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arXiv:2111.13572 · Physical Review Research

Chiral orbital order of interacting bosons without higher bands

Marco Fedele Di Liberto, Nathan Goldman

Published Apr 27, 2023• 9 citations
arXivHTMLPDF

Abstract

Ultracold atoms loaded into higher Bloch bands provide an elegant setting for realizing many-body quantum states that spontaneously break time-reversal symmetry through the formation of chiral orbital order. The applicability of this strategy remains nonetheless limited due to the finite lifetime of atoms in high-energy bands. Here we introduce an alternative framework, suitable for bosonic gases, which builds on assembling square plaquettes pierced by a $\ensuremath{\pi}$ flux (half a magnetic-flux quantum). This setting is shown to be formally equivalent to an interacting bosonic gas loaded into $p$ orbitals, and we explore the consequences of the resulting chiral orbital order, both for weak and strong on-site interactions. We demonstrate the emergence of a chiral superfluid vortex lattice, exhibiting a long-lived gapped collective mode that is characterized by local chiral currents. This chiral superfluid phase is shown to undergo a phase transition to a chiral Mott insulator for sufficiently strong interactions. Our work establishes coupled $\ensuremath{\pi}$-flux plaquettes as a practical route for the emergence of orbital order and chiral phases of matter.

DOI
10.1103/physrevresearch.5.023064

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Ultracold atoms loaded into higher Bloch bands provide an elegant setting for realizing many-body quantum states that spontaneously break time-reversal symmetry through the formation of chiral orbital order. The applicability of this strategy remains nonetheless limited due to the finite lifetime of atoms in high-energy bands. Here we introduce an alternative framework, suitable for bosonic gases, which builds on assembling square plaquettes pierced by a \ensuremathπ\ensuremath{\pi}\ensuremathπ flux (half a magnetic-flux quantum). This setting is shown to be formally equivalent to an interacting bosonic gas loaded into ppp orbitals, and we explore the consequences of the resulting chiral orbital order, both for weak and strong on-site interactions. We demonstrate the emergence of a chiral superfluid vortex lattice, exhibiting a long-lived gapped collective mode that is characterized by local chiral currents. This chiral superfluid phase is shown to undergo a phase transition to a chiral Mott insulator for sufficiently strong interactions. Our work establishes coupled \ensuremathπ\ensuremath{\pi}\ensuremathπ-flux plaquettes as a practical route for the emergence of orbital order and chiral phases of matter.
Orbital order and chiral currents of interacting bosons with π\piπ-flux
Higher Bloch bands provide a remarkable setting for realizing many-body states that spontaneously break time-reversal symmetry, offering a promising path towards the realization of interacting topological phases. Here, we propose a different approach by which chiral orbital order effectively emerges in the low-energy physics of interacting bosons moving on a square plaquette pierced by a π\piπ-flux. We analyze the low-energy excitations of the condensate in terms of two orbital degrees of freedom and identify a gapped collective mode corresponding to the out-of-phase oscillations of the relative density and phase of the two orbitals. We further highlight the chiral nature of the ground state by revealing the cyclotron-like dynamics of the density upon quenching an impurity potential on a single site. Our single-plaquette results can be used as building blocks for extended dimerized lattices, as we exemplify using the BBH model of higher-order topological insulators. Our results provide a distinct direction to realize interacting orbital-like models that spontaneously break time-reversal symmetry, without resorting to higher bands nor to external drives.
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Interacting bosons on a single plaquette threaded by a $\ensuremath{\pi}$ flux can spontaneously break time-reversal symmetry, resulting in a chiral loop current. Connecting such bosonic $\ensuremath{\pi}$-flux plaquettes in a dispersive configuration was recently shown to lead to long-range chiral order. Here, instead, we design a chain of $\ensuremath{\pi}$-flux plaquettes that exhibits an all-flat-bands single-particle energy spectrum and an extensive set of local symmetries. Using Elitzur's theorem, we show that these local symmetries prevent the emergence of long-range chiral order. Moreover, projecting the dynamics to a Creutz ladder model with an effective intrarung interaction allows one to derive simple spin Hamiltonians capturing the ground-state degeneracy and the low-energy excitations, and to confirm the absence of chiral order. Nevertheless, we show how to obtain gauge-invariant information from a mean-field approach, which explicitly breaks gauge-invariance. Finally, we observe an impurity self-pinning phenomenon, when an extra boson is added on top of a ground state at integer filling, resulting in a nondispersive density peak. Exact diagonalization benchmarks are also provided, and experimental perspectives are discussed.
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