We construct many-body scar states in multi-flavour fermionic lattice models that possess strong magnetic or superconducting correlations of a given type specified by a unitary matrix $A$. One of the states maximizes the one-point correlations over the full Hilbert space and has the form of the BCS wavefunction. It may always be made the ground state by adding the correlations as a "pairing potential" to any Hamiltonian supporting group-invariant scars. In our single-flavour, spin-full fermions example we consider a superconducting $A$. The BCS scar ground state is a linear combination of the well-known $η$-pairing states. In the multi-orbital fermions example the BCS-like ground state maximizes unconventional magnetic correlations. The broad class of eligible Hamiltonians includes many conventional condensed matter interactions. The part of the Hamiltonian that governs the exact dynamics of the scar subspace coincides with the BCS mean-field Hamiltonian. We therefore show that its eigenstates are many-body scars that are decoupled from the rest of the Hilbert space and thereby protected from thermalization. Our results point out a connection between the fields of superconductivity and weak ergodicity breaking (many-body scars) and will hopefully encourage further investigations. They also provide the first feasible protocol to initialize a fermionic system to a scar state in (a quantum simulator) experiment.
We construct many-body scar states in multi-flavour fermionic lattice models that possess strong magnetic or superconducting correlations of a given type specified by a unitary matrix A. One of the states maximizes the one-point correlations over the full Hilbert space and has the form of the BCS wavefunction. It may always be made the ground state by adding the correlations as a "pairing potential" to any Hamiltonian supporting group-invariant scars. In our single-flavour, spin-full fermions example we consider a superconducting A. The BCS scar ground state is a linear combination of the well-known η-pairing states. In the multi-orbital fermions example the BCS-like ground state maximizes unconventional magnetic correlations. The broad class of eligible Hamiltonians includes many conventional condensed matter interactions. The part of the Hamiltonian that governs the exact dynamics of the scar subspace coincides with the BCS mean-field Hamiltonian. We therefore show that its eigenstates are many-body scars that are decoupled from the rest of the Hilbert space and thereby protected from thermalization. Our results point out a connection between the fields of superconductivity and weak ergodicity breaking (many-body scars) and will hopefully encourage further investigations. They also provide the first feasible protocol to initialize a fermionic system to a scar state in (a quantum simulator) experiment.
Weak ergodicity breaking in interacting quantum systems may occur due to the existence of a subspace dynamically decoupled from the rest of the Hilbert space. In two-orbital spinful lattice systems, we construct such subspaces that are in addition distinguished by strongest inter-orbital and spin-singlet or spin-triplet, long-range superconducting pairing correlations. All unconventional pairing types we consider are local in space and unitary. Alternatively to orbitals, the additional degree of freedom could originate from the presence of two layers or through any other mechanism. Required Hamiltonians are rather non-exotic and include chemical potential, Hubbard, and spin-orbit interactions typically used for two-orbital superconducting materials. Each subspace is spanned by a family of group-invariant quantum many-body scars combining both 2e and 4e pairing/clustering contributions. One of the basis states has the form of a BCS wavefunction and can always be made the ground state by adding a mean-field pairing potential. Analytical results in this work are lattice-, dimension- and (mostly) system size-independent. We confirm them by exact numerical diagonalization in small systems.
Motivated by recent observations of ergodicity breaking due to Hilbert space fragmentation in 1D Fermi-Hubbard chains with a tilted potential [Scherg et al., arXiv:2010.12965], we show that the same system also hosts quantum many-body scars in a regime U≈Δ≫J at electronic filling factor ν=1. We numerically demonstrate that the scarring phenomenology in this model is similar to other known realizations such as Rydberg atom chains, including persistent dynamical revivals and ergodicity-breaking many-body eigenstates. At the same time, we show that the mechanism of scarring in the Fermi-Hubbard model is different from other examples in the literature: the scars originate from a subgraph, representing a free spin-1 paramagnet, which is weakly connected to the rest of the Hamiltonian's adjacency graph. Our work demonstrates that correlated fermions in tilted optical lattices provide a platform for understanding the interplay of many-body scarring and other forms of ergodicity breaking, such as localization and Hilbert space fragmentation.
