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:2511.02218

Quasi-Solid and Supersolid from Quasiperiodic Long-Range Interactions

Chao Zhang

cond-mat.quant-gasquant-phSubmitted Nov 4, 2025• Announced Nov 5, 2025• 1 citation
v1 · Nov 4, 2025v2 · Jan 8, 2026
arXivHTMLPDF

Abstract

We investigate hard-core bosons in one dimension with quasiperiodic long-range interactions defined by V_ij = V0 cos(pi * alpha * i) cos(pi * alpha * j), where alpha = (sqrt(5) - 1)/2 is the inverse golden ratio. Large-scale quantum Monte Carlo simulations reveal incompressible density plateaus at incommensurate fillings tied to Fibonacci ratios. These plateaus feature emergent nonuniform density profiles and robust long-range correlations, as captured by the structure factor. Depending on filling and interaction strength, the system realizes either a quasi-solid phase with suppressed superfluidity, a quasi-supersolid phase where density order coexists with finite superfluid density, or a superfluid phase. Our results demonstrate that purely interaction-induced quasiperiodicity, without external potential or disorder, can stabilize novel quantum phases that simultaneously break translational symmetry and sustain quantum coherence.

Related papers

Stability of dipolar bosons in a quasiperiodic potential

Paolo Molignini, Barnali Chakrabarti

Quasiperiodic potentials and dipolar interactions each impose long-range order in quantum systems, but their interplay unlocks a rich landscape of unexplored quantum phases. In this work, we investigate how dipolar bosonic crystals respond to correlated disorder in the form of quasiperiodic potentials. Using exact numerical simulations and a suite of observables—including order parameters, energy, density distributions, and two-body coherence measures—we explore one-dimensional dipolar bosons in quasiperiodic lattices at both commensurate and incommensurate fillings. Our results reveal a complex competition between superfluid, Mott-insulator, density-wave, and crystalline phases, governed by the intricate balance of dipolar interactions, kinetic energy, and disorder strength. Crucially, we identify mechanisms that influence dipolar crystals, showing their surprising robustness even in the presence of strong quasiperiodic disorder. Strikingly, we challenge previous claims by demonstrating that a crystal phase—expected to precede full crystallization—does not emerge in the ground state. Instead, its traits appear only under moderate disorder, but never fully develop, giving way to a direct transition from a charge density wave to a crystal state. These findings provide new insights into the resilience of many-body quantum phases in complex environments and pave the way for engineering exotic quantum states in ultracold atomic systems.

arXiv:2502.04429•Physical Review Research•Jun 9, 2025•10 citations

Quasicrystalline Bose Glass in the Absence of Disorder and Quasidisorder

Matteo Ciardi, Adriano Angelone, Fabio Mezzacapo +1 more

We study the low-temperature phases of interacting bosons on a two-dimensional quasicrystalline lattice. By means of numerically exact path integral Monte Carlo simulations, we show that for sufficiently weak interactions the system is a homogeneous Bose-Einstein condensate that develops density modulations for increasing filling factor. The simultaneous occurrence of sizeable condensate fraction and density modulation can be interpreted as the analogous, in a quasicrystalline lattice, of supersolid phases occurring in conventional periodic lattices. For sufficiently large interaction strength and particle density, global condensation is lost and quantum exchanges are restricted to specific spatial regions. The emerging quantum phase is therefore a Bose glass, which here is stabilized in the absence of any source of disorder or quasidisorder, purely as a result of the interplay between quantum effects, particle interactions and quasicrystalline substrate. This finding clearly indicates that (quasi)disorder is not essential to observe Bose glass physics. Our results are of interest for ongoing experiments on (quasi)disorder-free quasicrystalline lattices.

