Related papers: Local topological order inhibits thermal stability…
Topological band insulators which are dynamically generated by electron-electron interactions have been the- oretically proposed in two and three dimensional lattice models. We present evidence that the two-dimensional version can be…
This work is concerned with thermal quantum states of Hamiltonians on spin and fermionic lattice systems with short range interactions. We provide results leading to a local definition of temperature, thereby extending the notion of…
We address the question of whether symmetry-protected topological (SPT) order can persist at nonzero temperature, with a focus on understanding the thermal stability of several models studied in the theory of quantum computation. We present…
We establish a connection between ground states of local quantum Hamiltonians and thermal states of classical spin systems. For any discrete classical statistical mechanical model in any spatial dimension, we find an associated quantum…
The exploration of topological states is of significant fundamental and practical importance in contemporary condensed matter physics, for which the extension to two-dimensional (2D) organometallic systems is particularly attractive. Using…
Topological phases of matter are the center of much current interest, with promising potential applications in, e.g., topologically-protected transport and quantum computing. Traditionally such states are prepared by tuning the system…
Topological orders are a class of exotic states of matter characterized by patterns of long-range entanglement. Certain topologically ordered systems are proposed as potential realization of fault-tolerant quantum computation. Topological…
We prove that the Gibbs states of classical, and commuting-Pauli, Hamiltonians are stable under weak local decoherence: i.e., we show that the effect of the decoherence can be locally reversed. In particular, our conclusions apply to…
We investigate to what extent a suitably chosen system Hamiltonian can counteract local dissipative processes and preserve entanglement in the stationary state. The results determine prospects and limitations of dissipative state…
Topological invariants are conventionally known to be responsible for protection of extended states against disorder. A prominent example is the presence of topologically protected extended-states in two-dimensional (2D) quantum Hall…
We study the stability of topological order against local perturbations by considering the effect of a magnetic field on a spin model -- the toric code -- which is in a topological phase. The model can be mapped onto a quantum loop gas…
A gapped ground state of a quantum spin system has a natural length scale set by the gap. This length scale governs the decay of correlations. A common intuition is that this length scale also controls the spatial relaxation towards the…
While solid-state devices offer naturally reliable hardware for modern classical computers, thus far quantum information processors resemble vacuum tube computers in being neither reliable nor scalable. Strongly correlated many body states…
We point out certain symmetry induced constraints on topological order in Mott Insulators (quantum magnets with an odd number of spin $\tfrac{1}{2}$ per unit cell). We show, for example, that the double semion topological order is…
Topological quantum memory can protect information against local errors up to finite error thresholds. Such thresholds are usually determined based on the success of decoding algorithms rather than the intrinsic properties of the mixed…
We investigate how imposing kinetic restrictions on quantum particles that would otherwise hop freely on a two-dimensional lattice can lead to topologically ordered states. The kinetically constrained models introduced here are derived as a…
This article investigates the stability of the ground state subspace of a canonical parent Hamiltonian of a Matrix product state against local perturbations. We prove that the spectral gap of such a Hamiltonian remains stable under weak…
Topological color codes are among the stabilizer codes with remarkable properties from quantum information perspective. In this paper we construct a four-valent lattice, the so called ruby lattice, governed by a 2-body Hamiltonian. In a…
We develop a stability theory for contractive local IFSs on compact metric spaces. Unlike the classical global setting, local systems may exhibit a richer symbolic and geometric structure, including code spaces that are not of finite type…
Many-body localization (MBL) has been proposed to enable and protect topological order in all eigenstates, vastly expanding the traditional ground-state setting. However, for the most intriguing case of two-dimensional (2D) systems with…