It has been shown [K. Pakrouski et al., Phys. Rev. Lett. 125, 230602 (2020)] that three families of highly symmetric states are many-body scars for any spin-21 fermionic Hamiltonian of the form H0+OT, where T is a generator of an appropriate Lie group. One of these families consists of the well-known $\ensuremath{\eta}$-pairing states. In addition to having the usual properties of scars, these families of states are insensitive to electromagnetic noise and have advantages for storing and processing quantum information. In this paper we show that a number of well-known coupling terms, such as the Hubbard and the Heisenberg interactions, and the Hamiltonians containing them, are of the required form and support these states as scars without fine tuning. The explicit H0+OT decomposition for a number of most commonly used models, including topological ones, is provided. To facilitate possible experimental implementations, we discuss the conditions for the low-energy subspace of these models to be comprised solely of scars. Further, we write all the generators T that can be used as building blocks for designing new models with scars, most interestingly including the spin-orbit coupled hopping and superconducting pairing terms. We expand this framework to the non-Hermitian open systems and demonstrate that for them the scar subspace continues to undergo coherent time evolution and exhibit the ``revivals.'' A full numerical study of an extended two-dimensional tJU model explicitly illustrates the novel properties of the invariant scars and supports our findings.
We present a systematic framework to construct model Hamiltonians that have unconventional superconducting pairing states as exact energy eigenstates, by incorporating multibody interactions (i.e., interactions among more than two particles). The multibody interactions are introduced in a form of the local density-density coupling in such a way that any pair configuration in real space has a constant interaction energy by canceling the two-body and multibody interactions. Our approach is applicable to both spinless and spinful models in any spatial dimensions and on any bipartite lattices, facilitating an exhaustive extension of Yang's s − wave η − pairing state to various other unconventional pairing symmetries ( p − wave , d − wave , f − wave , etc.). Particularly, the constructed eigenstates have off-site pairs with finite center-of-mass momentum, which leads to superconducting states with either even-parity and spin-triplet or odd-parity and spin-singlet symmetry. We verify that the two-dimensional spinful Hubbard model on a square lattice with the multibody interactions has the spin-triplet d − wave pairing state as an energy eigenstate, which can be regarded as a quantum many-body scar state as evidenced from the numerical analysis of the pair correlation function, entanglement entropy, and level statistics. We also discuss other examples, including spin-triplet f − wave pairing states on a honeycomb lattice and spin-singlet p − wave pairing states in a one-dimensional chain. These findings open up the possibility of realizing nonequilibrium unconventional superconductivity in a long-lived manner protected against thermalization.
We present a class of Hamiltonians H for which a sector of the Hilbert space invariant under a Lie group G, which is not a symmetry of H, possesses the essential properties of many-body scar states. These include the absence of thermalization and the "revivals" of special initial states in time evolution. A particular class of examples concerns interacting spin-1/2 fermions on a lattice consisting of N sites (it includes deformations of the Fermi-Hubbard model as special cases), and we show that it contains two families of N+1 scar states. One of these families, which was found in recent literature, comprises the well-known η-pairing states. We find another family of scar states that is U(N) invariant. Both families and most of the group-invariant scar states produced by our construction, in general, give rise to the off-diagonal long range order, which survives at high temperatures and is insensitive to the details of the dynamics. Such states could be used for reliable quantum information processing because the information is stored nonlocally and thus cannot be easily erased by local perturbations. In contrast, other scar states we find are product states, which could be easily prepared experimentally. The dimension of scar subspace is directly controlled by the choice of group G and can be made exponentially large.
Quantum many-body scars (QMBSs) are a novel paradigm for the violation of the eigenstate thermalization hypothesis—Hamiltonians of these systems exhibit mid-spectrum eigenstates that are equidistant in energy and which possess low entanglement and evade thermalization for long times. We present a novel approach to understanding the anomalous dynamical behavior in these systems. Specifically, we postulate that QMBS Hamiltonians H can generically be partitioned into a set of terms O a which do not commute over the entire Hilbert space, but commute to all orders within the subspace of scar states. All states in the scar subspace thus evolve according to a “broken unitary” U s ( t ) = ∏ a e − i O a t , where H = ∑ a O a , which provides a simple interpretation of the anomalous dynamical features exhibited by quantum scars; they evolve in time according to a simpler unitary operator allowing for revivals. It is found that the observed dynamical decoupling is often a direct consequence of simple local conditions, which when satisfied lead to recurring aspects of QMBSs, including equidistant eigenvalues, many-body revivals, and sub-volume-law entanglement entropy. Two classes of scar models emerge in this picture—those with a finite set of O a , as pertaining of, for instance, scars in the AKLT model, and those with an extensive set of such operators, such as eta pairing scar states in the Hubbard model. Besides discussing how many well-known scar models fit into the above picture, we show how the broken unitary formalism captures many known scar construction methods, known in the literature and generalizes others such as quasiparticles matrix product state (MPS) based methods, and the Shiraishi-Mori approach. Published by the American Physical Society 2024