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arXiv:2410.01780 · Physical review. B./Physical review. B

Fate of chiral order and impurity self-pinning in flat bands with local symmetry

Maxime Burgher, Marco Fedele Di Liberto, Nathan Goldman, Ivan Amelio

Published Feb 25, 2025• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.111.064514

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Interacting bosons on a single plaquette threaded by a \ensuremathπ\ensuremath{\pi}\ensuremathπ flux can spontaneously break time-reversal symmetry, resulting in a chiral loop current. Connecting such bosonic \ensuremathπ\ensuremath{\pi}\ensuremathπ-flux plaquettes in a dispersive configuration was recently shown to lead to long-range chiral order. Here, instead, we design a chain of \ensuremathπ\ensuremath{\pi}\ensuremathπ-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.
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.
Strongly interacting bosons that live in a lattice with degeneracy in its lowest-energy band experience frustration that can prevent the formation of a Bose-Einstein condensate. Such systems form an ideal playground to investigate spin-liquid behavior. We use the variational principle and the Chern-Simons technique of fermionization of hard-core bosons on the kagome lattice to find that below lattice filling fraction $\ensuremath{\nu}=\frac{1}{3}$ the system favors a topologically ordered chiral spin-liquid state that is gapped in bulk, spontaneously breaks time-reversal symmetry, and supports massless chiral bosonic edge mode. We construct the many-body variational wave function of the state and show that the corresponding energy coincides with the energy of the flat band. This result proves that the ground state of the system cannot stabilize a Bose condensate below $\ensuremath{\nu}=\frac{1}{3}$. The fermionization and variational scheme we outline apply to any non-Bravais lattice. We distinguish between the roles played by the Chern-Simons gauge field in lattices with a flat band and those exhibiting a moatlike dispersion (which is degenerate along a closed contour in the reciprocal space). We also suggest experimental probes to differentiate the proposed ground state from a condensate.
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 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 $\ensuremath{\pi}$-flux plaquettes as a practical route for the emergence of orbital order and chiral phases of matter.
Neutral-atom quantum simulators provide a powerful platform for realizing strongly correlated phases, enabling access to dynamical signatures of quasiparticles and symmetry breaking processes. Motivated by recent observations of quantum phases in flux-frustrated ladders with non-vanishing ground state currents, we investigate interacting bosons on the dimerized BBH lattice in two dimensions-originally introduced in the context of higher-order topology. After mapping out the phase diagram, which includes vortex superfluid (V-SF), vortex Mott insulator (V-MI), and featureless Mott insulator (MI) phases, we focus on the integer filling case. There, the MI/V-SF transition simultaneously breaks the Z2T\mathbb Z_2^{T}Z2T​ and U(1) symmetries, where Z2T\mathbb Z_2^{T}Z2T​ corresponds to time-reversal symmetry (TRS). Using a slave-boson description, we resolve the excitation spectrum across the transition and uncover a chiral Higgs mode whose mass softens at criticality, providing a dynamical hallmark of emergent chirality that manifests via the oscillation of the loop currents in quench dynamics. Our results establish an experimentally realistic setting for probing unconventional TRS-broken phases and quasiparticles with intrinsic chirality in strongly interacting quantum matter.
A bosonic Creutz-Hubbard ladder is studied by solving the interacting Bose-Hubbard model, with the help of exact diagonalization method. Under certain parameters, a single-particle energy spectrum possessing two flat energy bands is obtained. Due to these flat bands, we identify the spontaneous disorder in the presence of interaction, which breaks the translational symmetry of lattice system. Out of flat bands and taking a flux quanta asπ/2, the checkerboard phase associated with Meissner currents can be observed, as well as the regular biased ladder (BL) phase, which particularly presents a novel type of interlaced chiral current. We further figure out a modulated BL phase, whose imbalance on the occupancies between two legs is constant, whereas the density distribution on either leg oscillates periodically, followed by compound currents.
Chiral topological orders formed in correlated fermion systems have been widely explored. However, the mechanism of how they emerge from interacting fermions is still unclear. Here, we propose a susceptibility condition. Under this condition, we show that chiral topological orders can spontaneously take place in correlated fermion systems. The condition leads to a low-energy effective theory of bosons with strong frustration, mimicking flat-band systems. The frustration then melts the long-range orders and results in topological orders with time-reversal symmetry breaking. We apply the theory to strongly correlated semiconductors doped to the metallic phase. An excitonic topological order with semionic excitations and a chiral excitonic edge state is revealed. We also discuss the application to frustrated magnets. The theory predicts a chiral spin-liquid state, which is numerically confirmed by our tensor network calculations. These results demonstrate an indicator for chiral topological orders, which bridges the existing gap between interacting fermions and correlated topological matter.