Alioscia Hamma

Ground state entanglement and geometric entropy in the Kitaev model

We study the entanglement properties of the ground state in Kitaevs model. This is a two-dimensional spin system with a torus topology and nontrivial four-body interactions between its spins. For a generic partition

Bipartite entanglement and entropic boundary law in lattice spin systems

(A,B)

Topological Entanglement Rényi Entropy and Reduced Density Matrix Structure

of the lattice we calculate analytically the von Neumann entropy of the reduced density matrix

Adiabatic approximation with exponential accuracy for many-body systems and quantum computation

\rho_A

Quantum bose-hubbard model with an evolving graph as a toy model for emergent spacetime

in the ground state. We prove that the geometric entropy associated with a region

Quantum Adiabatic Brachistochrone

A

Ground-state factorization and correlations with broken symmetry

is linear in the length of its boundary. Moreover, we argue that entanglement can probe the topology of the system and reveal topological order. Finally, no partition has zero entanglement and we find the partition that maximizes the entanglement in the given ground state.

Quantum phase transition between cluster and antiferromagnetic states

We investigate bipartite entanglement in spin-1/2 systems on a generic lattice. For states that are an equal superposition of elements of a group G of spin flips acting on the fully polarized state |0>{sup xn}, we find that the von Neumann entropy depends only on the boundary between the two subsystems A and B. These states are stabilized by the group G. A physical realization of such states is given by the ground state manifold of the Kitaevs model on a Riemann surface of genus g. For a square lattice, we find that the entropy of entanglement is bounded from above and below by functions linear in the perimeter of the subsystem A and is equal to the perimeter (up to an additive constant) when A is convex. The entropy of entanglement is shown to be related to the topological order of this model. Finally, we find that some of the ground states are absolutely entangled, i.e., no partition has zero entanglement. We also provide several examples for the square lattice.

Entanglement, fidelity, and topological entropy in a quantum phase transition to topological order

We generalize the topological entanglement entropy to a family of topological Rényi entropies parametrized by a parameter alpha, in an attempt to find new invariants for distinguishing topologically ordered phases. We show that, surprisingly, all topological Rényi entropies are the same, independent of alpha for all nonchiral topological phases. This independence shows that topologically ordered ground-state wave functions have reduced density matrices with a certain simple structure, and no additional universal information can be extracted from the entanglement spectrum.

Quantum entanglement in random physical states.

We derive a version of the adiabatic theorem that is especially suited for applications in adiabatic quantum computation, where it is reasonable to assume that the adiabatic interpolation between the initial and final Hamiltonians is controllable. Assuming that the Hamiltonian is analytic in a finite strip around the real time axis, that some number of its time-derivatives vanish at the initial and final times, and that the target adiabatic eigenstate is non-degenerate and separated by a gap from the rest of the spectrum, we show that one can obtain an error between the final adiabatic eigenstate and the actual time-evolved state which is exponentially small in the evolution time, where this time itself scales as the square of the norm of the time-derivative of the Hamiltonian, divided by the cube of the minimal gap.