Related papers: Split Property and Fermionic String Order
We consider a class of ground states for quantum spin chains on an integer lattice. First we show that presence of the spectral gap between the ground state energy and the rest of spectrum implies the split property of certain subsystems.As…
We present analytical and numerical results on symmetry properties of staggered fermions with taste splitting mass terms. As staggered species split differently for different types of taste splitting masses, various lattice symmetry…
We investigate the persistence of spectral gaps of one-dimensional frustration free quantum lattice systems under weak perturbations and with open boundary conditions. Assuming the interactions of the system satisfy a form of local…
We study lattice constructions of gapped fermionic phases of matter. We show that the construction of fermionic Symmetry Protected Topological orders by Gu and Wen has a hidden dependence on a discrete spin structure on the Euclidean…
We show the boundedness of entanglement entropy for (bipartite) pure states of quantum spin chains implies split property of subsystems. As a corollary the infinite volume ground states for 1-dim spin chains with the spectral gap between…
We study the ground states of lattice Hamiltonians that are invariant under permutations, in the limit where the number of lattice sites, N -> \infty. For spin systems, these are product states, a fact that follows directly from the quantum…
Entanglement between the constituents of a quantum system is an essential resource in the implementation of many quantum processes and algorithms. Indeed, universal quantum computation is possible by measuring individual qubits comprising…
The anticommuting properties of fermionic operators, together with the presence of parity conservation, affect the concept of entanglement in a composite fermionic system. Hence different points of view can give rise to different reasonable…
We demonstrate that hidden long range order is always present in the gapped phases of interacting fermionic systems on one dimensional lattices. It is captured by correlation functions of appropriate nonlocal charge and/or spin operators,…
String breaking is a non-perturbative long-distance feature of QCD that is involved in for example meson decays. A mixing analysis of lattice operators at zero temperature gives the level splitting and mixing energy between the broken and…
We investigate the general properties of lattice spin models with emerging fermionic excitations. We argue that fermions always come in pairs and their creation operator always has a string-like structure with the newly created particles…
In this paper, we investigate the ground state properties of a mixture of two species of fermionic atoms in one-dimensional optical lattice, as described by the asymmetric Hubbard model. The quantum phase transition from density wave to…
We extend the formalism of Matrix Product States (MPS) to describe one-dimensional gapped systems of fermions with both unitary and anti-unitary symmetries. Additionally, systems with orientation-reversing spatial symmetries are considered.…
Motivated by experimental progress in the growth of heavy transition metal oxides, we theoretically study a class of lattice models of interacting fermions with strong spin-orbit coupling. Focusing on interactions of intermediate strength,…
The problem of motion of a single electron interacting with a periodic lattice of two-level systems is investigated within a spinless fermion model. The Green's function is calculated in a single-site dynamical coherent potential…
A new formulation for fermions on the lattice based on a discretization of a second order formalism is proposed. A comparison with the first order formalism in connection with the $U(1)$ anomaly and the doubling problem is presented. The…
Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation…
String field theory is a candidate for a full non-perturbative definition of string theory. We aim to define string field theory on a space-time lattice to investigate its behaviour at the quantum level. Specifically, we look at string…
We show that the existence of string order in a given quantum state is intimately related to the presence of a local symmetry by proving that both concepts are equivalent within the framework of finitely correlated states. Once this…
We illustrate some problems that are related to the existence of an underlying linear structure at the level of the property lattice associated with a physical system, for the particular case of two explicitly separated spin 1/2 objects…