Abstract
We study in detail the properties of the quantum East model, an interacting quantum spin chain inspired by simple kinetically constrained models of classical glasses. Through a combination of analytics, exact diagonalization, and tensor-network methods, we show the existence of a transition, from a fast to a slow thermalization regime, which manifests itself throughout the spectrum. On the slow side, by exploiting the localization of the ground state and the form of the Hamiltonian, we explicitly construct a large (exponential in size) number of nonthermal states that become exact finite-energy-density eigenstates in the large size limit, as expected for a true phase transition. A “superspin” generalization allows us to find a further large class of area-law states proved to display very slow relaxation. These states retain memory of their initial conditions for extremely long times. Our numerical analysis reveals that the localization properties are not limited to the ground state and that many eigenstates have large overlap with product states and can be approximated well by matrix product states at arbitrary energy densities. The mechanism that induces localization to the ground state, and hence the nonthermal behavior of the system, can be extended to a wide range of models including a number of simple spin chains. We discuss implications of our results for slow thermalization and nonergodicity more generally in disorder-free systems with constraints, and we give numerical evidence that these results may be extended to two-dimensional systems.
9 More- Received 7 November 2019
- Revised 5 March 2020
- Accepted 15 April 2020
DOI:https://doi.org/10.1103/PhysRevX.10.021051
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Some ensembles of many interacting quantum particles fall outside the traditional rules of thermalization. Of particular interest is the so-called many-body localization phenomenon, in which an isolated quantum system fails to thermalize and retains a memory of its initial state. Understanding how and why this occurs is relevant to studies of condensed matter, quantum information, and statistical mechanics. Here, we analyze a mathematical model of an interacting quantum spin chain and find a new mechanism that induces localization without the need for disorder.
We show that in the quantum East model, a disorder-free spin chain model inspired by the dynamics of classical glasses, one can find behavior similar to many-body localization. By changing a parameter in the mathematical model, we find that some dynamical properties of the system change abruptly. In particular, we prove that there are many possible initial configurations for which the time evolution is extremely slow. We also find that these effects are not limited to this model, but also apply to a much broader class of models that share some similarities with the quantum East model.
While others have reported signatures of slow dynamics in numerical simulations of the quantum East model, we go beyond to explain mathematically the origin of those effects and to prove several things for large system sizes. Our results open the door to a broader class of nonthermalizing models with theoretical interest but potentially also practical implications for the robust storage of quantum information.