arXiv:2212.13178•Physical Review Letters•Oct 26, 2023•18 citations

Exploring Quantum Phases of Dipolar Gases through Quasicrystalline Confinement

Vinicius Zampronio, Alejandro Mendoza-Coto, Tommaso Macrì +1 more

The effects of frustration on extended supersolid states is a largely unexplored subject in the realm of cold-atom systems. In this work, we explore the impact of quasicrystalline lattices on the supersolid phases of dipolar bosons. Our findings reveal that weak quasicrystalline lattices can induce a variety of modulated phases, merging the inherent solid pattern with a quasiperiodic decoration induced by the external potential. As the lattice becomes stronger, we observe a superquasicrystal phase and a Bose glass phase. Our results, supported by a detailed discussion on experimental feasibility using dysprosium atoms and quasicrystalline optical lattice potentials, open a new avenue in the exploration of long-range interacting quantum systems in aperiodic environments. We provide a solid foundation for future experimental investigations, potentially confirming our theoretical predictions and contributing profoundly to the field of quantum gases in complex external potentials.

arXiv:2403.03118•Physical Review Letters•Nov 6, 2024•6 citations

Supersolid phase in two-dimensional soft-core bosons at finite temperature

Sebastiano Peotta, G. Spada, S. Giorgini +2 more

The supersolid phase of soft-core bosons in two dimensions is investigated using the self-consistent Hartree-Fock and quantum Monte Carlo methods. An approximate phase diagram at finite temperatures is initially constructed using the mean-field approach, which is subsequently validated through precise path-integral simulations, enabling a microscopic characterization of the various phases. Superfluid and melting/freezing transitions are analyzed through the superfluid density and the long-range behavior of correlation functions associated with positional and orientational order, in accordance with the general picture of Berezinskii-Kosterlitz-Thouless transitions. A broad region at low temperatures is identified where the supersolid phase exists, separating the uniform superfluid phase from the normal quasicrystal phase. Additionally, a potential intermediate hexatic phase with quasi-long-range orientational order is identified in a narrow region between the normal solid and fluid phases. These findings establish self-consistent Hartree-Fock theory beyond the local density approximation as an effective tool, complementary to computationally intensive quantum Monte Carlo simulations, for investigating the melting of the supersolid phase and the possible emergence of the hexatic superfluid phase in bosonic systems with various interaction potentials.

arXiv:2504.03482•Physical review. B./Physical review. B•Nov 7, 2025•2 citations

Self-induced Bose glass phase in quantum quasicrystals

Matheus Grossklags, M. Ciardi, Vinicius Zampronio +2 more

We study the emergence of Bose glass phases in self sustained bosonic quasicrystals induced by a pair interaction between particles of Lifshitz–Petrich type. By using a mean-field variational method designed in momentum space as well as Gross–Pitaevskii simulations we determine the phase diagram of the model. The study of the local and global superfluid fraction allows the identification of supersolid, super quasicrystal, Bose glass and insulating phases. The Bose glass phase emerges as a quasicrystal phase in which the global superfluidity is essentially zero, while the local superfluidity remains finite in certain ring structures of the quasicrystalline pattern. Furthermore, we perform continuous space Path Integral Monte Carlo simulations for a case in which the interaction between particles stabilizes a quasicrystal phase. Our results show that as the strength of the interaction between particles is increased the system undergoes a sequence of states consistent with the super quasicrystal, Bose glass, and quasicrystal insulator thermodynamic phases.

arXiv:2308.12434•Results in Physics•Sep 28, 2024•5 citations

Study of long-range orders of hard-core bosons coupled to cooperative normal modes in two-dimensional lattices

