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:2004.00954 · Physical Review Research

Coexistence of localized and extended phases: Many-body localization in a harmonic trap

Titas Chanda, Ruixiao Yao, Jakub Zakrzewski

Published Aug 18, 2020• 38 citations
arXivHTMLPDF

Abstract

This work shows that interacting particles in a one dimensional optical lattice with strong harmonic confinement behave in a unique way, resulting in an exotic coexistence between spatially separated regions of localized and extended domains. The position of the border between two regions is estimated using local static field arguments coming from Stark localization

DOI
10.1103/physrevresearch.2.032039

Related papers

Many-body localization of bosons in an optical lattice: Dynamics in disorder-free potentials

Ruixiao Yao, Jakub Zakrzewski

The phenomenon of many-body Stark localization of bosons in tilted optical lattice is studied. Despite the fact that no disorder is necessary for Stark localization to occur, it is very similar to well-known many-body localization (MBL) in sufficiently strong disorder. Not only the mean gap ratio reaches Poissonian value as characteristic for localized situations, but also the eigenstates reveal multifractal character as in standard MBL. Stark localization enables a coexistence of spacially separated thermal and localized phases in the harmonic trap similarly to fermions. Stark localization may also lead to spectacular trapping of particles in a reversed harmonic field which naively might be considered as an unstable configuration.

arXiv:2007.04745•Physical review. B./Physical review. B•Sep 23, 2020•52 citations

Quantum correlations and spatial localization in trapped one-dimensional ultra-cold Bose–Bose–Bose mixtures

Tran Duong Anh-Tai, Miguel A. García-March, Thomas Busch +1 more

We systematically investigate and illustrate the complete ground-state phase diagram for a one-dimensional, three-species mixture of a few repulsively interacting bosons trapped harmonically. To numerically obtain the solutions to the many-body Schrödinger equation, we employ the improved Exact Diagonalization method (Anh-Tai et al 2023 SciPost Phys. 15 048), which is capable of treating strongly-correlated few-body systems from first principles in an efficiently truncated Hilbert space. We present our comprehensive results for all possible combinations of intra- and interspecies interactions in the extreme limits that are either the ideal limit (g = 0) or close to the hard-core limit (). These results show the emergence of unique ground-state properties related to correlations, coherence and spatial localization stemming from strongly repulsive interactions.

•Jan 1, 2025•0 citations

Quantum correlations and spatial localization in trapped one-dimensional ultra-cold Bose–Bose–Bose mixtures

Tran Duong Anh-Tai, Miguel Ángel García-March, Thomas Busch +1 more

Abstract We systematically investigate and illustrate the complete ground-state phase diagram for a one-dimensional, three-species mixture of a few repulsively interacting bosons trapped harmonically. To numerically obtain the solutions to the many-body Schrödinger equation, we employ the improved Exact Diagonalization method (Anh-Tai et al 2023 SciPost Phys. 15 048), which is capable of treating strongly-correlated few-body systems from first principles in an efficiently truncated Hilbert space. We present our comprehensive results for all possible combinations of intra- and interspecies interactions in the extreme limits that are either the ideal limit (g = 0) or close to the hard-core limit ( g → ∞ ). These results show the emergence of unique ground-state properties related to correlations, coherence and spatial localization stemming from strongly repulsive interactions.

arXiv:2501.15358•New Journal of Physics•Jun 26, 2025•5 citations

Many-body localization of bosons in optical lattices

Piotr Sierant, Jakub Zakrzewski

Many-body localization for a system of bosons trapped in a one-dimensional lattice is discussed. Two models that may be realized for cold atoms in optical lattices are considered. The model with a random on-site potential is compared with previously introduced random interactions model. While the origin and character of the disorder in both systems is different they show interesting similar properties. In particular, many-body localization appears for a sufficiently large disorder as verified by a time evolution of initial density wave states as well as using statistical properties of energy levels for small system sizes. Starting with different initial states, we observe that the localization properties are energy-dependent which reveals an inverted many-body localization edge in both systems (that finding is also verified by statistical analysis of energy spectrum). Moreover, we consider computationally challenging regime of transition between many body localized and extended phases where we observe a characteristic algebraic decay of density correlations which may be attributed to subdiffusion (and Griffiths-like regions) in the studied systems. Ergodicity breaking in the disordered Bose–Hubbard models is compared with the slowing-down of the time evolution of the clean system at large interactions.

arXiv:1712.02628•New Journal of Physics•Apr 3, 2018•74 citations

Stark Many-Body Localization in One-Dimensional Bose Gas under the Continuous Limit

Zihan Zhao, Zhongchi Zhang, Huaichuan Wang +3 more

Many-body localization, an emergent quantum phenomenon, challenges the fundamental principles of thermodynamics and has attracted significant attention. In this study, we demonstrate Stark many-body localization in a one-dimensional Bose gas under the continuous limit, a scenario that extends well beyond the conventional tight-binding model commonly employed in most discussions. This localization occurs within a background harmonic trap without any random disorder, where the potential gradient effectively halts thermalization. Contrary to prior studies on Stark localization, our findings reveal that an increasing gradient does not necessarily lead to greater localization. Instead, we observe a complex transition within this continuous interacting system. Another surprising result is that a higher initial density, which typically correlates with a higher collisional rate and thermalization rate, actually induces stronger localization in this one-dimensional model. Additionally, we observe a density plateau with zero compressibility and low-density fluctuations, which may signal an insulating behavior associated with prethermalization during nonequilibrium dynamics.

