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We show that the bulk-boundary correspondence for topological insulators can be modified in the presence of non-Hermiticity. We consider a one-dimensional tight-binding model with gain and loss as well as long-range hopping. The system is…
Many-body spin systems represent a paradigmatic platform for the realization of emergent states of matter in a strongly interacting regime. Spin models are commonly studied in one-dimensional periodic chains, whose lattice constant is on…
We propose how to create a non-trivial Haldane phase in atomic two-component Fermi-gas loaded on one-dimensional (1-D) optical lattice with trap potential. The Haldane phase is naturally formed on $p$-band Mott core in a wide range of the…
Despite the extensive studies of topological systems, the experimental characterizations of strongly nonlinear topological phases have been lagging. To address this shortcoming, we design and build elliptically geared isostatic…
Non-reciprocal systems have been shown to exhibit various interesting wave phenomena, such as the non-Hermitian skin effect, which causes accumulation of modes at boundaries. Recent research on discrete systems showed that this effect can…
Non-Hermitian topological matter provides a platform for engineering phenomena that go beyond the capabilities of Hermitian systems, enabling the use of losses to engineer topological phenomena. Non-Hermitian models often rely on artificial…
Topological phases are characterized by their entanglement properties, which is manifest in a direct relation between entanglement spectra and edge states discovered by Li and Haldane. We propose to leverage the power of synthetic quantum…
The seminal Haldane model brings up a paradigm beyond the quantum Hall effect to look for a plethora of topological phases in the honeycomb and other lattices. Here we dwell into this model considering a full parameter space in the presence…
Non-Abelian topological charges (NATCs), characterized by their noncommutative algebra, offer a framework for describing multigap topological phases beyond conventional Abelian invariants. While higher-order topological phases (HOTPs) host…
Kitaev model has both Abelian and non-Abelian anyonic excitations. It can act as a starting point for topological quantum computation. However, this model Hamiltonian is difficult to implement in natural condensed matter systems. Here we…
We have simulated a half-filled $1D$ $p$-wave periodic Anderson model with numerically exact projector quantum Monte Carlo technique, and the system is indeed located in the Haldane-like state as detected in previous works on the $p$-wave…
We investigate the non-Hermitian Haldane model on hyperbolic $\{8, 3\}$ and $\{12, 3\}$ lattices, and showcase its intriguing topological properties in the simultaneous presence of non-Hermitian effect and hyperbolic geometry. From bulk…
We propose an innovative quantum emulator based on Moire superlattices showing that, by employing periodical modulation on each lattice site, one can create tunable, artificial gauge fields with imprinting Peierls phases on the hopping…
The possibility of topological phase transition with or without a magnetic flux trapped in the cells of a class of decorated lattices is explored in details.Using a tight binding Hamiltonian and a real space decimation scheme we…
Nontrivial topological invariant of bulk electronic wavefunctions in two-dimensional quantum crystals leaves its footprints on the edge, dislocation, and corner modes. Here we investigate non-unitary time dynamics of these topological modes…
Topological phenomena in non-Hermitian systems have recently become a subject of great interest in the photonics and condensed-matter communities. In particular, the possibility of observing topologically-protected edge states in…
The moir\'e superlattice formed by ABC stacked trilayer graphene aligned with a hexagonal boron nitride substrate (TG/h-BN) provides an interesting system where both the bandwidth and the topology can be tuned by an applied perpendicular…
Using Quantum Monte Carlo simulations, we study spin-1/2 diagonal ladders coupled by ferromagnetic Heisenberg interactions. The model can also be viewed as usual ladders with ferromagnetic rung couplings coupled by antiferromagnetic…
We introduce the concept of tetris chains, which are linear arrays of 4-site molecules that differ by their intermolecular hopping geometry. We investigate the fermionic symmetry-protected topological Haldane phase in these systems using…
We theoretically investigate coupled gyration modes of magnetic solitons whose distances to the nearest neighbors are staggered. In a one-dimensional bipartite lattice, analogous to the Su-Schrieffer-Heeger model, there is a mid-gap…