Amrita Ghosh, Sreenija Yarlagadda

Understanding the microscopic mechanism of coexisting long-range orders (such as lattice supersolidity) in strongly correlated systems is a subject of immense interest. We study the possible manifestations of long-range orders, including lattice-supersolid phases with differently broken symmetry, in a two-dimensional square lattice system of hard-core bosons (HCBs) coupled to archetypal cooperative/coherent normal-mode distortions such as those in perovskites. At strong HCB-phonon coupling, using a duality transformation to map the strong-coupling problem to a weak-coupling one, we obtain an effective Hamiltonian involving nearest-neighbor, next-nearest-neighbor, and next-to-next-nearest-neighbor hoppings and repulsions. Using stochastic series expansion quantum Monte Carlo, we construct the phase diagram of the system. As coupling strength is increased, we find that the system undergoes a first-order quantum phase transition from a superfluid to a checkerboard solid at half-filling and from a superfluid to a diagonal striped solid [with crystalline ordering wave vector $\stackrel{P\vec}{Q}=(2\ensuremath{\pi}/3,2\ensuremath{\pi}/3)$ or $(2\ensuremath{\pi}/3,4\ensuremath{\pi}/3)]$ at one-third filling without showing any evidence of supersolidity. On tuning the system away from these commensurate fillings, checkerboard supersolid is generated near half-filling whereas a rare diagonal striped supersolid is realized near one-third filling. Interestingly, there is an asymmetry in the extent of supersolidity about one-third filling. Within our framework, we also provide an explanation for the observed checkerboard and stripe formations in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{NiO}}_{4}$ at $x=1/2$ and $x=1/3$.

