Marco Cozzini

Quantum fidelity and quantum phase transitions in matrix product states

Matrix product states, a key ingredient of numerical algorithms widely employed in the simulation of quantum spin chains, provide an intriguing tool for quantum phase transition engineering. At critical values of the control parameters on which their constituent matrices depend, singularities in the expectation values of certain observables can appear, in spite of the analyticity of the ground state energy. For this class of generalized quantum phase transitions, we test the validity of the recently introduced fidelity approach, where the overlap modulus of ground states corresponding to slightly different parameters is considered. We discuss several examples, successfully identifying all the present transitions. We also study the finite size scaling of fidelity derivatives, pointing out its relevance in extracting critical exponents.

Quantum phase transitions and quantum fidelity in free fermion graphs

In this paper we analyze the ground-state phase diagram of a class of fermionic Hamiltonians by looking at the fidelity of ground states corresponding to slightly different Hamiltonian parameters. The Hamiltonians under investigation can be considered as the variable range generalization of the fermionic Hamiltonian obtained by the Jordan-Wigner transformation of the

Ground state fidelity and quantum phase transitions in free Fermi systems

XY

Macroscopic dynamics of a Bose-Einstein condensate containing a vortex lattice

spin chain in a transverse magnetic field. Under periodic boundary conditions, the matrices of the problem become circulant and the models are exactly solvable. Their free-ends counterparts are instead analyzed numerically. In particular, we focus on the long-range model corresponding to a fully connected directed graph, providing asymptotic results in the thermodynamic limit, as well as the finite-size scaling analysis of the second-order quantum phase transitions of the system. A strict relation between fidelity and single particle spectrum is demonstrated, and a peculiar gapful transition due to the long-range nature of the coupling is found. A comparison between fidelity and another transition marker borrowed from quantum information, i.e., single site entanglement, is also considered.

Fermi Gases in Slowly Rotating Traps: Superfluid versus Collisional Hydrodynamics

We compute the fidelity of the ground states of general quadratic fermionic Hamiltonians and analyse its connections with quantum phase transitions. Each of these systems is characterized by an L × L real matrix whose polar decomposition, into a non-negative ΛΦ and a unitary T, contains all the relevant ground state (GS) information. The boundaries between different regions in the GS phase diagram are given by the points of, possibly asymptotic, singularity of ΛΦ. This latter in turn implies a critical drop of the fidelity function. We present general results as well as their exemplification by a model of fermions on a totally connected graph.

Fidelity approach to the Hubbard model

Starting from the equations of rotational hydrodynamics we study the macroscopic behavior of a trapped Bose-Einstein condensate containing a large number of vortices. The stationary configurations of the system, the frequencies of the collective excitations, and the expansion of the condensate are investigated as a function of the angular velocity of the vortex lattice. The time evolution of the condensate and of the lattice geometry induced by a sudden deformation of the trap is also discussed and compared with the recent experimental results of P. Engels et al. [Phys. Rev. Lett. 89, 100403 (2002)].

Tkachenko Oscillations and the Compressibility of a Rotating Bose-Einstein Condensate

The dynamic behavior of a Fermi gas confined in a deformed trap rotating at low angular velocity is investigated in the framework of hydrodynamic theory. The differences exhibited by a normal gas in the collisional regime and a superfluid are discussed. Special emphasis is given to the collective oscillations excited when the deformation of the rotating trap is suddenly removed or when the rotation is suddenly stopped. The presence of vorticity in the normal phase is shown to give rise to precession and beating phenomena which are absent in the superfluid phase.

Oscillations of a Bose-Einstein Condensate Rotating in a Harmonic Plus Quartic Trap

We use the fidelity approach to quantum critical points to study the zero-temperature phase diagram of the one-dimensional Hubbard model. Using a variety of analytical and numerical techniques, we analyze the fidelity metric in various regions of the phase diagram with particular care to the critical points. Specifically we show that close to the Mott transition, taking place at on-site repulsion

Vortex lattices in Bose-Einstein condensates: From the Thomas-Fermi regime to the lowest-Landau-level regime

U=0

Scissors mode of a rotating Bose-Einstein condensate

and electron density