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arXiv:1708.08070 · Physical Review Letters

Symmetry Protected Dynamical Symmetry in the Generalized Hubbard Models

Jinlong Yu, Ning G. Sun, Hui Zhai

Published Nov 30, 2017• 19 citations
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Abstract

In this Letter we present a theorem on the dynamics of the generalized Hubbard models. This theorem shows that the symmetry of the single-particle Hamiltonian can protect a kind of dynamical symmetry driven by the interactions. Here the dynamical symmetry refers to the phenomenon that time evolution of certain observables are symmetric between the repulsive and attractive Hubbard models. We demonstrate our theorem with three different examples in which the symmetry involves bipartite lattice symmetry, reflection symmetry, and translation symmetry, respectively. Each of these examples relates to one recent cold atom experiment on the dynamics in the optical lattices where such a dynamical symmetry is manifested. These experiments include expansion dynamics of cold atoms, chirality of atomic motion within a synthetic magnetic field, and melting of charge-density-wave order. Therefore, our theorem provides a unified view of these seemingly disparate phenomena.

DOI
10.1103/physrevlett.119.225302

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In this Letter we present a theorem on the dynamics of the generalized Hubbard models. This theorem shows that the symmetry of the single-particle Hamiltonian can protect a kind of dynamical symmetry driven by the interactions. Here the dynamical symmetry refers to the phenomenon that time evolution of certain observables are symmetric between the repulsive and attractive Hubbard models. We demonstrate our theorem with three different examples in which the symmetry involves bipartite lattice symmetry, reflection symmetry, and translation symmetry, respectively. Each of these examples relates to one recent cold atom experiment on the dynamics in the optical lattices where such a dynamical symmetry is manifested. These experiments include expansion dynamics of cold atoms, chirality of atomic motion within a synthetic magnetic field, and melting of charge-density-wave order. Therefore, our theorem provides a unified view of these seemingly disparate phenomena.
We show symmetric dynamics in dissipative quantum many-body systems. Given some conditions on the Hamiltonian and the jump operators, the time evolution of certain observables can be identical for ferromagnetic and antiferromagnetic interactions in an Ising model with external fields or for repulsive and attractive interactions in a Hubbard model. We present two theorems to determine the existence of such a dynamical symmetry in dissipative quantum systems. The symmetry under the steady state is present independently on the initial state. Further constraint on the initial state leads to a stronger dynamical symmetry in real-time evolutions. We demonstrate the application of our theorems in dissipative Ising and Hubbard models. In addition, for the Fermi-Hubbard model, our results also reveal a connection between spin and charge densities in dissipative dynamics. We validate the discussions with numerical simulations performed using tensor network algorithms.
We investigate an unconventional symmetry in time-periodically driven systems, the Floquet dynamical symmetry (FDS). Unlike the usual symmetries, the FDS gives symmetry sectors that are equidistant in the Floquet spectrum and protects quantum coherence between them from dissipation and dephasing, leading to two kinds of time crystals: the discrete time crystal and discrete time quasicrystal that have different periodicity in time. We show that these time crystals appear in the Bose- and Fermi-Hubbard models under ac fields and their periodicity can be tuned only by adjusting the strength of the field. These time crystals arise only from the FDS and thus appear in both dissipative and isolated systems and in the presence of disorder as long as the FDS is respected. We discuss their experimental realizations in cold atom experiments and generalization to the SU(N)-symmetric Hubbard models.
Symmetry plays a fundamental role in understanding complex quantum matter, particularly in classifying topological quantum phases, which have attracted great interests in the recent decade. An outstanding example is the time-reversal invariant topological insulator, a symmetry-protected topological (SPT) phase in the symplectic class of the Altland-Zirnbauer classification. We report the observation for ultracold atoms of a noninteracting SPT band in a one-dimensional optical lattice and study quench dynamics between topologically distinct regimes. The observed SPT band can be protected by a magnetic group and a nonlocal chiral symmetry, with the band topology being measured via Bloch states at symmetric momenta. The topology also resides in far-from-equilibrium spin dynamics, which are predicted and observed in experiment to exhibit qualitatively distinct behaviors in quenching to trivial and nontrivial regimes, revealing two fundamental types of spin-relaxation dynamics related to bulk topology. This work opens the way to expanding the scope of SPT physics with ultracold atoms and studying nonequilibrium quantum dynamics in these exotic systems.
The existence of $\ensuremath{\eta}$-pairing eigenstates in the fermionic Hubbard model is fundamentally rooted in the $\ensuremath{\eta}$-pairing symmetry, which may hold for systems with nonuniform Hubbard interaction UUU. In this work, we present a generalized Hubbard model containing a variety of pseudospin terms that break the SO4{\mathrm{SO}}_{4}SO4​ symmetry but retain the $\ensuremath{\eta}$-pairing symmetry. This allows us to construct a variety of correlated systems possessing $\ensuremath{\eta}$-pairing eigenstates. We exemplify our findings by considering a modified Hubbard model associated with alternative magnetic fields and on-site repulsion. We find that the same quasi-$\ensuremath{\eta}$-pairing eigenstate exhibits two distinct dynamic behaviors in the two models. Numerical results of the time evolution driven by several typical Hamiltonians accord with the analytic predictions and provide a method for the control of an $\ensuremath{\eta}$-pairing wave packet with the aid of a time-dependent Hamiltonian.
We study the attractive Hubbard model within the dynamical mean-field theory, to elucidate how the pseudogap and superconductivity at strong attractive interaction are related to those found in the repulsive Hubbard model, and thereby to bridge cold fermions and cuprate high-temperature superconductors from a microscopic point of view. We propose that a unified understanding is obtained by investigating single-particle excitation dynamics, in which emergent and hidden fermions coupled to quasiparticles consistently account for the numerical results in both attractive and repulsive cases. In the attractive case, the quasiparticle dynamics is observable by virtually breaking a tightly bound pair, where we find two qualitatively different regions crossing over each other within the strong-coupling superconductivity phase. Among them, the region close to the critical temperature shares characteristic dynamics with the repulsive interaction case, where the normal and anomalous parts of the self-energy show strong low-energy peaks while they are hidden in the quasiparticle spectral weight. These prominent self-energy peaks are understood by the coupling of the quasiparticle to the hidden fermionic excitation, emergent from a strong-coupling effect. The pseudogap above the critical temperature is also accounted for by the same hidden fermion.
We study the two-dimensional (2D) Hubbard model using exact diagonalization for spin-1/2 fermions on the triangular and honeycomb lattices decorated with a single hexagon per site. In certain parameter ranges, the Hubbard model maps to a quantum compass model on those lattices. On the triangular lattice, the compass model exhibits collinear stripe antiferromagnetism, implying d-density wave charge order in the original Hubbard model. On the honeycomb lattice, the compass model has a unique, quantum disordered ground state that transforms nontrivially under lattice reflection. The ground state of the Hubbard model on the decorated honeycomb lattice is thus a 2D fermionic symmetry-protected topological phase. This state-protected by time-reversal and reflection symmetries-cannot be connected adiabatically to a free-fermion topological phase.