- The paper demonstrates that a charge-density wave state retains memory in a tilted Fermi-Hubbard chain, highlighting non-ergodic dynamics driven by kinetic constraints.
- Experimental and numerical methods, including exact diagonalization and TEBD, verify that large tilt energies fragment the Hilbert space and hinder thermalization.
- The study challenges the eigenstate thermalization hypothesis by showing that non-disordered systems can exhibit long-lived non-ergodic behavior, urging further quantum many-body research.
Observing Non-Ergodicity Due to Kinetic Constraints in Tilted Fermi-Hubbard Chains
The paper of thermalization in isolated quantum many-body systems presents a fundamentally intriguing set of challenges in quantum information theory. While prior research has reasonably characterized non-ergodic behavior in integrable and many-body localized (MBL) systems—attributed to an abundance of conserved quantities—the emergence of non-ergodic dynamics in systems lacking disorder, such as the tilted one-dimensional (1D) Fermi-Hubbard model, prompts further investigation into ergodicity-breaking mechanisms. This work elucidates non-ergodic behavior by examining the tilted 1D Fermi-Hubbard model without disorder, revealing prolonged memory retention of the initial state, which can be ascribed to emergent kinetic constraints.
The 1D Fermi-Hubbard model in a tilted optical lattice, experimentally realizable with ultracold atoms, is engineered to explore non-ergodicity in a setting devoid of disorder. Although theoretical advancements have acknowledged non-ergodic regimes in specific limiting cases, a comprehensive understanding of this model's thermalization properties remained elusive. This research empirically and numerically investigates the relaxation dynamics of a charge-density wave (CDW) initial state, indicating an unexpected long-lived memory of the initial conditions. Numerical simulations corroborate these findings and point to kinetic constraints as the primary drivers of these emergent dynamics.
The significance of exploring non-ergodic behavior within this system is underscored by its theoretical implication for the eigenstate thermalization hypothesis (ETH), which posits that individual eigenstates emulate thermal ensembles in ergodic systems. The paper of states that defy ETH in nominally ergodic systems reveals new insights into the landscape between ergodicity and localization—a domain enriched by findings on many-body scar states and dipole-conserving models, well-known for their fragmented Hilbert spaces. This work proposes a novel view where kinetic constraints promote fragmentation and consequently lead to non-ergodic dynamics.
The experimental arrangement fields a degenerate Fermi gas, occupying the lowest band of an optical lattice, while the system's dynamics mapped to a tilted lattice regime eschews disorder entirely. Through manipulations enabled by Feshbach resonance, dynamics are initiated within an ensemble of interacting fermions subjected to a linear potential gradient (tilt). Diverse tilt strengths and interaction regimes are surveyed; notably, alterations in contrast between tilt and Hubbard interaction potential unveil a persistent imbalance in particle distribution, evincing non-ergodic evolution over extended temporal scales.
Furthermore, numerical approaches leveraging exact diagonalization (ED) and time-evolving block decimation (TEBD) affirm the experimental results and assist in explicating how emergent kinetic constraints—such as inoperative degrees of freedom within isolated Hamiltonian subspaces—engender the observed behavior. The construction of effective Hamiltonians via perturbative techniques elucidates how kinetic constraints are promoted within these systems by large tilt energies, fostering Hilbert space fragmentation and dipole conservation that prohibit simplistic thermalization.
Beyond its immediate empirical demonstrations, this paper delivers pivotal insights into more systematic investigations of lattice models with potential tunable kinetic constraints, urging further paper on related phenomena like Stark MBL and its compatibility with fragmented space attributes. Additionally, this paper carnations the prospect of artificially constructing other strongly-fragmented models, potentially leveraging quantum simulators to explore phenomena like time crystals or drive-induced localization. In striving to further bridge the nexus between experimental findings and theoretical constructs, this research fortifies our comprehension of non-ergodic phenomena and enriches the quantum statistical mechanics discourse by unraveling non-ergodicity's nuanced interplay with initial state configuration and input constraints.