Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2303.02170 · Science Advances

Flat-band localization and interaction-induced delocalization of photons

Jeronimo G. C. Martinez, Christie Chiu, Basil M. Smitham, Andrew Houck

Published Dec 15, 2023• 39 citations
arXivHTMLPDF

Abstract

Lattices with dispersionless, or flat, energy bands have attracted substantial interest in part due to the strong dependence of particle dynamics on interactions. Using superconducting circuits, we experimentally study the dynamics of one and two particles in a single plaquette of a lattice whose band structure consists entirely of flat bands. We first observe strictly localized dynamics of a single particle, the hallmark of all-bands-flat physics. Upon initializing two particles on the same site, we see an interaction-enabled delocalized walk across the plaquette. We further find localization in Fock space for two particles initialized on opposite sides of the plaquette. These results mark the first experimental observation of a quantum walk that becomes delocalized due to interactions and establishes a key building block in superconducting circuits for studying flat-band dynamics with strong interactions.

DOI
10.1126/sciadv.adj7195

Related papers

Digital quantum simulation of flat-band and all-bands-flat dynamics for tunable quantum transport

Mrinal Kanti Giri, Pochung Chen

Abstract Flat-band systems offer a uniquely powerful tool for quantum control in dynamics due to their characteristic feature of having a dispersionless energy band. Simulating such highly sensitive systems on current digital quantum computers is a challenging task, due to the intrinsic limitations of the noisy intermediate-scale quantum devices. Here we present high-fidelity digital quantum simulations of flat-band (FB) and all-bands-flat (ABF) lattices, using an advanced tensor network based variational optimization approach to compress the circuit depth. With the compressed quantum circuits, we first explore single-particle dynamics and observe two distinct behaviours: strong localization in ABF lattices and delocalization in FB lattices. By integrating FB and ABF lattices into a one-dimensional hybrid structure, we achieve controllable quantum transport, where the ABF lattice acts as a quantum switch. Extending to two-particle dynamics, we show that transport remains controllable by tuning the hopping amplitude alone, even in the presence of interactions. These results establish FB engineered systems as a promising pathway for scalable control of quantum transport in emerging quantum technologies, with potential applications in qubit isolation, particle trapping, and state transfer.

arXiv:2508.08734•Quantum Science and Technology•Jul 24, 2026•0 citations

Superconducting circuit simulator of Bose-Hubbard model with a flat band

Xiu–Hao Deng, Chen-Yen Lai, Chih-Chun Chien

Recent advance in quantum simulations of interacting photons using superconducting circuits offers opportunities for investigating the Bose-Hubbard model in various geometries with hopping coefficients and self-interactions tuned to both signs. Here we investigate phenomena related to localized states associated with a flat band supported by the sawtooth geometry. A localization-delocalization transition emerges in the noninteracting regime as the sign of hopping coefficient is changed. In the presence of interactions, patterns of localized states approach a uniform density distribution for repulsive interactions while interesting localized density patterns can arise in a strongly attractive regime. The density patterns indicate the underlying inhomogeneity of the simulator. Two-particle correlations can further distinguish the nature of the localized states in attractive and repulsive interaction regimes. We also survey possible experimental implementations of the simulator.

arXiv:1602.01559•Physical review. B./Physical review. B•Feb 26, 2016•18 citations

