Emergent Fermi sea in a system of interacting bosons

Ying-Hai Wu and J. K. Jain

Phys. Rev. A 91, 063623 – Published 22 June 2015

Abstract

An understanding of the possible ways in which interactions can produce fundamentally new emergent many-body states is a central problem of condensed-matter physics. We ask if a Fermi sea can arise in a system of bosons subject to contact interaction. Based on exact diagonalization studies and variational wave functions, we predict that such a state is likely to occur when a system of two-component bosons in two dimensions, interacting via a species-independent contact interaction, is exposed to a synthetic magnetic field of strength that corresponds to a filling factor of unity. The fermions forming the SU(2) singlet Fermi sea are bound states of bosons and quantized vortices, formed as a result of the repulsive interaction between bosons in the lowest Landau level.

Received 25 November 2014

DOI:https://doi.org/10.1103/PhysRevA.91.063623

Authors & Affiliations

Ying-Hai Wu^1,2 and J. K. Jain¹

¹Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
²Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany

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Vol. 91, Iss. 6 — June 2015

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Images

Figure 1
Energy spectra of two-component bosons with SU(2)-invariant contact interaction on a sphere (dashes). The dots represent the energies of the CF trial states $Ψ_{singlet}^{CF - FS}$ . The values of $(N_{↑}, N_{↓}, 2 Q)$ are (a) $(6, 6, 11)$ and (b) $(7, 7, 13)$ . The horizontal coordinate is the linear combination $L + 0.3 S$ so the states with the same $L$ but different $S$ can be distinguished by their relative shifts. The spin quantum numbers are also shown in different colors as indicated by the inset of (a).
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Figure 2
Energy spectra of two-component bosons with SU(2)-invariant contact interaction on a disk (dashes). The number of particles is (a) $N = 6$ and (b) $N = 12$ . The horizontal coordinate is the linear combination $L_{z} + 0.3 S$ so the states with the same $L_{z}$ but different $S$ can be distinguished by their relative shifts. The spin quantum numbers are also shown in different colors as in Fig. 1. There is a clear cusp at $L_{z} = N (N - 1) / 2$ , with a spin-singlet ground state. The dot shows the energy of the CF wave function, and the number above the dot is the overlap between this wave function and the exact ground state.
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Figure 3
Energy spectra two-component bosons with SU(2)-invariant contact interaction on disk. The number of particles is (a) $N = 6$ and (b) $N = 12$ . For simplicity, the spin quantum numbers are not shown. Some of the compact states where the energies have a downward cusp are indicated by arrows. The $L_{z} = 15$ state in (a) and the $L_{z} = 66$ state in (b) are the ones that would evolve into the CF Fermi sea in the thermodynamic limit. The dots mark the Halperin 221 state which is the maximum-density zero-energy eigenstate.
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Figure 4
Density profiles and pair distribution functions of the exact ground state and the CF trial state for the $N = 12$ system on a disk. The distance $r$ is measured in units of the magnetic length $ℓ_{B} = \sqrt{ℏ c / e B}$ . As we restrict $m \leq 16$ in exact diagonalizations, we have normalized the density profiles by that of a uniform state with total filling $ν = 1$ . In (b) and (d), the two lines show $g_{↑ ↑}$ and $g_{↓ ↑}$ as indicated by the symbols in their vicinities.
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Figure 5
Density profiles and pair distribution functions of the three lowest-energy exact eigenstates and the corresponding CF trial states (from top to bottom, labeled 1, 2, and 3) for the $N = 14$ system on sphere. The distance $r$ is measured in units of the magnetic length $ℓ_{B} = \sqrt{ℏ c / e B}$ and the density values are given in units of $ℓ_{B}^{- 2}$ . In (c), (d), (g), (h), (k), and (l), the two lines show $g_{↑ ↑}$ and $g_{↓ ↑}$ as indicated by the symbols in their vicinities.
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Figure 6
Energy spectra of one-component bosons at $ν = 1$ on a sphere (dashes). The system parameters are (a, c) $(N, 2 Q) = (13, 12)$ and (b, d) $(N, 2 Q) = (14, 13)$ . Panels (a) and (b) are for the two-body interaction $H_{1 - comp}^{(2)}$ with $C_{2}^{(2)} = 0.2$ , while (c) and (d) are for the three-body interaction $H_{1 - comp}^{(2)}$ with $C_{2}^{(3)} = 0.2$ . The dots show the energies of the wave functions $Ψ_{1 - comp}^{CF}$ with respect to the $H_{1 - comp}^{(2)}$ in (a) and (c) and $H_{1 - comp}^{(2)}$ in (b) and (d). The zero two-body or three-body pseudopotentials are chosen to be 1 and used as units of the energy values.
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