Dynamical signatures of symmetry protected topology following symmetry breaking

We investigate topological signatures in the short-time non-equilibrium dynamics of symmetry protected topological (SPT) systems starting from initial states which break the protecting symmetry. Naively, one might expect that topology loses meaning when a protecting symmetry is broken. Defying this intuition, we illustrate, in an interacting Su-Schrieffer-Heeger (SSH) model, how this combination of symmetry breaking and quench dynamics can give rise to both single-particle and many-body signatures of topology. From the dynamics of the symmetry broken state, we find that we are able to dynamically probe the equilibrium topological phase diagram of a symmetry respecting projection of the post-quench Hamiltonian. In the ensemble dynamics, we demonstrate how spontaneous symmetry breaking (SSB) of the protecting symmetry can result in a quantized many-body topological `invariant which is not pinned under unitary time evolution. We dub this `dynamical many-body topology (DMBT). We show numerically that both the pure state and ensemble signatures are remarkably robust, and argue that these non-equilibrium signatures should be quite generic in SPT systems, regardless of protecting symmetries or spatial dimension.

Evidence of pair-density wave in doping Kitaev spin liquid on the honeycomb lattice

We study the effects of doping the Kitaev model on the honeycomb lattice where the spins interact via the bond-directional interaction $J_K$, which is known to have a quantum spin liquid as its exact ground state. The effect of hole doping is studied within the $t$-$J_K$ model on a three-leg cylinder using density-matrix renormalization group. Upon light doping, we find that the ground state of the system has quasi-long-range charge-density-wave correlations but short-range single-particle correlations. The dominant pairing channel is the even-parity superconducting pair-pair correlations with $d$-wave-like symmetry, which oscillate in sign as a function of separation with a period equal to that of the spin-density wave and two times the charge-density wave. Although these correlations fall rapidly (possibly exponentially) at long distances, this is never-the-less the first example where a pair-density wave is the strongest SC order on a bipartite lattice. Our results may be relevant to ${rm Na_2IrO_3}$ and $alpha$-${rm RuCl_3}$ upon doping.

Ground state phase diagram of the doped Hubbard model on the 4-leg cylinder

We study the ground state properties of the Hubbard model on a 4-leg cylinder with doped hole concentration per site $deltaleq 12.5%$ using density-matrix renormalization group. By keeping a large number of states for long system sizes, we find that the nature of the ground state is remarkably sensitive to the presence of next-nearest-neighbor hopping $t$. Without $t$ the ground state of the system corresponds with the insulating filled stripe phase with long-range charge-density-wave (CDW) order and short-range incommensurate spin correlations appears. However, for a small negative $t$ a phase characterized by coexisting algebraic d-wave superconducting (SC)- and algebraic CDW correlations. In addition, it shows short range spin- and fermion correlations consistent with a canonical Luther-Emery (LE) liquid, except that the charge- and spin periodicities are consistent with half-filled stripes instead of the $4 k_F$ and $2 k_F$ wavevectors generic for one dimensional chains. For a small positive $t$ yet another phase takes over showing similar SC and CDW correlations. However, the fermions are now characterized by a (near) infinite correlation length while the gapped spin system is characterized by simple staggered antiferromagnetic correlations. We will show that this is consistent with a LE formed from a weakly coupled (BCS like) d-wave superconductor on the ladder where the interactions have only the effect to stabilize a cuprate style magnetic resonance.

Nature of a single doped hole in two-leg Hubbard and $t$-$J$ ladders

In this paper, we have systematically studied the single hole problem in two-leg Hubbard and $t$-$J$ ladders by large-scale density-matrix renormalization group calculations. We found that the doped hole in both models behaves similarly with each other while the three-site correlated hopping term is not important in determining the ground state properties. For more insights, we have also calculated the elementary excitations, i.e., the energy gaps to the excited states of the system. In the strong rung limit, we found that the doped hole behaves as a Bloch quasiparticle in both systems where the spin and charge of the doped hole are tightly bound together. In the isotropic limit, while the hole still behaves like a quasiparticle in the long-wavelength limit, its spin and charge components are only loosely bound together with a nontrivial mutual statistics inside the quasiparticle. Our results show that this mutual statistics can lead to an important residual effect which dramatically changes the local structure of the ground state wavefunction.