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:1810.08209 · Physical review. B./Physical review. B

Investigating many-body mobility edges in isolated quantum systems

Xingbo Wei, Chen Cheng, Gao Xianlong, Rubem Mondaini

Published Apr 24, 2019• 34 citations
arXivHTMLPDF

Abstract

The existence of many-body mobility edges in closed quantum systems has been the focus of intense debate after the emergence of the description of the many-body localization phenomenon. Here we propose that this issue can be settled in experiments by investigating the time evolution of local degrees of freedom, tailored for specific energies and initial states. An interacting model of spinless fermions with exponentially long-ranged tunneling amplitudes, whose noninteracting version is known to display single-particle mobility edges, is used as the starting point upon which nearest-neighbor interactions are included. We verify the manifestation of many-body mobility edges by using numerous probes, suggesting that one cannot explain their appearance as merely being a result of finite-size effects. Lastly, our scheme of following the quantum time evolution at different energies is generic and can be promptly used in a variety of models.

DOI
10.1103/physrevb.99.165137

Related papers

Quantum nonergodicity and fermion localization in a system with a single-particle mobility edge

Xiaopeng Li, J. H. Pixley, Dong-Ling Deng +2 more

Quantum thermalization of isolated systems undergoing unitary time evolution is a fundamental problem in quantum statistical mechanics. Its study has been revived recently in the context of many-body Anderson localization. Previous works have focused on localization of many-body systems with all the single-particle states being localized. As a significant step forward, this work studies localization aspects of noninteracting many-particle systems in the presence of a single-particle mobility edge. By systemically investigating entanglement entropy scaling and nonthermal fluctuations in various lattice models, the authors establish a nonergodic extended phase as a generic intermediate phase (between purely ergodic extended and nonergodic localized phases) for the many-body localization transition of noninteracting fermions. This work also sheds light on the interacting transition scenario as well.

arXiv:1602.01849•Physical review. B./Physical review. B•May 31, 2016•104 citations

Mobility edge in long-range interacting many-body localized systems

Rozhin Yousefjani, Abolfazl Bayat

As disorder strength increases in quantum many-body systems a new phase of matter, the so-called many-body localization, emerges across the whole spectrum. This transition is energy dependent, a phenomenon known as mobility edge, such that the mid-spectrum eigenstates tend to localize at larger values of disorder in comparison to eigenstates near the edges of the spectrum. Many-body localization becomes more sophisticated in long-range interacting systems. Here, by focusing on several quantities, we draw the phase diagram as a function of disorder strength and energy spectrum, for a various range of interactions. Regardless of the underlying transition type, either second-order or Kosterlitz-Thouless, our analysis consistently determines the mobility edge, i.e., the phase boundary across the spectrum. We show that, long-range interaction enhances the localization effect and shifts the phase boundary towards smaller values of disorder. In addition, we establish a hierarchy among the studied quantities concerning their corresponding transition boundary and critical exponents. Interestingly, we show that deliberately discarding some information of the system can mitigate finite-size effects and provide results in line with the analytical predictions at the thermodynamic limit.

arXiv:2209.01337•Physical review. B./Physical review. B•Jan 6, 2023•21 citations

Detecting a many-body mobility edge with quantum quenches

Piero Naldesi, Elisa Ercolessi, Tommaso Roscilde

The many-body localization (MBL) transition is a quantum phase transition involving highly excited eigenstates of a disordered quantum many-body Hamiltonian, which evolve from “extended/ergodic" (exhibiting extensive entanglement entropies and fluctuations) to “localized" (exhibiting area-law scaling of entanglement and fluctuations). The MBL transition can be driven by the strength of disorder in a given spectral range, or by the energy density at fixed disorder – if the system possesses a many-body mobility edge. Here we propose to explore the latter mechanism by using “quantum-quench spectroscopy", namely via quantum quenches of variable width which prepare the state of the system in a superposition of eigenstates of the Hamiltonian within a controllable spectral region. Studying numerically a chain of interacting spinless fermions in a quasi-periodic potential, we argue that this system has a many-body mobility edge; and we show that its existence translates into a clear dynamical transition in the time evolution immediately following a quench in the strength of the quasi-periodic potential, as well as a transition in the scaling properties of the quasi-stationary state at long times. Our results suggest a practical scheme for the experimental observation of many-body mobility edges using cold-atom setups.