PRX Quantum•Dec 15, 2025•0 citations

Ferromagnetism in Multi-Orbital Fermi Gas Loaded on a One-Dimensional Optical Lattice

Keita Kobayashi, Masahiko Okumura, Yukihiro Ota +2 more

We study a multi-orbital Fermi gas loaded on a one-dimensional optical lattice with harmonic trap potential. We show that this multi-orbital gas contains various quantum phases, i.e., (i) the ferromagnetic phase in large on–site interaction and (ii) the Haldane phase at half filling. Furthermore, our density-matrix renormalization-group simulations lead to systematic studies about the ground state, varying on–site interaction, spin imbalance, and total particle number, under spatial inhomogeneity originating from the trap potential. This trap potential produces a rich phase structure. In a metallic region, the phase-separated ferromagnetism appears, whereas in a central Mott core the Haldane phase is found. One of the remarkable features is that the ferromagnetic metal phase behaves as the edge state of the Haldane phase when these two phases coexist.

International Conference on Strongly Correlated Electron Systems (SCES)•Jun 16, 2014•0 citations
This work shows that interacting particles in a one dimensional optical lattice with strong harmonic confinement behave in a unique way, resulting in an exotic coexistence between spatially separated regions of localized and extended domains. The position of the border between two regions is estimated using local static field arguments coming from Stark localization
The phenomenon of many-body Stark localization of bosons in tilted optical lattice is studied. Despite the fact that no disorder is necessary for Stark localization to occur, it is very similar to well-known many-body localization (MBL) in sufficiently strong disorder. Not only the mean gap ratio reaches Poissonian value as characteristic for localized situations, but also the eigenstates reveal multifractal character as in standard MBL. Stark localization enables a coexistence of spacially separated thermal and localized phases in the harmonic trap similarly to fermions. Stark localization may also lead to spectacular trapping of particles in a reversed harmonic field which naively might be considered as an unstable configuration.
We systematically investigate and illustrate the complete ground-state phase diagram for a one-dimensional, three-species mixture of a few repulsively interacting bosons trapped harmonically. To numerically obtain the solutions to the many-body Schrödinger equation, we employ the improved Exact Diagonalization method (Anh-Tai et al 2023 SciPost Phys. 15 048), which is capable of treating strongly-correlated few-body systems from first principles in an efficiently truncated Hilbert space. We present our comprehensive results for all possible combinations of intra- and interspecies interactions in the extreme limits that are either the ideal limit (g = 0) or close to the hard-core limit (). These results show the emergence of unique ground-state properties related to correlations, coherence and spatial localization stemming from strongly repulsive interactions.
Abstract We systematically investigate and illustrate the complete ground-state phase diagram for a one-dimensional, three-species mixture of a few repulsively interacting bosons trapped harmonically. To numerically obtain the solutions to the many-body Schrödinger equation, we employ the improved Exact Diagonalization method (Anh-Tai et al 2023 SciPost Phys. 15 048), which is capable of treating strongly-correlated few-body systems from first principles in an efficiently truncated Hilbert space. We present our comprehensive results for all possible combinations of intra- and interspecies interactions in the extreme limits that are either the ideal limit (g = 0) or close to the hard-core limit ( g → ∞ ). These results show the emergence of unique ground-state properties related to correlations, coherence and spatial localization stemming from strongly repulsive interactions.
Many-body localization for a system of bosons trapped in a one-dimensional lattice is discussed. Two models that may be realized for cold atoms in optical lattices are considered. The model with a random on-site potential is compared with previously introduced random interactions model. While the origin and character of the disorder in both systems is different they show interesting similar properties. In particular, many-body localization appears for a sufficiently large disorder as verified by a time evolution of initial density wave states as well as using statistical properties of energy levels for small system sizes. Starting with different initial states, we observe that the localization properties are energy-dependent which reveals an inverted many-body localization edge in both systems (that finding is also verified by statistical analysis of energy spectrum). Moreover, we consider computationally challenging regime of transition between many body localized and extended phases where we observe a characteristic algebraic decay of density correlations which may be attributed to subdiffusion (and Griffiths-like regions) in the studied systems. Ergodicity breaking in the disordered Bose–Hubbard models is compared with the slowing-down of the time evolution of the clean system at large interactions.
Many-body localization, an emergent quantum phenomenon, challenges the fundamental principles of thermodynamics and has attracted significant attention. In this study, we demonstrate Stark many-body localization in a one-dimensional Bose gas under the continuous limit, a scenario that extends well beyond the conventional tight-binding model commonly employed in most discussions. This localization occurs within a background harmonic trap without any random disorder, where the potential gradient effectively halts thermalization. Contrary to prior studies on Stark localization, our findings reveal that an increasing gradient does not necessarily lead to greater localization. Instead, we observe a complex transition within this continuous interacting system. Another surprising result is that a higher initial density, which typically correlates with a higher collisional rate and thermalization rate, actually induces stronger localization in this one-dimensional model. Additionally, we observe a density plateau with zero compressibility and low-density fluctuations, which may signal an insulating behavior associated with prethermalization during nonequilibrium dynamics.
We study a multi-orbital Fermi gas loaded on a one-dimensional optical lattice with harmonic trap potential. We show that this multi-orbital gas contains various quantum phases, i.e., (i) the ferromagnetic phase in large on–site interaction and (ii) the Haldane phase at half filling. Furthermore, our density-matrix renormalization-group simulations lead to systematic studies about the ground state, varying on–site interaction, spin imbalance, and total particle number, under spatial inhomogeneity originating from the trap potential. This trap potential produces a rich phase structure. In a metallic region, the phase-separated ferromagnetism appears, whereas in a central Mott core the Haldane phase is found. One of the remarkable features is that the ferromagnetic metal phase behaves as the edge state of the Haldane phase when these two phases coexist.