Abstract
The concept of geometrical frustration has led to rich insights into condensed matter physics, especially as a mechansim to produce exotic low energy states of matter. Here we show that frustration provides a natural vehicle to generate models exhibiting anomalous thermalization of various types within high energy states. We consider three classes of non-integrable frustrated spin models: (I) systems with local conserved quantities where the number of symmetry sectors grows exponentially with the system size but more slowly than the Hilbert space dimension, (II) systems with exact eigenstates that are singlet coverings, and (III) flat band systems hosting magnon crystals. We argue that several 1D and 2D models from class (I) exhibit disorder-free localization in high energy states so that information propagation is dynamically inhibited on length scales greater than a few lattice spacings. We further show that models of class (II) and (III) exhibit quantum many-body scars -- eigenstates of non-integrable Hamiltonians with finite energy density and anomalously low entanglement entropy. Our results demonstrate that magnetic frustration supplies a means to systematically construct classes of non-integrable models exhibiting anomalous thermalization in mid-spectrum states.
Highlights
There is strong evidence that most eigenstates of nonintegrable many-body Hamiltonians, if sufficiently far from the spectral edges, are “thermal” in the sense that expectation values of local observables on such eigenstates match well the predictions of statistical mechanics [1]
Geometrical frustration leads to an extensive number of local conservation laws that is smaller than the number of degrees of freedom
We have shown that standard eigenstate thermalization hypothesis (ETH) scaling is violated for one example from this class, the fully frustrated ladder, which instead most closely resembles the behavior seen in integrable models
Summary
There is strong evidence that most eigenstates of nonintegrable many-body Hamiltonians, if sufficiently far from the spectral edges, are “thermal” in the sense that expectation values of local observables on such eigenstates match well the predictions of statistical mechanics [1]. One widely known example of anomalous thermalization is in integrable quantum systems where there is no level repulsion between eigenvalues and the long-time averages of local observables approach a distribution that is tethered to the presence of an extensive number of conserved quantities [7] Another well-known example is the many-body localized (MBL) phase in interacting disordered systems in which high-energy states have area law entanglement and in which an extensive number of local integrals of the motion are emergent [8]. In this paper we describe how geometrical frustration supplies a mechanism to construct models with anomalous thermalization including both disorder-free localization and many-body scar states.
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