Subspace restricted thermalization in a correlated-hopping model with strong Hilbert space fragmentation characterized by irreducible strings
arxiv(2024)
摘要
We introduce a one-dimensional correlated-hopping model of spinless fermions
in which a particle can hop between two neighboring sites only if the sites to
the left and right of those two sites have different particle numbers. Using a
bond to site mapping, this model involving four-site terms can be mapped to an
assisted pair-flipping model involving only three-site terms. This model shows
strong Hilbert space fragmentation (HSF). We define irreducible strings (IS) to
label the different fragments, determine the number of fragments, and the sizes
of fragments corresponding to some special IS. In some classes of fragments,
the Hamiltonian can be diagonalized completely, and in others it can be seen to
have a structure characteristic of models which are not fully integrable. In
the largest fragment in our model, the number of states grows exponentially
with the system size, but the ratio of this number to the total Hilbert space
dimension tends to zero exponentially in the thermodynamic limit. Within this
fragment, we provide numerical evidence that only a weaker version of
eigenstate thermalization hypothesis (ETH) remains valid; we call this the
subspace-restricted ETH. This is a modification of the usual ETH which combines
the strong and weak versions of ETH and is also applicable to fragments of all
dimensions. To understand the out-of-equilibrium dynamics of the model, we
study the infinite-temperature time-dependent autocorrelation functions
starting from a random initial state; we find that these exhibit a different
behavior near the boundary compared to the bulk. We finally propose an
experimental setup to realize our correlated-hopping model.
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