Related papers: Frustration-free Hamiltonian with Topological Orde…
Symmetry Protected Topological (SPT) phases are a minimal generalization of the concept of topological insulators to interacting systems. In this paper we describe the classification and properties of such phases for three dimensional(3D)…
Generalized PT symmetry provides crucial insight into the sign problem for two classes of models. In the case of quantum statistical models at non-zero chemical potential, the free energy density is directly related to the ground state…
We propose an exotic scenario that topological superconductivity can emerge by doping strongly interacting fermionic systems whose spin degrees of freedom form bosonic symmetry protected topological (SPT) state. Specifically, we study a…
Higher-order networks encode the many-body interactions of complex systems ranging from the brain to biological transportation networks. Simplicial and cell complexes are ideal higher-order network representations for investigating…
We study the phase diagram of a topological string-net type lattice model in the presence of geometrically frustrated interactions. These interactions drive several phase transitions that reduce the topological order, leading to a rich…
Searches for possible new quantum phases and classifications of quantum phases have been central problems in physics. Yet, they are indeed challenging problems due to the computational difficulties in analyzing quantum many-body systems and…
Despite growing interest in beyond-group symmetries in quantum condensed matter systems, there are relatively few microscopic lattice models explicitly realizing these symmetries, and many phenomena have yet to be studied at the microscopic…
We prove that estimating the ground state energy of a translationally-invariant, nearest-neighbour Hamiltonian on a 1D spin chain is QMAEXP-complete, even for systems of low local dimension (roughly 40). This is an improvement over the best…
Higher-order topological insulators have a modified bulk-boundary correspondence compared to other topological phases: instead of gapless edge or surface states, they have gapped edges and surfaces, but protected modes at corners or hinges.…
We classify one-dimensional symmetry-protected topological (SPT) phases protected by dipole symmetries. A dipole symmetry comprises two sets of symmetry generators: charge and dipole operators, which together form a non-trivial algebra with…
In this paper we introduce the concept of characteristic number that are proven to be useful in the study of the combinatorics of graph cohomology. We claim that it is a good combinatorial counterpart for geometric Betti numbers. We then…
Topological insulators in free fermion systems have been well characterized and classified. However, it is not clear in strongly interacting boson or fermion systems what symmetry protected topological orders exist. In this paper, we…
In closed quantum systems, strong randomness can localize many-body excitations, preventing ergodicity. An interesting consequence is that high energy excited states can exhibit quantum coherent properties, such as symmetry protected…
From atomic crystals to bird flocks, most forms of order are captured by the concept of spontaneous symmetry breaking. This paradigm was challenged by the discovery of topological order, in materials where the number of accessible states is…
In this letter, we propose an application of String Order Parameter (SOP), commonly used in quantum spin systems, to identify symmetry-protected topological phase (SPT) in fermionic systems in the example of the dimerized fermionic chain.…
We study the correlated Haldane-Hubbard model with single-particle gain and loss, focusing on its non-Hermitian phase diagram and the ensuing non-unitary dynamic properties. The interplay of interactions and non-hermiticity results in…
We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify "gapped"…
Hamiltonicity is an important property in parallel and distributed computation. Existence of Hamiltonian cycle allows efficient emulation of distributed algorithms on a network wherever such algorithm exists for linear-array and ring, and…
Motivated by the abundance of symmetry breaking states in magic-angle twisted bilayer graphene and other two-dimensional materials, we study superconducting (SC) and charge orders in two-dimensional topological flat bands in the strong…
The dynamical evolution of an open quantum system can be governed by the Lindblad equation of the density matrix. In this paper, we propose to characterize the density matrix topology by the topological invariant of its modular Hamiltonian.…