23 research outputs found
A dynamical mean-field theory study of stripe order and d-wave superconductivity in the two-dimensional Hubbard model
We use cellular dynamical mean-field theory with extended unit cells to study
the ground state of the two-dimensional repulsive Hubbard model at finite
doping. We calculate the energy of states with d-wave superconductivity
coexisting with spatially uniform magnetic order and find that they are
energetically favoured in a large doping region as compared to the uniform
solution. We study the spatial form of the superconducting and magnetic order
parameters at different doping values.Comment: 11 pages, 6 figure
Theory of the Loschmidt echo and dynamical quantum phase transitions in disordered Fermi systems
In this work we develop the theory of the Loschmidt echo and dynamical phase
transitions in non-interacting strongly disordered Fermi systems after a
quench. In finite systems the Loschmidt echo displays zeros in the complex time
plane that depend on the random potential realization. Remarkably, the zeros
coalesce to form a 2D manifold in the thermodynamic limit, atypical for 1D
systems, crossing the real axis at a sharply-defined critical time. We show
that this dynamical phase transition can be understood as a transition in the
distribution function of the smallest eigenvalue of the Loschmidt matrix, and
develop a finite-size scaling theory. Contrary to expectations, the notion of
dynamical phase transitions in disordered systems becomes decoupled from the
equilibrium Anderson localization transition. Our results highlight the
striking qualitative differences of quench dynamics in disordered and
non-disordered many-fermion systems.Comment: 7 pages including appendices, 4 figure
Complexity of fermionic states
How much information a fermionic state contains? To address this fundamental
question, we define the complexity of a particle-conserving many-fermion state
as the entropy of its Fock space probability distribution, minimized over all
Fock representations. The complexity characterizes the minimum computational
and physical resources required to represent the state and store the
information obtained from it by measurements. Alternatively, the complexity can
be regarded a Fock space entanglement measure describing the intrinsic
many-particle entanglement in the state. We establish universal lower bound for
the complexity in terms of the single-particle correlation matrix eigenvalues
and formulate a finite-size complexity scaling hypothesis. Remarkably,
numerical studies on interacting lattice models suggest a general
model-independent complexity hierarchy: ground states are exponentially less
complex than average excited states which, in turn, are exponentially less
complex than generic states in the Fock space. Our work has fundamental
implications on how much information is encoded in fermionic states.Comment: 5+5 pages, 3+2 Fig
Topological phase transitions in the repulsively interacting Haldane-Hubbard model
Using dynamical mean-field theory and exact diagonalization we study the
phase diagram of the repulsive Haldane-Hubbard model, varying the interaction
strength and the sublattice potential difference. In addition to the quantum
Hall phase with Chern number and the band insulator with present
already in the noninteracting model, the system also exhibits a Mott
insulating phase, and a quantum Hall phase. We explain the latter phase
by a spontaneous symmetry breaking where one of the spin-components is in the
Hall state and the other in the band insulating state.Comment: Updated version, 6 pages, 4 figure