77 research outputs found
The bilinear-biquadratic model on the complete graph
We study the spin-1 bilinear-biquadratic model on the complete graph of N
sites, i.e., when each spin is interacting with every other spin with the same
strength. Because of its complete permutation invariance, this Hamiltonian can
be rewritten as the linear combination of the quadratic Casimir operators of
su(3) and su(2). Using group representation theory, we explicitly diagonalize
the Hamiltonian and map out the ground-state phase diagram of the model.
Furthermore, the complete energy spectrum, with degeneracies, is obtained
analytically for any number of sites
Temperature driven quenches in the Ising model: appearance of negative RĂ©nyi mutual information
We study the dynamics of the transverse field Ising chain after a local quench
in which two independently thermalised chains are joined together and are left
to evolve unitarily. In the emerging non-equilibrium steady state the RĂ©nyi
mutual information with different indices are calculated between two adjacent
segments of the chain, and are found to scale logarithmically in the subsystem
size. Surprisingly, for RĂ©nyi indices > 2 we find cases where the prefactor of
the logarithmic dependence is negative. The fact that the naively defined RĂ©nyi
mutual information might be negative has been pointed out before, however, we
provide the first example for this scenario in a realistic many-body setup. Our
numerical and analytical results indicate that in this setup it can be negative for
any index > 2 while it is always positive for < 2. Interestingly, even for
> 2 the calculated prefactors show some universal features: for example, the
same prefactor is also shown to govern the logarithmic time dependence of the
RĂ©nyi mutual information before the system relaxes locally to the steady state.
In particular, it can decrease in the non-equilibrium evolution after the quench
Entanglement entropy in quantum spin chains with broken reflection symmetry
We investigate the entanglement entropy of a block of L sites in quasifree
translation-invariant spin chains concentrating on the effect of reflection
symmetry breaking. The majorana two-point functions corresponding to the
Jordan-Wigner transformed fermionic modes are determined in the most general
case; from these it follows that reflection symmetry in the ground state can
only be broken if the model is quantum critical. The large L asymptotics of the
entropy is calculated analytically for general gauge-invariant models, which
has, until now, been done only for the reflection symmetric sector. Analytical
results are also derived for certain non-gauge-invariant models, e.g., for the
Ising model with Dzyaloshinskii-Moriya interaction. We also study numerically
finite chains of length N with a non-reflection-symmetric Hamiltonian and
report that the reflection symmetry of the entropy of the first L spins is
violated but the reflection-symmetric Calabrese-Cardy formula is recovered
asymptotically. Furthermore, for non-critical reflection-symmetry-breaking
Hamiltonians, we find an anomaly in the behavior of the "saturation entropy" as
we approach the critical line. The paper also provides a concise but extensive
review of the block entropy asymptotics in translation invariant quasifree spin
chains with an analysis of the nearest neighbor case and the enumeration of the
yet unsolved parts of the quasifree landscape.Comment: 12 pages and 4 figure
Entanglement negativity in two-dimensional free lattice models
We study the scaling properties of the ground-state entanglement between
finite subsystems of infinite two-dimensional free lattice models, as measured
by the logarithmic negativity. For adjacent regions with a common boundary, we
observe that the negativity follows a strict area law for a lattice of harmonic
oscillators, whereas for fermionic hopping models the numerical results
indicate a multiplicative logarithmic correction. In this latter case, we
conjecture a formula for the prefactor of the area-law violating term, which is
entirely determined by the geometries of the Fermi surface and the boundary
between the subsystems. The conjecture is tested against numerical results and
a good agreement is found.Comment: 11 pages, 6 figures, published versio
Efficient qudit based scheme for photonic quantum computing
Linear optics is a promising alternative for the realization of quantum
computation protocols due to the recent advancements in integrated photonic
technology. In this context usually qubit based quantum circuits are
considered, however, photonic systems naturally allow also for d-ary, i.e.,
qudit based, algorithms. This work investigates qudits defined by the possible
photon number states of a single photon in d > 2 optical modes. We demonstrate
how to construct locally optimal non-deterministic many-qudit gates using
linear optics and photon number resolving detectors, and explore the use of
qudit cluster states in the context of a d-ary optimization problem. We find
that the qudit cluster states require less optical modes and are encoded by a
fewer number of entangled photons than the qubit cluster states with similar
computational capabilities. We illustrate the benefit of our qudit scheme by
applying it to the k-coloring problem.Comment: 19 pages, 6 figure
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