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:2208.10509 · Physical review. B./Physical review. B

Quantum breakdown model: From many-body localization to chaos with scars

Biao Lian

Published Mar 30, 2023• 12 citations
arXivHTMLPDF

Abstract

We propose a quantum model of fermions simulating the electrical breakdown process of dielectrics. The model consists of $M$ sites with $N$ fermion modes per site and has a conserved charge $Q$. It has an on-site chemical potential $\ensuremath{\mu}$ with disorder $W$ and an interaction of strength $J$ restricting each fermion to excite two more fermions when moving forward by one site. We show that the $N=3$ model with disorder $W=0$ shows a Hilbert space fragmentation and is exactly solvable except for very few Krylov subspaces. The analytical solution shows that the $N=3$ model exhibits many-body localization (MBL) as $M\ensuremath{\rightarrow}\ensuremath{\infty}$, which is stable against $W>0$ as our exact diagonalization (ED) shows. At $N>3$, our ED suggests an MBL to quantum chaos crossover at small $W$ as $M/N$ decreases across 1, and persistent MBL at large $W$. At $W=0$, an exactly solvable many-body scar flat band exists in many charge $Q$ sectors, which has a nonzero measure in the thermodynamic limit. We further calculate the time evolution of a fermion added to the particle vacuum, which shows a breakdown (dielectric) phase when $\ensuremath{\mu}/J<1/2$ ($\ensuremath{\mu}/J>1/2$) if $W\ensuremath{\ll}J$, and no breakdown if $W\ensuremath{\gg}J$.

DOI
10.1103/physrevb.107.115171

Related papers

Two-dimensional quantum breakdown model with Krylov subspace many-body localization

Xinyu Liu, Biao Lian

We propose a two-dimensional (2D) quantum breakdown model of hardcore bosons interacting with disordered spins which would be classical without the bosons. It resembles particles incident into supersaturated vapor. The model exhibits a set of subsystem symmetries and has a strong fragmentation into Krylov subspaces in each symmetry sector. The Hamiltonian in each Krylov subspace maps to a single-particle problem in a Cayley-tree-like graph. At zero disorder, the Krylov subspaces exhibit either (possible) integrable features or quantum chaos with quantum scar states showing irregular energy and degeneracy patterns. At nonzero disorders, they enter a 2D many-body localization (MBL) phase beyond certain disorder strength ${W}_{*}$, as indicated by Poisson level spacing statistics and entanglement entropy growing as $logt$ with time $t$. Our theoretical arguments suggest ${W}_{*}$ is finite or zero for boson number ${N}_{b}\ensuremath{\lesssim}{L}^{\ensuremath{\gamma}}/logL$ ($1/2\ensuremath{\le}\ensuremath{\gamma}\ensuremath{\le}1$) as system size $L\ensuremath{\rightarrow}\ensuremath{\infty}$. This gives a more stringent condition for MBL than that in the 1D quantum breakdown models. This model reveals the possibility of MBL in systems of quantum particles interacting with classical degrees of freedom.

arXiv:2311.10968•Physical review. B./Physical review. B•Feb 6, 2025•3 citations

From the quantum breakdown model to the lattice gauge theory

Yu-Min Hu, Biao Lian

Abstract The one-dimensional quantum breakdown model, which features spatially asymmetric fermionic interactions simulating the electrical breakdown phenomenon, exhibits an exponential U(1) symmetry and a variety of dynamical phases including many-body localization and quantum chaos with quantum scar states. We investigate the minimal quantum breakdown model with the minimal number of on-site fermion orbitals required for the interaction and identify a large number of local conserved charges in the model. We then reveal a mapping between the minimal quantum breakdown model in certain charge sectors and a quantum link model which simulates the U(1) lattice gauge theory and show that the local conserved charges map to the gauge symmetry generators. A special charge sector of the model further maps to the PXP model, which shows quantum many-body scars. This mapping unveils the rich dynamics in different Krylov subspaces characterized by different gauge configurations in the quantum breakdown model.

arXiv:2405.08273•AAPPS bulletin•Aug 26, 2024•6 citations

Quantum fragmentation in the extended quantum breakdown model

Bo‐Ting Chen, Abhinav Prem, Nicolas Regnault +1 more

We introduce a one-dimensional (1D) extended quantum breakdown model comprising a fermionic and a spin degree of freedom per site, and featuring a spatially asymmetric breakdown-type interaction between the fermions and spins. Our model resembles the breakdown process of particles incident into a cloud chamber with nonzero quantum amplitudes of both exciting and not exciting the local vapor atoms. We analytically show that, in the absence of any magnetic field for the spins, the model exhibits Hilbert space fragmentation within each symmetry sector into exponentially many Krylov subspaces and hence displays nonthermal dynamics. Here, we demonstrate that the fragmentation naturally occurs in an entangled basis and thus provides an example of ``quantum fragmentation.'' Besides establishing the nature of fragmentation analytically, we also study the long-time behavior of the entanglement entropy and its deviation from the expected Page value as a probe of ergodicity in the system. Upon introducing a magnetic field for the spins, most of the Krylov subspaces merge and the model becomes chaotic. Finally, we study the effects of strong randomness on the system and observe behavior similar to that of many-body localized systems.

