One-body reduced density matrix of trapped impenetrable anyons in one dimension

Marmorini, Giacomo; Calabrese, Pasquale

doi:10.1088/1742-5468/2016/07/073106

Cited by 27 publications

(35 citation statements)

References 74 publications

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“…with e − (k) given in (96). All the functions appearing in (98) and in (96) for the R (−) matrix have a well defined thermodynamic limit. Now it only remains to sum over the µ's in (94).…”

Section: A Summation Of Form Factors For ψmentioning

confidence: 99%

“…The literature on 1D anyonic models has been growing steadily in the last years spurred by several experimental proposals of realizing such systems with ultracold atoms in optical lattices using Raman-assisted tunneling [84,85], periodically driven lattices [86] or multicolor lattice-depth modulation [87,88]. Much of the attention was focused on single component systems like the anyonic Lieb-Liniger model [89][90][91] for which we know the ground state characterization [90,92], asymptotic behavior of the correlation functions for homogeneous [26,27,59,[93][94][95] and trapped systems [96,97], entanglement [98,99], and nonequilibrium [100][101][102] properties. In the case of multi-component anyonic systems, such as the one considered in this paper, there are fewer known results, especially from the analytical point of view [103][104][105].…”

Section: Introductionmentioning

confidence: 99%

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Correlation functions of one-dimensional strongly interacting two-component gases

Pâţu¹

2019

Phys. Rev. A

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We address the problem of calculating the correlation functions of one-dimensional two-component gases with strong repulsive contact interactions. The model considered in this paper describes particles with fractional statistics and in appropriate limits reduces to the Gaudin-Yang model or the spinor Bose gas. In the case of impenetrable particles we derive a Fredholm determinant representation for the temperature-, time-, and space-dependent correlation functions which is very easy to implement numerically and constitute the starting point for the analytical investigation of the asymptotics. Making use of this determinant representation and the solution of an associated Riemann-Hilbert problem we derive the low-energy asymptotics of the correlators in the spin-incoherent regime characterized by near ground-state charge degrees of freedom but a highly thermally disordered spin sector. The asymptotics present features reminiscent of spin-charge separation with the spin part exponentially decaying in space separation and oscillating with a period proportional to the statistics parameter while the charge part presents scaling with anomalous exponents which cannot be described by any unitary conformal field theory. The momentum distribution and the Fourier transform of the dynamical Green's function are asymmetrical for arbitrary statistics, a direct consequence of the broken space-reversal symmetry. Due to the exponential decay the momentum distribution n(k) at zero temperature does not present algebraic singularities but the tails obey the universal decay lim k→±∞ n(k) ∼ C/k 4 with the amplitude C given by Tan's contact. As a function of the statistics parameter the contact is a monotonic function reaching its minimum for the fermionic system and the maximum for the bosonic system.

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Section: A Summation Of Form Factors For ψmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Correlation functions of one-dimensional strongly interacting two-component gases

Pâţu¹

2019

Phys. Rev. A

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“…Although anyons were originally proposed for two dimensional (2D) systems, one-dimensional (1D) anyons have been theoretically studied as well [19][20][21][22][23][24][25][26][27]. The exotic properties of 1D (Abelian) anyon models include asymmetric momentum distributions [28][29][30][31][32][33], particle dynamics [34][35][36], entanglement properties [37][38][39] or statistically induced Mott insulator to superfluid quantum phase transitions [40][41][42][43]. Despite this theoretical interest, the experimental realization of 1D anyons is still missing.…”

Section: Introductionmentioning

confidence: 99%

Probing the exchange statistics of one-dimensional anyon models

2018

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We propose feasible scenarios for revealing the modified exchange statistics in one-dimensional anyon models in optical lattices based on an extension of the multicolor lattice-depth modulation scheme introduced in [Phys. Rev. A 94, 023615 (2016)]. We show that the fast modulation of a two-component fermionic lattice gas in the presence a magnetic field gradient, in combination with additional resonant microwave fields, allows for the quantum simulation of hardcore anyon models with periodic boundary conditions. Such a semi-synthetic ring set-up allows for realizing an interferometric arrangement sensitive to the anyonic statistics. Moreover, we show as well that simple expansion experiments may reveal the formation of anomalously bound pairs resulting from the anyonic exchange.

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“…In Sec. II, we introduce the single-particle density matrix for 1D SU(κ) fermions in terms of separate spatial and spin parts of the density matrix with anyonic statistics [55][56][57]. In Sec.…”

Section: Introductionmentioning

confidence: 99%

Spin-incoherent Luttinger liquid of one-dimensional SU( κ ) fermions

Jen

Yip

2018

Phys. Rev. A

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We theoretically investigate one-dimensional (1D) SU(κ) fermions in the regime of spin-incoherent Luttinger liquid. We specifically focus on the Tonks-Girardeau gas limit where its density is sufficiently low that effective repulsions between atoms become infinite. In such case, spin exchange energy of 1D SU(κ) fermions vanishes and all spin configurations are degenerate, which automatically puts them into spin-incoherent regime. In this limit, we are able to express the single-particle density matrices in terms of those of anyons. This allows us to numerically simulate the number of particles up to N = 32. We numerically calculate single-particle density matrices in two cases: (1) equal populations for each spin components (balanced) and (2) all Sz manifolds included. In contrast to noninteracting multi-component fermions, the momentum distributions are broadened due to strong interactions. As κ increases, the momentum distributions are less broadened for fixed N , while they are more broadened for fixed number of particle per spin component. We then compare numerically calculated high momentum tails with analytical predictions which are proportional to 1/p 4 , in good agreement. Thus, our theoretical study provides a comparison with the experiments of repulsive multicomponent alkaline-earth fermions with a tunable SU(κ) spin-symmetry in the spin-incoherent regime.

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One-body reduced density matrix of trapped impenetrable anyons in one dimension

Cited by 27 publications

References 74 publications

Correlation functions of one-dimensional strongly interacting two-component gases

Correlation functions of one-dimensional strongly interacting two-component gases

Probing the exchange statistics of one-dimensional anyon models

Spin-incoherent Luttinger liquid of one-dimensional SU( κ ) fermions

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