arXiv:1610.01447•Physical review. B./Physical review. B•Sep 6, 2017•6 citations
We investigate hard-core bosons in one dimension with quasiperiodic long-range interactions defined by V_ij = V0 cos(pi * alpha * i) cos(pi * alpha * j), where alpha = (sqrt(5) - 1)/2 is the inverse golden ratio. Large-scale quantum Monte Carlo simulations reveal incompressible density plateaus at incommensurate fillings tied to Fibonacci ratios. These plateaus feature emergent nonuniform density profiles and robust long-range correlations, as captured by the structure factor. Depending on filling and interaction strength, the system realizes either a quasi-solid phase with suppressed superfluidity, a quasi-supersolid phase where density order coexists with finite superfluid density, or a superfluid phase. Our results demonstrate that purely interaction-induced quasiperiodicity, without external potential or disorder, can stabilize novel quantum phases that simultaneously break translational symmetry and sustain quantum coherence.
Quasiperiodic potentials and dipolar interactions each impose long-range order in quantum systems, but their interplay unlocks a rich landscape of unexplored quantum phases. In this work, we investigate how dipolar bosonic crystals respond to correlated disorder in the form of quasiperiodic potentials. Using exact numerical simulations and a suite of observables—including order parameters, energy, density distributions, and two-body coherence measures—we explore one-dimensional dipolar bosons in quasiperiodic lattices at both commensurate and incommensurate fillings. Our results reveal a complex competition between superfluid, Mott-insulator, density-wave, and crystalline phases, governed by the intricate balance of dipolar interactions, kinetic energy, and disorder strength. Crucially, we identify mechanisms that influence dipolar crystals, showing their surprising robustness even in the presence of strong quasiperiodic disorder. Strikingly, we challenge previous claims by demonstrating that a crystal phase—expected to precede full crystallization—does not emerge in the ground state. Instead, its traits appear only under moderate disorder, but never fully develop, giving way to a direct transition from a charge density wave to a crystal state. These findings provide new insights into the resilience of many-body quantum phases in complex environments and pave the way for engineering exotic quantum states in ultracold atomic systems.
We study the low-temperature phases of interacting bosons on a two-dimensional quasicrystalline lattice. By means of numerically exact path integral Monte Carlo simulations, we show that for sufficiently weak interactions the system is a homogeneous Bose-Einstein condensate that develops density modulations for increasing filling factor. The simultaneous occurrence of sizeable condensate fraction and density modulation can be interpreted as the analogous, in a quasicrystalline lattice, of supersolid phases occurring in conventional periodic lattices. For sufficiently large interaction strength and particle density, global condensation is lost and quantum exchanges are restricted to specific spatial regions. The emerging quantum phase is therefore a Bose glass, which here is stabilized in the absence of any source of disorder or quasidisorder, purely as a result of the interplay between quantum effects, particle interactions and quasicrystalline substrate. This finding clearly indicates that (quasi)disorder is not essential to observe Bose glass physics. Our results are of interest for ongoing experiments on (quasi)disorder-free quasicrystalline lattices.
The effects of frustration on extended supersolid states is a largely unexplored subject in the realm of cold-atom systems. In this work, we explore the impact of quasicrystalline lattices on the supersolid phases of dipolar bosons. Our findings reveal that weak quasicrystalline lattices can induce a variety of modulated phases, merging the inherent solid pattern with a quasiperiodic decoration induced by the external potential. As the lattice becomes stronger, we observe a superquasicrystal phase and a Bose glass phase. Our results, supported by a detailed discussion on experimental feasibility using dysprosium atoms and quasicrystalline optical lattice potentials, open a new avenue in the exploration of long-range interacting quantum systems in aperiodic environments. We provide a solid foundation for future experimental investigations, potentially confirming our theoretical predictions and contributing profoundly to the field of quantum gases in complex external potentials.
The supersolid phase of soft-core bosons in two dimensions is investigated using the self-consistent Hartree-Fock and quantum Monte Carlo methods. An approximate phase diagram at finite temperatures is initially constructed using the mean-field approach, which is subsequently validated through precise path-integral simulations, enabling a microscopic characterization of the various phases. Superfluid and melting/freezing transitions are analyzed through the superfluid density and the long-range behavior of correlation functions associated with positional and orientational order, in accordance with the general picture of Berezinskii-Kosterlitz-Thouless transitions. A broad region at low temperatures is identified where the supersolid phase exists, separating the uniform superfluid phase from the normal quasicrystal phase. Additionally, a potential intermediate hexatic phase with quasi-long-range orientational order is identified in a narrow region between the normal solid and fluid phases. These findings establish self-consistent Hartree-Fock theory beyond the local density approximation as an effective tool, complementary to computationally intensive quantum Monte Carlo simulations, for investigating the melting of the supersolid phase and the possible emergence of the hexatic superfluid phase in bosonic systems with various interaction potentials.
We study the emergence of Bose glass phases in self sustained bosonic quasicrystals induced by a pair interaction between particles of Lifshitz–Petrich type. By using a mean-field variational method designed in momentum space as well as Gross–Pitaevskii simulations we determine the phase diagram of the model. The study of the local and global superfluid fraction allows the identification of supersolid, super quasicrystal, Bose glass and insulating phases. The Bose glass phase emerges as a quasicrystal phase in which the global superfluidity is essentially zero, while the local superfluidity remains finite in certain ring structures of the quasicrystalline pattern. Furthermore, we perform continuous space Path Integral Monte Carlo simulations for a case in which the interaction between particles stabilizes a quasicrystal phase. Our results show that as the strength of the interaction between particles is increased the system undergoes a sequence of states consistent with the super quasicrystal, Bose glass, and quasicrystal insulator thermodynamic phases.
Understanding the microscopic mechanism of coexisting long-range orders (such as lattice supersolidity) in strongly correlated systems is a subject of immense interest. We study the possible manifestations of long-range orders, including lattice-supersolid phases with differently broken symmetry, in a two-dimensional square lattice system of hard-core bosons (HCBs) coupled to archetypal cooperative/coherent normal-mode distortions such as those in perovskites. At strong HCB-phonon coupling, using a duality transformation to map the strong-coupling problem to a weak-coupling one, we obtain an effective Hamiltonian involving nearest-neighbor, next-nearest-neighbor, and next-to-next-nearest-neighbor hoppings and repulsions. Using stochastic series expansion quantum Monte Carlo, we construct the phase diagram of the system. As coupling strength is increased, we find that the system undergoes a first-order quantum phase transition from a superfluid to a checkerboard solid at half-filling and from a superfluid to a diagonal striped solid [with crystalline ordering wave vector $\stackrel{P\vec}{Q}=(2\ensuremath{\pi}/3,2\ensuremath{\pi}/3)$ or $(2\ensuremath{\pi}/3,4\ensuremath{\pi}/3)]$ at one-third filling without showing any evidence of supersolidity. On tuning the system away from these commensurate fillings, checkerboard supersolid is generated near half-filling whereas a rare diagonal striped supersolid is realized near one-third filling. Interestingly, there is an asymmetry in the extent of supersolidity about one-third filling. Within our framework, we also provide an explanation for the observed checkerboard and stripe formations in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{NiO}}_{4}$ at x=1/2x=1/2x=1/2 and x=1/3x=1/3x=1/3.