Quasiparticle localization and ergodicity breaking in flat-band lattice models

Koushik Swaminathan

In lattice models, destructive interference can quench single-particle motion and produce (nearly) dispersionless Bloch bands, known as flat bands. Suppressing kinetic energy enhances the role of interactions and can lead to pairing, constrained dynamics, and localization-like behavior even in translationally invariant settings. This thesis studies attractive Hubbard-type interactions in such flat-band systems using an isolated-band (projected) description, which yields an effective Hamiltonian in a Wannier-orbital basis. The π-flux dice lattice is a convenient focus because its two lowest bands are perfectly flat and degenerate, and their subspace admits compactly localized Wannier functions. This makes the projection straightforward to implement and yields a projected Hamiltonian with a simple, short-range structure. A one-dimensional reference model is used alongside the dice lattice to separate and benchmark the effects of different processes. In Publication I, we construct a class of exact many-body eigenstates of the projected Hamiltonian of generic lattice models with flat bands in which localized unpaired quasiparticles coexist with a background of paired particles in the zero-momentum state. This general result motivates the study of a specific model, the π-flux dice-lattice. Using exact diagonalization and realtime evolution from few-particle initial states, we show that two-body bound states behave ergodically. At the same time, the density and spin distribution retain strong memory of the initial quasiparticle positions at long times. These results demonstrate localization-like dynamics in a translationally invariant flat-band model, where memory arises from projection-induced constraints rather than quenched disorder. In Publication II, we introduce a one-dimensional on-site/bond singlet model whose terms mirror those of the projected dice-lattice Hamiltonian, with tunable couplings controlling their relative strengths. Exact diagonalization shows that, for some couplings, the spectrum and dynamics of the on-site/bond-singlet model closely reproduce those of the projected dice lattice. We then use spectral statistics to probe how the different dynamical regimes manifest in energy-level correlations. In Publication III, we apply spectral statistics to the projected dice lattice using higher-order spacing and gap-ratio diagnostics. We find a robust parity dependence: even particle-number sectors show multi-block GOE behavior within fixed symmetry sectors, while odd particle-number sectors exhibit exact doublets and inter-doublet correlations that are GUE at even orders. The appearance of distinct random-matrix ensembles (GOE and GUE) within the same physical model is an unusual and interesting feature, which calls for a deeper understanding of the hidden symmetry structure of the Hamiltonians obtained by projecting onto the flat-band subspace in the dice lattice and other lattice models with flat bands realized with ultracold gases in optical lattices and in the newly discovered class of moiré materials.

•Jan 1, 2026•0 citations

Flat-Band (De)localization Emulated with a Superconducting Qubit Array

Ilan T. Rosen, Sarah E. Muschinske, Cora N. Barrett +10 more

Arrays of coupled superconducting qubits are analog quantum simulators able to emulate a wide range of tight-binding models in parameter regimes that are difficult to access or adjust in natural materials. In this work, we use a superconducting qubit array to emulate a tight-binding model on the rhombic lattice, which features flat bands. Enabled by broad adjustability of the dispersion of the energy bands and of on-site disorder, we examine regimes where flat-band localization and Anderson localization compete. We observe disorder-induced localization for dispersive bands and disorder-induced delocalization for flat bands. Remarkably, we find a sudden transition between the two regimes and, in its vicinity, the semblance of quantum critical scaling.

arXiv:2410.07878•Physical Review X•Jun 16, 2025•13 citations

Enhancement of pairing correlations due to nearly flat bands in the plaquette-Lieb Hubbard model

Kai Cheng, Shi-Chao Fang, Zhongbing Huang

Motivated by recent research works on the flat-band correlated electron systems, we construct a plaquette-Lieb lattice, which exhibits nearly flat bands close to the Fermi level around half-filling, when the inter-plaquette hopping integral is much smaller than the intra-plaquette one. A detailed comparison study with the well-known checkerboard lattice indicates that there exist significant differences for the pairing property between the two lattices, and the nearly flat bands on the plaquette-Lieb lattice strongly enhance the [Formula: see text]-wave pairing correlation for repulsive on-site Hubbard interaction and [Formula: see text]-wave pairing correlation for attractive on-site Hubbard interaction. Our study not only provides a new lattice with nearly flat bands, but also deepens the understanding of electronic structure on superconductivity.

