Quantum Anomaly, Universal Relations, and Breathing Mode of a Two-Dimensional Fermi Gas

Hofmann, Johannes

doi:10.1103/physrevlett.108.185303

Cited by 110 publications

(89 citation statements)

References 45 publications

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“…Universal contact relations should also hold in this case [6,[17][18][19][20]. Interestingly, a recent experiment [21] has found that the monopole breathing mode is essentially undamped and has no interaction-dependent shift [22][23][24]. This implies a scale invariance in the system [25] that has also been observed in weakly interacting 2D Bose gases [26].…”

Section: Introductionmentioning

confidence: 84%

Dimensional effects on the momentum distribution of bosonic trimer states

Bellotti¹,

Frederico²,

Yamashita³

et al. 2013

Phys. Rev. A

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The momentum distribution is a powerful probe of strongly interacting systems that are expected to display universal behavior. This is contained in the contact parameters which relate few-and many-body properties. Here we consider a Bose gas in two dimensions and explicitly show that the two-body contact parameter is universal and then demonstrate that the momentum distribution at next-to-leading order has a logarithmic dependence on momentum which is vastly different from the three-dimensional case. Based on this, we propose a scheme for measuring the effective dimensionality of a quantum many-body system by exploiting the functional form of the momentum distribution.

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Section: Introductionmentioning

confidence: 84%

Dimensional effects on the momentum distribution of bosonic trimer states

Bellotti¹,

Frederico²,

Yamashita³

et al. 2013

Phys. Rev. A

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“…However, the true inter-atomic interactions break the scaling invariance, and this leads to the frequency shift of breathing modes. In two-component Fermi gas with s-wave interactions, one finds that this shift is related to the contact of the system [38,39], and in particular, at unitarity, the scaling invariance is regained [40]. However, quite differently for a single component Fermi gas with p-wave interaction in two dimensions, the scaling invariance is also broken even at resonance when a → ∞ due to the existence of the contact C R .…”

Section: Breathing Mode and Contactsmentioning

confidence: 94%

Strongly interacting p -wave Fermi gas in two dimensions: Universal relations and breathing mode

Zhang

2017

Phys. Rev. A

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The contact is an important concept that characterizes the universal properties of a strongly interacting quantum gas. It appears in both thermodynamic (energy, pressure, etc.) and dynamic quantities (radio-frequency and Bragg spectroscopies, etc.) of the system. Very recently, the concept of contact has been extended to higher partial waves, in particular, the p-wave contacts have been experimentally probed in recent experiment. So far discussions on p-wave contacts have been limited to three-dimensions. In this paper, we generalize the p-wave contacts to two-dimensions and derive a series of universal relations, including the adiabatic relations, high momentum distribution, virial theorem and pressure relation. At high temperature and low density limit, we calculated the pwave contacts explicitly using virial expansion. A formula which directly connects the shift of the breathing mode frequency and the p-wave contacts are given in a harmonically trapped system. Finally, we also derive the relationships between interaction parameters in three and two dimensional Fermi gas and discuss possible experimental realization of two dimensional Fermi gas with p-wave interactions.

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“…The possibility of measuring the effects of quantum anomalies in nonrelativistic systems has prompted the development of quantum-field-theoretical approaches in the mathematical description of such anomalies [1][2][3][4][5]. In particular, we have recently developed a path-integral, Fujikawa approach to the calculation of anomalous corrections to virial theorems and equations of state for systems with a classical SO(2, 1) symmetry [6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Bose and Fermi statistics and the regularization of the nonrelativistic Jacobian for the scale anomaly

Lin

Ordóñez

2016

Phys. Rev. D

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We regulate in Euclidean space the Jacobian under scale transformation for two-dimensional nonrelativistic fermions and bosons interacting via contact interaction and compare the resulting scaling anomalies. For fermions, Grassmannian integration inverts the Jacobian: however, this effect is cancelled by the regularization procedure and a result similar to that of bosons is attained. We show the independence of the result with respect to the regulating function, and show the robustness of our methods by comparing the procedure with an effective potential method using both cutoff and ζ-function regularization.

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Quantum Anomaly, Universal Relations, and Breathing Mode of a Two-Dimensional Fermi Gas

Cited by 110 publications

References 45 publications

Dimensional effects on the momentum distribution of bosonic trimer states

Dimensional effects on the momentum distribution of bosonic trimer states

Strongly interacting p -wave Fermi gas in two dimensions: Universal relations and breathing mode

Bose and Fermi statistics and the regularization of the nonrelativistic Jacobian for the scale anomaly

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