arXiv:2401.16480•Physical review. B./Physical review. B•Oct 3, 2024•5 citations

Spontaneous particle-hole symmetry breaking in a disordered two-site quantum breakdown model

Kinya Guan

We study spontaneous particle-hole symmetry breaking in a disordered two-site quantum breakdown model. The model is solvable in the limit of a large number of fermionic modes on each site. For a small ratio of the numbers of modes on the two sites, we derive the free energy analytically and find a finite-temperature symmetry-breaking transition. This transition changes from continuous to first order as the number of fermions produced in each conversion increases. Numerical results show that both types of transition persist beyond this regime, with an order-parameter exponent close to $1/2$ for continuous transitions.

arXiv:2610.24669•Oct 17, 2026•0 citations

Stability of the Many-Body Scars in Fermionic Spin-1/2 Models

Patrice Kolb, Kiryl Pakrouski

We study the stability of the many-body scars in spin-1/2 fermionic systems under the most typical perturbations in relevant materials. We find that some families of scars are completely insensitive to certain perturbations. In some other cases they are stable to the first order in perturbation theory. Our analytical results apply to a large class of Hamiltonians that are known [arXiv:2106.10300] to support exact many-body scars. For the numerical calculations we choose the deformed $t-J-U$ model that includes both Heisenberg and Hubbard interactions. We propose two new stability measures that are based on physical observables rather than the fidelity to the exact initial wavefunction. They enable the experimental detection of scars and are more reliable from the theoretical and numerical perspectives. One of these measures may potentially find applications in other systems where the exact many-body scars are equally spaced in energy. In small systems and at small perturbations, a regime particularly relevant for quantum simulators, we identify and describe an additional stability exhibited by the many-body scars. For larger perturbation strengths we observe a distinct mode of ergodicity breaking that is consistent with many-body localization.

arXiv:2305.17164•May 26, 2023•0 citations

Periodically-driven quantum many-body systems, many-body localization and machine learning

Pedro Ponte

Despite the exponentially large amount of information required in the quantum description of many-body systems, finite size numerical simulations have paved the way for recent progress in the understanding of quantum phases of matter both in and out-of-equilibrium. \n \nIn this spirit, using exact diagonalization for a small number of spins ~ 20, first, we investigate the fate of both ergodic quantum many-body systems that thermalize at long times and systems with quenched disorder that exhibit many-body localization (MBL) and fail to thermalize (due to an extensive set of local conserved degrees of freedom) under periodic driving. Ergodic systems always delocalize in energy space and heat up to infinite temperature, for both local driving, in which the time dependence of the Hamiltonian is restricted to a few contiguous degrees of freedom, and global driving. On the other hand, MBL systems remain localized at finite energy density for local driving, while in the case of global driving these systems can either heat up to infinite temperature or remain localized depending on the parameters of the drive. Underlying the latter is the emergence of an effective time independent MBL Hamiltonian describing the long time dynamics of the system. These numerical predictions have recently been verified experimentally in a one dimensional quasi-disordered optical lattice of interacting fermions wherein unitary time evolution can be experimentally probed. \n \nSubsequently, we study the stability of MBL systems with respect to another perturbation, in this case by thermal inclusions, which remains poorly understood. We consider a simple model to address this question: a two level system interacting with 𝑁 localized bits subject to random fields. In the large 𝑁 limit, the localized bits are thermalized for any nonzero ratio of interactions to disorder strength. Moreover, at finite 𝑁, in the transition region, the single-site eigenstate entanglement entropies exhibit bimodal distributions, so that localized bits are either "on" (strongly entangled) or "off" (weakly entangled) in eigenstates. The clusters of "on" bits vary significantly between eigenstates of the same sample, which provides evidence for a heterogenous discontinuous transition out of the localized phase in single site observables. These results also imply the MBL phase is unstable in systems with short-range interactions and quenched randomness in dimensions 𝑑 that are high but finite. \n \nThe second part of this thesis is motivated by the recent breakthroughs of artificial intelligence in domains such as computer vision involving highly dimensional data of complexity not unlike the one found in the description of many-body systems. Using Monte Carlo simulations to generate synthetic data, we find that kernel methods, a class of machine learning algorithms, can learn the mathematical \nform of physical discriminators associated with phase transitions, such as order parameters and Hamiltonian constraints, for a set of two dimensional spin models: the ferromagnetic Ising model, a conserved-order-parameter Ising model, and the Ising gauge theory. \n \nOur work shows that the combination of numerical simulations with the ability of machine learning algorithms for automatic feature detection hold promise to become standard tools in the exploration and characterization of different phases of matter in condensed matter and other many-body systems.