International Journal of Modern Physics C•Jan 15, 2022•0 citations

Circuit quantum electrodynamics simulator of flat band physics in a Lieb lattice

Zi-He Yang, Yan-Pu Wang, Zheng‐Yuan Xue +4 more

The concept of flat band plays an important role in strongly correlated many-body physics. However, the demonstration of the flat band physics is highly nontrivial due to intrinsic limitations in conventional condensed-matter materials. Here we propose a circuit quantum electrodynamics simulator of the two-dimensional (2D) Lieb lattice exhibiting a flat middle band. By exploiting the parametric conversion method, we design a photonic Lieb lattice with in situ tunable hopping strengths in a 2D array of coupled superconducting transmissionline resonators. Moreover, the flexibility of our proposal enables the incorporation of both the artificial gauge field and the strong photon-photon interaction in a time- and site-resolved manner. To unambiguously demonstrate the synthesized flat band, we further investigate the observation of the flat band localization of microwave photons through the pumping and the steady-state measurements of only a few sites on the lattice. Requiring only current level of technique and being robust against imperfections in realistic circuits, our scheme can be readily tested in experiment and may pave a new way towards the realization of exotic photonic quantum Hall fluids including anomalous quantum Hall effect and bosonic fractional quantum Hall effect without magnetic field.

