallani, Leonardo; Jansen, Karl; Lewenstein, Maciej; Montangero, Simone; Muschik, Christine A.; Reznik, Benni; Rico, E.; Tagliacozzo, Luca; Acoleyen, Karel Van; Verstraete, Frank; Wiese, U.‐J.; Wingate, Matthew; Zakrzewski, Jakub; Zoller, P.

doi:10.1140/epjd/e2020-100571-8

Cited by 473 publications

(326 citation statements)

References 264 publications

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“…Thus, great effort is currently being put in giving dynamics to synthetic gauge potentials [36,37]. The usual top-down approach [38][39][40], using the Kogut-Susskind formalism [41] and quantum link models [42], builds on the knowledge gathered from lattice gauge theories [43].…”

Section: Introductionmentioning

confidence: 99%

Synthetic flux attachment

Valentí-Rojas

Westerberg

Öhberg

2020

Phys. Rev. Research

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Topological field theories emerge at low energy in strongly correlated condensed matter systems and appear in the context of planar gravity. In particular, the study of Chern-Simons terms gives rise to the concept of flux attachment when the gauge field is coupled to matter, yielding flux-charge composites. We investigate the generation of flux attachment in a Bose-Einstein condensate in the presence of nonlinear synthetic gauge potentials. In doing so, we identify the U (1) Chern-Simons gauge field as a singular density-dependent gauge potential, which in turn can be expressed as a Berry connection. We envisage a proof-of-concept scheme where the artificial gauge field is perturbatively induced by an effective light-matter detuning created by interparticle interactions. At a mean field level, we recover the action of a "charged" superfluid minimally coupled to both a background and a Chern-Simons gauge field. Remarkably, a localized density perturbation in combination with a nonlinear gauge potential gives rise to an effective composite boson model of fractional quantum Hall effect, displaying anyonic vortices.

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Section: Introductionmentioning

confidence: 99%

Synthetic flux attachment

Valentí-Rojas

Westerberg

Öhberg

2020

Phys. Rev. Research

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“…Clearly, a deeper understanding of a possible lattice gauge theory origin of the model is desirable. This seems relevant considering also that low dimensional lattice gauge theories are being understood nowadays with modern tools from quantum information theory (such as matrix product states or tensor networks) and from the point of view of quantum simulation [22]. Alternatively, one could view the τ deformed matrix model as a phenomenological model which may incorporate some interesting physical features of gauge theory.…”

Section: Jhep09(2020)081 4 Discussionmentioning

confidence: 99%

“…We can study this limit by computing the average of the term [cos(θ/2)] 2ν in the two phases of the GWW matrix model, described by the density of states of the model [4], and also given below. Expressing the power of the cosine in terms of a sum of multiple-angle cosines: 22) we can then use a non-trivial but well-known result available for averages with ρ(φ) in the GWW model, [4,[18][19][20]:…”

Section: Jhep09(2020)081mentioning

confidence: 99%

Multiple phases in a generalized Gross-Witten-Wadia matrix model

Russo

Tierz

2020

J. High Energ. Phys.

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We study a unitary matrix model of the Gross-Witten-Wadia type, extended with the addition of characteristic polynomial insertions. The model interpolates between solvable unitary matrix models and is the unitary counterpart of a deformed Cauchy ensemble. Exact formulas for the partition function and Wilson loops are given in terms of Toeplitz determinants and minors and large N results are obtained by using Szegö theorem with a Fisher-Hartwig singularity. In the large N (planar) limit with two scaled couplings, the theory exhibits a surprisingly intricate phase structure in the two-dimensional parameter space.

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“…[18] and references quoted therein for a recent QCD study and Ref. [19] for interesting quantum simulations of lattice gauge theories).…”

Section: Introductionmentioning

confidence: 99%

Fermion and photon gap-equations in Minkowski space within the Nakanishi integral representation method

Mezrag

Salmè

2021

Eur. Phys. J. C

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The approach based on the Nakanishi integral representation of n-leg transition amplitudes is extended to the treatment of the self-energies of a fermion and an (IR-regulated) vector boson, in order to pave the way for constructing a comprehensive application of the technique to both gap- and Bethe-Salpeter equations, in Minkowski space. The achieved result, namely a 6-channel coupled system of integral equations, eventually allows one to determine the three Källén–Lehman weights for fully dressing the propagators of fermion and photon. A first consistency check is also provided. The presented formal elaboration points to embed the characteristics of the non-perturbative regime at a more fundamental level. It yields a viable tool in Minkowski space for the phenomenological investigation of strongly interacting theories, within a QFT framework where the dynamical ingredients are made transparent and under control.

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Simulating lattice gauge theories within quantum technologies

Cited by 473 publications

References 264 publications

Synthetic flux attachment

Synthetic flux attachment

Multiple phases in a generalized Gross-Witten-Wadia matrix model

Fermion and photon gap-equations in Minkowski space within the Nakanishi integral representation method

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