arXiv:1607.01285•SciPost Physics•Oct 27, 2016•71 citations

Particle density mobility edge

Pietro Brighi, Dmitry A. Abanin, Maksym Serbyn

Many-body localization provides a mechanism to avoid thermalization in isolated interacting quantum systems. The breakdown of thermalization may be complete, when all eigenstates in the many-body spectrum become localized, or partial, when the so-called many-body mobility edge separates localized and delocalized parts of the spectrum. Previously, De Roeck et al. [arXiv:1506.01505] suggested a possible instability of the many-body mobility edge in energy density. The local ergodic regions - so called - resonantly spread throughout the system, leading to delocalization. In order to study such instability mechanism, in this work we design a model featuring many-body mobility edge in particle density: the states at small particle density are localized, while increasing the density of particles leads to delocalization. Using numerical simulations with matrix product states we demonstrate the stability of MBL with respect to small bubbles in large dilute systems for experimentally relevant timescales. In addition, we demonstrate that processes where the bubble spreads are favored over processes that lead to resonant tunneling, suggesting a possible mechanism behind the observed stability of many-body mobility edge. We conclude by proposing experiments to probe particle density mobility edge in Bose-Hubbard model.

•May 6, 2020•0 citations

Stability of mobility edges in disordered interacting systems

Pietro Brighi, Dmitry A. Abanin, Maksym Serbyn

Many-body localization provides a mechanism to avoid thermalization in isolated interacting quantum systems. The breakdown of thermalization may be complete, when all eigenstates in the many-body spectrum become localized, or partial, when the so-called many-body mobility edge separates localized and delocalized parts of the spectrum. Previously, De Roeck et al. [Phys. Rev. B 93, 014203 (2016)] suggested a possible instability of the many-body mobility edge in energy density. The local ergodic regions---so-called ``bubbles''---resonantly spread throughout the system, leading to delocalization. In order to study such instability mechanism, in this work we design a model featuring many-body mobility edge in particle density: the states at small particle density are localized, while increasing the density of particles leads to delocalization. Using numerical simulations with matrix product states, we demonstrate the stability of many-body localization with respect to small bubbles in large dilute systems for experimentally relevant timescales. In addition, we demonstrate that processes where the bubble spreads are favored over processes that lead to resonant tunneling, suggesting a possible mechanism behind the observed stability of many-body mobility edge. We conclude by proposing experiments to probe particle density mobility edge in the Bose-Hubbard model.

arXiv:2005.02999•Physical review. B./Physical review. B•Aug 26, 2020•20 citations

Statistics of noninteracting many-body fermionic states: The question of a many-body mobility edge

Ke Huang, DinhDuy Vu, S. Das Sarma +1 more

In this work, we study the statistics of a generic noninteracting many-body fermionic system whose single-particle counterpart has a single-particle mobility edge (SPME). We first prove that the spectrum and the extensive conserved quantities follow the multivariate normal distribution with a vanishing standard deviation $\ensuremath{\sim}O(1/\sqrt{L})$ in the thermodynamic limit, regardless of SPME. Consequently, the theorem rules out an infinite-temperature or high-temperature many-body mobility edge (MBME) for generic noninteracting fermionic systems in any dimension. Further, we also prove that the spectrum of a one-dimensional fermionic many-body system with short-range interactions is qualitatively similar to that of a noninteracting many-body system up to the third-order moment. These results partially explain why neither short-range [Phys. Rev. B 107, 035129 (2023)] nor long-range interacting systems exhibit an infinite-temperature MBME in a one-dimensional system.

