Dynamical properties of the Haldane chain with bond disorder

By using Lanczos exact diagonalization and quantum Monte Carlo combined with stochastic analytic continuation, we study the dynamical properties of the $S=1$ antiferromagnetic Heisenberg chain with different strengths of bond disorder. In the weak disorder region, we find weakly coupled bonds which can induce additional low-energy excitation below the one-magnon mode. As the disorder increases, the average Haldane gap closes at $delta_{Delta}sim 0.5$ with more and more low-energy excitations coming out. After the critical disorder strength $delta_csim 1$, the system reaches a random-singlet phase with prominent sharp peak at $omega=0$ and broad continuum at $omega>0$ of the dynamic spin structure factor. In addition, we analyze the distribution of random spin domains and numerically find three kinds of domains hosting effective spin-1/2 quanta or spin-1 sites in between. These spins can form the weakly coupled long-range singlets due to quantum fluctuation which contribute to the sharp peak at $omega=0$.

Characterizing random-singlet state in two-dimensional frustrated quantum magnets and implications for the double perovskite Sr$_2$CuTe$_{1-x}$W$_{x}$O$_6$

Motivated by experimental observation of the non-magnetic phase in the compounds with frustration and disorder, we study the ground state of the spin-$1/2$ square-lattice Heisenberg model with randomly distributed nearest-neighbor $J_1$ and next-nearest-neighbor $J_2$ couplings. By using the density matrix renormalization group (DMRG) calculation on cylinder system with circumference up to $10$ lattice sites, we identify a disordered phase between the Neel and stripe magnetic phase with growing $J_2 / J_1$ in the presence of strong randomness. The vanished spin-freezing parameter indicates the absent spin glass order. The large-scale DMRG results unveil the size-scaling behaviors of the spin-freezing parameter, the power-law decay of average spin correlation, and the exponential decay of typical spin correlation, which all agree with the corresponding behavior in the one-dimensional random singlet (RS) state and characterize the RS nature of this non-magnetic state. The DMRG simulation also opens new insight and opportunities for characterizing a class of non-magnetic states in two-dimensional frustrated magnets with disorder. We also compare with existing experiments and suggest more measurements for understanding the spin-liquid-like behavior in the double perovskite Sr$_2$CuTe$_{1-x}$W$_{x}$O$_6$.

Visualizing a Bosonic Symmetry Protected Topological Phase in an Interacting Fermion Model

Symmetry protected topological (SPT) phases in free fermion and interacting bosonic systems have been classified, but the physical phenomena of interacting fermionic SPT phases have not been fully explored. Here, employing large-scale quantum Monte Carlo simulation, we investigate the edge physics of a bilayer Kane-Mele-Hubbard model with zigzag ribbon geometry. Our unbiased numerical results show that the fermion edge modes are gapped out by interaction, while the bosonic edge modes remain gapless at the $(1+1)d$ boundary, before the bulk quantum phase transition to a topologically trivial phase. Therefore, finite fermion gaps both in the bulk and on the edge, together with the robust gapless bosonic edge modes, prove that our system becomes an emergent bosonic SPT phase at low energy, which is, for the first time, directly observed in an interacting fermion lattice model.

Quantum critical point of Dirac fermion mass generation without spontaneous symmetry breaking

We study a lattice model of interacting Dirac fermions in $(2+1)$ dimension space-time with an SU(4) symmetry. While increasing interaction strength, this model undergoes a {it continuous} quantum phase transition from the weakly interacting Dirac semimetal to a fully gapped and nondegenerate phase without condensing any Dirac fermion bilinear mass operator. This unusual mechanism for mass generation is consistent with recent studies of interacting topological insulators/superconductors, and also consistent with recent progresses in lattice QCD community.

Diagnosis of interaction-driven topological phase via exact diagonalization

We propose a general scheme for diagnosing interaction-driven topological phases in the weak interaction regime using exact diagonalization (ED). The scheme comprises the analysis of eigenvalues of the point-group operators for the many-body eigenstates and the correlation functions for physical observables to extract the symmetries of the order parameters and the topological numbers of the underlying ground states at the thermodynamic limit from a relatively small size system afforded by ED. As a concrete example, we investigate the interaction effects on the half-filled spinless fermions on the checkerboard lattice with a quadratic band crossing point. Numerical results support the existence of a spontaneous quantum anomalous Hall phase purely driven by a nearest-neighbor weak repulsive interaction, separated from a nematic Mott insulator phase at strong repulsive interaction by a first-order phase transition.