•Mar 9, 2018•0 citations
We propose a quantum model of fermions simulating the electrical breakdown process of dielectrics. The model consists of MMM sites with NNN fermion modes per site and has a conserved charge QQQ. It has an on-site chemical potential \ensuremathμ\ensuremath{\mu}\ensuremathμ with disorder WWW and an interaction of strength JJJ restricting each fermion to excite two more fermions when moving forward by one site. We show that the N=3N=3N=3 model with disorder W=0W=0W=0 shows a Hilbert space fragmentation and is exactly solvable except for very few Krylov subspaces. The analytical solution shows that the N=3N=3N=3 model exhibits many-body localization (MBL) as M\ensuremath→\ensuremath∞M\ensuremath{\rightarrow}\ensuremath{\infty}M\ensuremath→\ensuremath∞, which is stable against W>0W>0W>0 as our exact diagonalization (ED) shows. At N>3N>3N>3, our ED suggests an MBL to quantum chaos crossover at small WWW as M/NM/NM/N decreases across 1, and persistent MBL at large WWW. At W=0W=0W=0, an exactly solvable many-body scar flat band exists in many charge QQQ sectors, which has a nonzero measure in the thermodynamic limit. We further calculate the time evolution of a fermion added to the particle vacuum, which shows a breakdown (dielectric) phase when \ensuremathμ/J<1/2\ensuremath{\mu}/J<1/2\ensuremathμ/J<1/2 (\ensuremathμ/J>1/2\ensuremath{\mu}/J>1/2\ensuremathμ/J>1/2) if W\ensuremath≪JW\ensuremath{\ll}JW\ensuremath≪J, and no breakdown if W\ensuremath≫JW\ensuremath{\gg}JW\ensuremath≫J.
We propose a two-dimensional (2D) quantum breakdown model of hardcore bosons interacting with disordered spins which would be classical without the bosons. It resembles particles incident into supersaturated vapor. The model exhibits a set of subsystem symmetries and has a strong fragmentation into Krylov subspaces in each symmetry sector. The Hamiltonian in each Krylov subspace maps to a single-particle problem in a Cayley-tree-like graph. At zero disorder, the Krylov subspaces exhibit either (possible) integrable features or quantum chaos with quantum scar states showing irregular energy and degeneracy patterns. At nonzero disorders, they enter a 2D many-body localization (MBL) phase beyond certain disorder strength W∗{W}_{*}W∗​, as indicated by Poisson level spacing statistics and entanglement entropy growing as logtlogtlogt with time ttt. Our theoretical arguments suggest W∗{W}_{*}W∗​ is finite or zero for boson number ${N}_{b}\ensuremath{\lesssim}{L}^{\ensuremath{\gamma}}/logL$ ($1/2\ensuremath{\le}\ensuremath{\gamma}\ensuremath{\le}1$) as system size $L\ensuremath{\rightarrow}\ensuremath{\infty}$. This gives a more stringent condition for MBL than that in the 1D quantum breakdown models. This model reveals the possibility of MBL in systems of quantum particles interacting with classical degrees of freedom.
Abstract The one-dimensional quantum breakdown model, which features spatially asymmetric fermionic interactions simulating the electrical breakdown phenomenon, exhibits an exponential U(1) symmetry and a variety of dynamical phases including many-body localization and quantum chaos with quantum scar states. We investigate the minimal quantum breakdown model with the minimal number of on-site fermion orbitals required for the interaction and identify a large number of local conserved charges in the model. We then reveal a mapping between the minimal quantum breakdown model in certain charge sectors and a quantum link model which simulates the U(1) lattice gauge theory and show that the local conserved charges map to the gauge symmetry generators. A special charge sector of the model further maps to the PXP model, which shows quantum many-body scars. This mapping unveils the rich dynamics in different Krylov subspaces characterized by different gauge configurations in the quantum breakdown model.
We introduce a one-dimensional (1D) extended quantum breakdown model comprising a fermionic and a spin degree of freedom per site, and featuring a spatially asymmetric breakdown-type interaction between the fermions and spins. Our model resembles the breakdown process of particles incident into a cloud chamber with nonzero quantum amplitudes of both exciting and not exciting the local vapor atoms. We analytically show that, in the absence of any magnetic field for the spins, the model exhibits Hilbert space fragmentation within each symmetry sector into exponentially many Krylov subspaces and hence displays nonthermal dynamics. Here, we demonstrate that the fragmentation naturally occurs in an entangled basis and thus provides an example of ``quantum fragmentation.'' Besides establishing the nature of fragmentation analytically, we also study the long-time behavior of the entanglement entropy and its deviation from the expected Page value as a probe of ergodicity in the system. Upon introducing a magnetic field for the spins, most of the Krylov subspaces merge and the model becomes chaotic. Finally, we study the effects of strong randomness on the system and observe behavior similar to that of many-body localized systems.