arXiv:2306.11692•Physical review. B./Physical review. B•May 31, 2024•1 citation
The existence of many-body mobility edges in closed quantum systems has been the focus of intense debate after the emergence of the description of the many-body localization phenomenon. Here we propose that this issue can be settled in experiments by investigating the time evolution of local degrees of freedom, tailored for specific energies and initial states. An interacting model of spinless fermions with exponentially long-ranged tunneling amplitudes, whose noninteracting version is known to display single-particle mobility edges, is used as the starting point upon which nearest-neighbor interactions are included. We verify the manifestation of many-body mobility edges by using numerous probes, suggesting that one cannot explain their appearance as merely being a result of finite-size effects. Lastly, our scheme of following the quantum time evolution at different energies is generic and can be promptly used in a variety of models.
Quantum thermalization of isolated systems undergoing unitary time evolution is a fundamental problem in quantum statistical mechanics. Its study has been revived recently in the context of many-body Anderson localization. Previous works have focused on localization of many-body systems with all the single-particle states being localized. As a significant step forward, this work studies localization aspects of noninteracting many-particle systems in the presence of a single-particle mobility edge. By systemically investigating entanglement entropy scaling and nonthermal fluctuations in various lattice models, the authors establish a nonergodic extended phase as a generic intermediate phase (between purely ergodic extended and nonergodic localized phases) for the many-body localization transition of noninteracting fermions. This work also sheds light on the interacting transition scenario as well.
As disorder strength increases in quantum many-body systems a new phase of matter, the so-called many-body localization, emerges across the whole spectrum. This transition is energy dependent, a phenomenon known as mobility edge, such that the mid-spectrum eigenstates tend to localize at larger values of disorder in comparison to eigenstates near the edges of the spectrum. Many-body localization becomes more sophisticated in long-range interacting systems. Here, by focusing on several quantities, we draw the phase diagram as a function of disorder strength and energy spectrum, for a various range of interactions. Regardless of the underlying transition type, either second-order or Kosterlitz-Thouless, our analysis consistently determines the mobility edge, i.e., the phase boundary across the spectrum. We show that, long-range interaction enhances the localization effect and shifts the phase boundary towards smaller values of disorder. In addition, we establish a hierarchy among the studied quantities concerning their corresponding transition boundary and critical exponents. Interestingly, we show that deliberately discarding some information of the system can mitigate finite-size effects and provide results in line with the analytical predictions at the thermodynamic limit.
The many-body localization (MBL) transition is a quantum phase transition involving highly excited eigenstates of a disordered quantum many-body Hamiltonian, which evolve from “extended/ergodic" (exhibiting extensive entanglement entropies and fluctuations) to “localized" (exhibiting area-law scaling of entanglement and fluctuations). The MBL transition can be driven by the strength of disorder in a given spectral range, or by the energy density at fixed disorder – if the system possesses a many-body mobility edge. Here we propose to explore the latter mechanism by using “quantum-quench spectroscopy", namely via quantum quenches of variable width which prepare the state of the system in a superposition of eigenstates of the Hamiltonian within a controllable spectral region. Studying numerically a chain of interacting spinless fermions in a quasi-periodic potential, we argue that this system has a many-body mobility edge; and we show that its existence translates into a clear dynamical transition in the time evolution immediately following a quench in the strength of the quasi-periodic potential, as well as a transition in the scaling properties of the quasi-stationary state at long times. Our results suggest a practical scheme for the experimental observation of many-body mobility edges using cold-atom setups.
Many-body localization provides a mechanism to avoid thermalization in isolated interacting quantum systems. The breakdown of thermalization may be complete, when all eigenstates in the many-body spectrum become localized, or partial, when the so-called many-body mobility edge separates localized and delocalized parts of the spectrum. Previously, De Roeck et al. [arXiv:1506.01505] suggested a possible instability of the many-body mobility edge in energy density. The local ergodic regions - so called - resonantly spread throughout the system, leading to delocalization. In order to study such instability mechanism, in this work we design a model featuring many-body mobility edge in particle density: the states at small particle density are localized, while increasing the density of particles leads to delocalization. Using numerical simulations with matrix product states we demonstrate the stability of MBL with respect to small bubbles in large dilute systems for experimentally relevant timescales. In addition, we demonstrate that processes where the bubble spreads are favored over processes that lead to resonant tunneling, suggesting a possible mechanism behind the observed stability of many-body mobility edge. We conclude by proposing experiments to probe particle density mobility edge in Bose-Hubbard model.
Many-body localization provides a mechanism to avoid thermalization in isolated interacting quantum systems. The breakdown of thermalization may be complete, when all eigenstates in the many-body spectrum become localized, or partial, when the so-called many-body mobility edge separates localized and delocalized parts of the spectrum. Previously, De Roeck et al. [Phys. Rev. B 93, 014203 (2016)] suggested a possible instability of the many-body mobility edge in energy density. The local ergodic regions---so-called ``bubbles''---resonantly spread throughout the system, leading to delocalization. In order to study such instability mechanism, in this work we design a model featuring many-body mobility edge in particle density: the states at small particle density are localized, while increasing the density of particles leads to delocalization. Using numerical simulations with matrix product states, we demonstrate the stability of many-body localization with respect to small bubbles in large dilute systems for experimentally relevant timescales. In addition, we demonstrate that processes where the bubble spreads are favored over processes that lead to resonant tunneling, suggesting a possible mechanism behind the observed stability of many-body mobility edge. We conclude by proposing experiments to probe particle density mobility edge in the Bose-Hubbard model.
In this work, we study the statistics of a generic noninteracting many-body fermionic system whose single-particle counterpart has a single-particle mobility edge (SPME). We first prove that the spectrum and the extensive conserved quantities follow the multivariate normal distribution with a vanishing standard deviation $\ensuremath{\sim}O(1/\sqrt{L})$ in the thermodynamic limit, regardless of SPME. Consequently, the theorem rules out an infinite-temperature or high-temperature many-body mobility edge (MBME) for generic noninteracting fermionic systems in any dimension. Further, we also prove that the spectrum of a one-dimensional fermionic many-body system with short-range interactions is qualitatively similar to that of a noninteracting many-body system up to the third-order moment. These results partially explain why neither short-range [Phys. Rev. B 107, 035129 (2023)] nor long-range interacting systems exhibit an infinite-temperature MBME in a one-dimensional system.