<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi mathvariant="double-struck">C</mml:mi></mml:math>P<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" display="inline" overflow="scroll"><mml:mrow><mml:mo>(</mml:mo><mml:mi>N</mml:mi><mml:mspace width="-0.16667em"/><mml:mo>−</mml:mo><mml:mspace width="-0.16667em"/><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math> quantum field theories with alkaline-earth atoms

Laflamme, Catherine; Evans, Wynne; Dalmonte, Marcello; Gerber, Urs; Mejía-Díaz, Héctor; Bietenholz, Wolfgang; Wiese, U.‐J.; Zoller, P.

doi:10.1016/j.aop.2016.03.012

Cited by 38 publications

(33 citation statements)

References 53 publications

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“…The results presented here could be relevant in implementations of the CP N −1 model with alkaline-earth atoms in optical lattices of the kind discussed in Ref. [3]. Experimental verifications and lattice simulations could provide a way to verify the existence of spatial modulations in the ground state.…”

Section: Introductionmentioning

confidence: 59%

“…The connections are often sparked by the possibility of implementing quantum field theoretical models used in high energy physics with atomic lattices at low temperature and cleverly designed atomic traps [2]. An example recently discussed is that of alkaline-earth atoms with SU(N ) spins arranged on a twodimensional bipartite square lattice (with the transverse direction much smaller than the longitudinal one) [3]. One of the many interesting features of this setup is that its continuum low-energy limit is a known toy model for QCD, the CP N −1 model, a (1 + 1)-dimensional field theory consisting of N complex scalar fields subject to a constraint [4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

“…A one-dimensional realization of a finite string of atoms, like that of Ref. [3], provides territory to both the condensed matter and the high energy physicist to explore fundamental aspects of the phase structure of cold atomic lattices on one side, and the properties of the underlying continuum field theory (in the present case the CP N −1 model confined to an interval) on the other. In fact, the latter has been at the center of recent discussions revolving around the nature of the ground state, the role of boundary conditions and the possibility that the ground state may develop spatial variations [10][11][12][13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

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Ground state modulations in the CPN−1 model

et al. 2019

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In this work we examine a system consisting of a confined one-dimensional arrangement of atoms that we describe by using the 2-dimensional CP N −1 model, restricted to an interval and at finite temperature. We develop a method to obtain the bulk and boundary parts of the one-loop effective action as a function of the effective mass of the fluctuations. The formalism has the advantage of allowing for a systematic analysis of a large class of boundary conditions and to model the (adiabatic) response of the ground state to changes in the boundary conditions. In the case of periodic boundary conditions, we find that inhomogeneous phases are disfavored for intervals of large size. Away from periodic boundary conditions, our numerical results show that the ground state has a generic crystal-like structure that can be modulated by variations of the boundary conditions. The results presented here could be relevant for experimental implementations of nonlinear sigma models and could be tested by lattice numerical simulations.

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Section: Introductionmentioning

confidence: 59%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Ground state modulations in the CPN−1 model

et al. 2019

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“…Recently the simulation of quantum field theories using man-made physical systems has become a real possibility [1]. In [2,3] an experimental set-up to quantum simulate the CP(2) model using alkaline-earth atoms trapped in an optical lattice was proposed. The theoretical model for the proposed experiment is an SU(3) quantum spin ladder.…”

Section: Introductionmentioning

confidence: 99%

The CP(2) Model at Nonzero Chemical Potential

Evans¹,

Gerber²,

Wiese³

2017

Proceedings of 34th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2016)

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Recently the simulation of quantum field theories using man-made physical systems has become realistic. In this publication we present numerical results which support the use of quantum simulation experiments to study quantum field theories at non-zero chemical potential. We have numerically simulated the (1+1)-d CP(2) model, which shares several interesting features with QCD, namely asymptotic freedom, a dynamically generated mass gap and topological sectors, via dimensional reduction of a (2+1)-d microscopic theory of SU(3) quantum spins. Numerical results for the particle number density as a function of chemical potential are presented. 34th annual International Symposium on Lattice Field Theory

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“…The techniques discussed here for the bosonic case can also be applied to Fermi-Hubbard systems [18], for which optical lattice experiments with single-site resolution are rapidly becoming available [54][55][56][57]. It would be desirable to develop specific procedures to study models with other values of c (Ising, Z N clock, Potts) or with O(3) symmetry with a chemical potential, which have a similar phase diagram [58], and could be quantum simulated [59]. More insight on conformal symmetry could be gained by studying particle number fluctuations [60][61][62].…”

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confidence: 99%

Probing the conformal Calabrese-Cardy scaling with cold atoms

et al. 2017

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We demonstrate that current experiments using cold bosonic atoms trapped in one-dimensional optical lattices and designed to measure the second-order Rényi entanglement entropy S2, can be used to verify detailed predictions of conformal field theory (CFT) and estimate the central charge c. We discuss the adiabatic preparation of the ground state at half-filling where we expect a CFT with c = 1. This can be accomplished with a very small hopping parameter J, in contrast to existing studies with density one where a much larger J is needed. We provide two complementary methods to estimate and subtract the classical entropy generated by the experimental preparation and imaging processes. We compare numerical calculations for the classical O(2) model with a chemical potential on a 1+1 dimensional lattice, and the quantum Bose-Hubbard Hamiltonian implemented in the experiments. S2 is very similar for the two models and follows closely the Calabrese-Cardy scaling, (c/8) ln(Ns), for Ns sites with open boundary conditions, provided that the large subleading corrections are taken into account.PACS numbers: 05.10. Cc, 11.15.Ha, 11.25.Hf, 37.10.Jk, 67.85.Hj, 75.10.Hk The concept of universality provides a unified approach to the critical behavior of lattice models studied in condensed matter, lattice gauge theory (LGT) and experimentally accessible systems of cold atoms trapped in optical lattices. Conformal field theory (CFT) [1, 2] offers many interesting examples of universal behavior that can be observed for lattice models in two [3][4][5], three [6], and four [7,8] dimensions. Practical simulations for these models unavoidably involve a finite volume that breaks explicitly the conformal invariance. However, this symmetry breaking follows definite patterns dictated by the restoration of the symmetry at infinite volume and allows us to identify the universality class. In view of the rich collection of interesting CFTs, it would be highly desirable to study their universality classes using quantum simulations. In order to start this ambitious program, one needs a simple concrete example to demonstrate the feasibility of the idea.In this Letter, we propose to use the setup of ongoing cold atom experiments to quantum simulate the O(2) model with a chemical potential and check the predictions of CFT for the growth of the entanglement entropy with the size of the system corresponding to the universality class of the superfluid (SF) phase. The O(2) model is an extension of the Ising model where the spin is allowed to move on a circle, making an angle θ with respect to a direction of reference. This model can be used to describe easy plane ferromagnetism and the compactness of θ leads to topological configurations called vortices. Their unbinding provides a prime example of a Berezinski-Kosterlitz-Thouless transition [9,10] in a way that has also been advocated to apply for gauge theories near the boundary of the conformal window [11]. When space and Euclidean time are treated isotropically, this model has important common ...

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CP(N−1) quantum field theories with alkaline-earth atoms

Cited by 38 publications

References 53 publications

Ground state modulations in the CPN−1 model

Ground state modulations in the CPN−1 model

The CP(2) Model at Nonzero Chemical Potential

Probing the conformal Calabrese-Cardy scaling with cold atoms

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