We study spontaneous particle-hole symmetry breaking in a disordered two-site quantum breakdown model. The model is solvable in the limit of a large number of fermionic modes on each site. For a small ratio of the numbers of modes on the two sites, we derive the free energy analytically and find a finite-temperature symmetry-breaking transition. This transition changes from continuous to first order as the number of fermions produced in each conversion increases. Numerical results show that both types of transition persist beyond this regime, with an order-parameter exponent close to 1/21/21/2 for continuous transitions.
We study the stability of the many-body scars in spin-1/2 fermionic systems under the most typical perturbations in relevant materials. We find that some families of scars are completely insensitive to certain perturbations. In some other cases they are stable to the first order in perturbation theory. Our analytical results apply to a large class of Hamiltonians that are known [arXiv:2106.10300] to support exact many-body scars. For the numerical calculations we choose the deformed t−J−Ut-J-Ut−J−U model that includes both Heisenberg and Hubbard interactions. We propose two new stability measures that are based on physical observables rather than the fidelity to the exact initial wavefunction. They enable the experimental detection of scars and are more reliable from the theoretical and numerical perspectives. One of these measures may potentially find applications in other systems where the exact many-body scars are equally spaced in energy. In small systems and at small perturbations, a regime particularly relevant for quantum simulators, we identify and describe an additional stability exhibited by the many-body scars. For larger perturbation strengths we observe a distinct mode of ergodicity breaking that is consistent with many-body localization.
Despite the exponentially large amount of information required in the quantum description of many-body systems, finite size numerical simulations have paved the way for recent progress in the understanding of quantum phases of matter both in and out-of-equilibrium. \n \nIn this spirit, using exact diagonalization for a small number of spins ~ 20, first, we investigate the fate of both ergodic quantum many-body systems that thermalize at long times and systems with quenched disorder that exhibit many-body localization (MBL) and fail to thermalize (due to an extensive set of local conserved degrees of freedom) under periodic driving. Ergodic systems always delocalize in energy space and heat up to infinite temperature, for both local driving, in which the time dependence of the Hamiltonian is restricted to a few contiguous degrees of freedom, and global driving. On the other hand, MBL systems remain localized at finite energy density for local driving, while in the case of global driving these systems can either heat up to infinite temperature or remain localized depending on the parameters of the drive. Underlying the latter is the emergence of an effective time independent MBL Hamiltonian describing the long time dynamics of the system. These numerical predictions have recently been verified experimentally in a one dimensional quasi-disordered optical lattice of interacting fermions wherein unitary time evolution can be experimentally probed. \n \nSubsequently, we study the stability of MBL systems with respect to another perturbation, in this case by thermal inclusions, which remains poorly understood. We consider a simple model to address this question: a two level system interacting with 𝑁 localized bits subject to random fields. In the large 𝑁 limit, the localized bits are thermalized for any nonzero ratio of interactions to disorder strength. Moreover, at finite 𝑁, in the transition region, the single-site eigenstate entanglement entropies exhibit bimodal distributions, so that localized bits are either "on" (strongly entangled) or "off" (weakly entangled) in eigenstates. The clusters of "on" bits vary significantly between eigenstates of the same sample, which provides evidence for a heterogenous discontinuous transition out of the localized phase in single site observables. These results also imply the MBL phase is unstable in systems with short-range interactions and quenched randomness in dimensions 𝑑 that are high but finite. \n \nThe second part of this thesis is motivated by the recent breakthroughs of artificial intelligence in domains such as computer vision involving highly dimensional data of complexity not unlike the one found in the description of many-body systems. Using Monte Carlo simulations to generate synthetic data, we find that kernel methods, a class of machine learning algorithms, can learn the mathematical \nform of physical discriminators associated with phase transitions, such as order parameters and Hamiltonian constraints, for a set of two dimensional spin models: the ferromagnetic Ising model, a conserved-order-parameter Ising model, and the Ising gauge theory. \n \nOur work shows that the combination of numerical simulations with the ability of machine learning algorithms for automatic feature detection hold promise to become standard tools in the exploration and characterization of different phases of matter in condensed matter and other many-body systems.