This paper shows that local kinetic constraints in random many-body Hamiltonians can lead to ergodicity breaking, despite the Hilbert space not fragmenting. This is purely due to the constraints, in that the unconstrained system is ergodic. The mechanism underlying the emergence of the localized phase is qualitatively different from many-body localization in locally disordered Hamiltonians.
This paper shows that local kinetic constraints in random many-body Hamiltonians can lead to ergodicity breaking, despite the Hilbert space not fragmenting. This is purely due to the constraints, in that the unconstrained system is ergodic. The mechanism underlying the emergence of the localized phase is qualitatively different from many-body localization in locally disordered Hamiltonians.
Eigenstate thermalization hypothesis (ETH) has played a pivotal role in understanding ergodicity and its breaking in isolated quantum many-body systems. The recent experiment on 51-atom Rydberg quantum simulator by Bernien et al. [Nature (London) 551, 579 (2017)] and subsequent theoretical analysis have shown that hardcore kinetic constraint can lead to weak ergodicity breaking. In this work, we demonstrate, using 1d spin-1 PXP models, that miscellaneous type of ergodicity can be realized by adjusting the hardcore constraints between different components of nearest-neighbor spins. This includes ETH violation due to emergent shattering of Hilbert space into exponentially many subsectors of various sizes, a novel form of nonintegrability with an extensive number of local conserved quantities and strong ergodicity. We analyze these different forms of ergodicity and study their impact on the nonequilibrium dynamics of a Z2 initial state. We use forward-scattering approximation to understand the amount of Z2 oscillation present in these models. Our work shows that not only ergodicity breaking but an appropriate choice of constraints can lead to restoration of ergodicity as well.
Quantum many-body systems can exhibit distinct regimes where dynamics is either ergodic, dynamically exploring an extensive region of available state-space, or non-ergodic, where the dynamics may be restricted. An example is the many-body localization (MBL) transition, where disorder induces non-ergodic behaviour. Most measures of ergodicity notably rely on global quantities, such as level spacing statistics. We explore the ability for a subsystem to probe the ergodicity of dynamics via measurement of local observables, and use expected results from random matrix theory (RMT) as a benchmark for the ergodic regime. We exploit two predictions from RMT as ergodicity is broken: the time evolution of the quantum Fisher information, and a fluctuation-dissipation relation. These are investigated in three different ergodicity breaking mechanisms, namely, as a consequence of transition to integrability, MBL, and Quantum Many-Body Scars (QMBS). We show that the predicted behaviour from RMT can be used as a potential witness for transition to non-ergodic behaviour from the measurement of local observables alone.
Lattice gauge theories, the discrete counterparts of continuum gauge theories, provide a rich framework for studying non-equilibrium quantum dynamics. Recent studies suggest disorder-free localization in the lattice Schwinger model, but its origin remains unclear. Using a combination of analytical and numerical methods, we show that Hilbert space fragmentation emerges in the strong coupling limit, constraining particle dynamics and causing sharp jumps in entanglement entropy growth within charge sectors. By analyzing jump statistics, we find that entanglement growth follows a single-logarithmic or weak power-law dependence on time, rather than a double-logarithmic form. This suggests a single ergodicity-breaking regime that mimics many-body localization in finite systems due to fragmentation effects. Our findings clarify the nature of disorder-free localization and its distinction from conventional many-body localization, highlighting how gauge constraints influence thermalization in lattice gauge theories.
We investigate the effects of spatially localized conserved quantities on transport and thermalization in quantum and classical many-body systems. We consider several related models: the integrable quantum Volterra model, its nonintegrable classical limit, and two cellular automata derived from the latter. Although localized constraints are often associated with lattice gauge theories, our models do not admit such an interpretation. In systems with discrete degrees of freedom, these constraints induce uniform fragmentation of the Hilbert or configuration space. In the quantum Volterra model, we derive an exact mapping of the dynamics within each Hilbert-space fragment onto a quantum chiral Potts chain. We find that energy transport is ballistic, with identical transport coefficients across all fragments. In the nonintegrable classical limit, energy transport is diffusive, and we similarly find the diffusion constant to be independent of whether or not the constraints are fixed (resolved). Finally, in the cellular automata, we show that, despite leaving transport unaffected, localized constraints lead to a strong breakdown of local ergodicity.
A generic closed quantum many-body system will inevitably tend to thermalization, whose local information encoded in the initial state eventually scrambles into the full space, known as quantum ergodicity. A paradigmatic exception in closed quantum systems for strong ergodicity breaking is known as many-body localization, where strong disorder-induced localization prevents the occurrence of thermalization. It is generally recognized that a localized quantum system would be delocalized under dissipation induced by the environment. However, this consequence recently has received challenges where an exotic dissipation-induced localization mechanism is proposed, and transitions between localized and extended phases are found. In this Letter, we promote this mechanism to systems for weak ergodicity breaking hosting quantum many-body scars (QMBS). We find that the system relaxes to a steady state dominated by QMBS, and the dissipative dynamics exhibit dynamic revivals by suitably preparing an initial state. We point out an experimental realization of the controlled dissipation with a cold atomic setup. This makes the signature of ergodicity breaking visible over dissipative dynamics and offers potential possibilities for experimentally preparing stable QMBS with associated coherent dynamics.
We present the study of the structure of many-body eigenfunctions in a one-dimensional disordered spin chain.We discuss the choice of an appropriate basis in the Hilbert space, where the problem can be seen as an Anderson model defined on a high-dimensional non-trivial graph, determined by the many-body Hamiltonian.The comparison with the usual behavior of wave-functions in finite dimensional Anderson localization allows us to put in light the main differences of the many-body case.At high disorder, the typical eigenfunctions do not seem to localize though they occupy a infinitesimal portion of the Hilbert space in the thermodynamic limit.We perform a detailed analysis of the distribution of the wave-function coefficients and their peculiar scaling in the small and large disorder phase.We propose a criterion to identify the position of the transition by looking at the long tails of these distributions.The results coming from exact diagonalization show signs of breaking of ergodicity when the disorder reaches a critical value that agrees with the estimation of the many-body localization transition in the same model.