arXiv:1603.04686•Physical Review A•Jun 17, 2016•41 citations
Lattices with dispersionless, or flat, energy bands have attracted substantial interest in part due to the strong dependence of particle dynamics on interactions. Using superconducting circuits, we experimentally study the dynamics of one and two particles in a single plaquette of a lattice whose band structure consists entirely of flat bands. We first observe strictly localized dynamics of a single particle, the hallmark of all-bands-flat physics. Upon initializing two particles on the same site, we see an interaction-enabled delocalized walk across the plaquette. We further find localization in Fock space for two particles initialized on opposite sides of the plaquette. These results mark the first experimental observation of a quantum walk that becomes delocalized due to interactions and establishes a key building block in superconducting circuits for studying flat-band dynamics with strong interactions.
Abstract Flat-band systems offer a uniquely powerful tool for quantum control in dynamics due to their characteristic feature of having a dispersionless energy band. Simulating such highly sensitive systems on current digital quantum computers is a challenging task, due to the intrinsic limitations of the noisy intermediate-scale quantum devices. Here we present high-fidelity digital quantum simulations of flat-band (FB) and all-bands-flat (ABF) lattices, using an advanced tensor network based variational optimization approach to compress the circuit depth. With the compressed quantum circuits, we first explore single-particle dynamics and observe two distinct behaviours: strong localization in ABF lattices and delocalization in FB lattices. By integrating FB and ABF lattices into a one-dimensional hybrid structure, we achieve controllable quantum transport, where the ABF lattice acts as a quantum switch. Extending to two-particle dynamics, we show that transport remains controllable by tuning the hopping amplitude alone, even in the presence of interactions. These results establish FB engineered systems as a promising pathway for scalable control of quantum transport in emerging quantum technologies, with potential applications in qubit isolation, particle trapping, and state transfer.
Recent advance in quantum simulations of interacting photons using superconducting circuits offers opportunities for investigating the Bose-Hubbard model in various geometries with hopping coefficients and self-interactions tuned to both signs. Here we investigate phenomena related to localized states associated with a flat band supported by the sawtooth geometry. A localization-delocalization transition emerges in the noninteracting regime as the sign of hopping coefficient is changed. In the presence of interactions, patterns of localized states approach a uniform density distribution for repulsive interactions while interesting localized density patterns can arise in a strongly attractive regime. The density patterns indicate the underlying inhomogeneity of the simulator. Two-particle correlations can further distinguish the nature of the localized states in attractive and repulsive interaction regimes. We also survey possible experimental implementations of the simulator.
In lattice models, destructive interference can quench single-particle motion and produce (nearly) dispersionless Bloch bands, known as flat bands. Suppressing kinetic energy enhances the role of interactions and can lead to pairing, constrained dynamics, and localization-like behavior even in translationally invariant settings. This thesis studies attractive Hubbard-type interactions in such flat-band systems using an isolated-band (projected) description, which yields an effective Hamiltonian in a Wannier-orbital basis. The π-flux dice lattice is a convenient focus because its two lowest bands are perfectly flat and degenerate, and their subspace admits compactly localized Wannier functions. This makes the projection straightforward to implement and yields a projected Hamiltonian with a simple, short-range structure. A one-dimensional reference model is used alongside the dice lattice to separate and benchmark the effects of different processes. In Publication I, we construct a class of exact many-body eigenstates of the projected Hamiltonian of generic lattice models with flat bands in which localized unpaired quasiparticles coexist with a background of paired particles in the zero-momentum state. This general result motivates the study of a specific model, the π-flux dice-lattice. Using exact diagonalization and realtime evolution from few-particle initial states, we show that two-body bound states behave ergodically. At the same time, the density and spin distribution retain strong memory of the initial quasiparticle positions at long times. These results demonstrate localization-like dynamics in a translationally invariant flat-band model, where memory arises from projection-induced constraints rather than quenched disorder. In Publication II, we introduce a one-dimensional on-site/bond singlet model whose terms mirror those of the projected dice-lattice Hamiltonian, with tunable couplings controlling their relative strengths. Exact diagonalization shows that, for some couplings, the spectrum and dynamics of the on-site/bond-singlet model closely reproduce those of the projected dice lattice. We then use spectral statistics to probe how the different dynamical regimes manifest in energy-level correlations. In Publication III, we apply spectral statistics to the projected dice lattice using higher-order spacing and gap-ratio diagnostics. We find a robust parity dependence: even particle-number sectors show multi-block GOE behavior within fixed symmetry sectors, while odd particle-number sectors exhibit exact doublets and inter-doublet correlations that are GUE at even orders. The appearance of distinct random-matrix ensembles (GOE and GUE) within the same physical model is an unusual and interesting feature, which calls for a deeper understanding of the hidden symmetry structure of the Hamiltonians obtained by projecting onto the flat-band subspace in the dice lattice and other lattice models with flat bands realized with ultracold gases in optical lattices and in the newly discovered class of moiré materials.
Arrays of coupled superconducting qubits are analog quantum simulators able to emulate a wide range of tight-binding models in parameter regimes that are difficult to access or adjust in natural materials. In this work, we use a superconducting qubit array to emulate a tight-binding model on the rhombic lattice, which features flat bands. Enabled by broad adjustability of the dispersion of the energy bands and of on-site disorder, we examine regimes where flat-band localization and Anderson localization compete. We observe disorder-induced localization for dispersive bands and disorder-induced delocalization for flat bands. Remarkably, we find a sudden transition between the two regimes and, in its vicinity, the semblance of quantum critical scaling.
Motivated by recent research works on the flat-band correlated electron systems, we construct a plaquette-Lieb lattice, which exhibits nearly flat bands close to the Fermi level around half-filling, when the inter-plaquette hopping integral is much smaller than the intra-plaquette one. A detailed comparison study with the well-known checkerboard lattice indicates that there exist significant differences for the pairing property between the two lattices, and the nearly flat bands on the plaquette-Lieb lattice strongly enhance the [Formula: see text]-wave pairing correlation for repulsive on-site Hubbard interaction and [Formula: see text]-wave pairing correlation for attractive on-site Hubbard interaction. Our study not only provides a new lattice with nearly flat bands, but also deepens the understanding of electronic structure on superconductivity.
The concept of flat band plays an important role in strongly correlated many-body physics. However, the demonstration of the flat band physics is highly nontrivial due to intrinsic limitations in conventional condensed-matter materials. Here we propose a circuit quantum electrodynamics simulator of the two-dimensional (2D) Lieb lattice exhibiting a flat middle band. By exploiting the parametric conversion method, we design a photonic Lieb lattice with in situ tunable hopping strengths in a 2D array of coupled superconducting transmissionline resonators. Moreover, the flexibility of our proposal enables the incorporation of both the artificial gauge field and the strong photon-photon interaction in a time- and site-resolved manner. To unambiguously demonstrate the synthesized flat band, we further investigate the observation of the flat band localization of microwave photons through the pumping and the steady-state measurements of only a few sites on the lattice. Requiring only current level of technique and being robust against imperfections in realistic circuits, our scheme can be readily tested in experiment and may pave a new way towards the realization of exotic photonic quantum Hall fluids including anomalous quantum Hall effect and bosonic fractional quantum Hall effect without magnetic field.