2,552 research outputs found
The complexity of antiferromagnetic interactions and 2D lattices
Estimation of the minimum eigenvalue of a quantum Hamiltonian can be
formalised as the Local Hamiltonian problem. We study the natural special case
of the Local Hamiltonian problem where the same 2-local interaction, with
differing weights, is applied across each pair of qubits. First we consider
antiferromagnetic/ferromagnetic interactions, where the weights of the terms in
the Hamiltonian are restricted to all be of the same sign. We show that for
symmetric 2-local interactions with no 1-local part, the problem is either
QMA-complete or in StoqMA. In particular the antiferromagnetic Heisenberg and
antiferromagnetic XY interactions are shown to be QMA-complete. We also prove
StoqMA-completeness of the antiferromagnetic transverse field Ising model.
Second, we study the Local Hamiltonian problem under the restriction that the
interaction terms can only be chosen to lie on a particular graph. We prove
that nearly all of the QMA-complete 2-local interactions remain QMA-complete
when restricted to a 2D square lattice. Finally we consider both restrictions
at the same time and discover that, with the exception of the antiferromagnetic
Heisenberg interaction, all of the interactions which are QMA-complete with
positive coefficients remain QMA-complete when restricted to a 2D triangular
lattice.Comment: 35 pages, 11 figures; v2 added reference
Non glassy ground-state in a long-range antiferromagnetic frustrated model in the hypercubic cell
We analize the statistical mechanics of a long-range antiferromagnetic model
defined on a D-dimensional hypercube, both at zero and finite temperatures. The
associated Hamiltonian is derived from a recently proposed complexity measure
of Boolean functions, in the context of neural networks learning processes. We
show that, depending of the value of D, the system either presents a low
temperature antiferromagnetic stable phase or the global antiferromagnetic
order disappears at any temperature. In the last case the ground state is an
infinitely degenerated non-glassy one, composed by two equal size anti-aligned
antiferromagnetic domains. We also present some results for the ferromagnetic
version of the model.Comment: 8 pages, 5 figure
2D Hexagonal covalent organic radical frameworks as tunable correlated electron systems
Quantum materials hold huge technological promise but challenge the fundamental understanding of complex electronic interactions in solids. The Mott metal-insulator transition on half‐filled lattices is an archetypal demonstration of how quantum states can be driven by electronic correlation. Twisted bilayers of 2D materials provide an experimentally accessible means to probe such transitions, but these seemingly simple systems belie high complexity due to the myriad of possible interactions. Herein, it is shown that electron correlation can be simply tuned in experimentally viable 2D hexagonally ordered covalent organic radical frameworks (2D hex‐CORFs) based on single layers of half‐filled stable radical nodes. The presented carefully procured theoretical analysis predicts that 2D hex‐CORFs can be varied between a correlated antiferromagnetic Mott insulator state and a semimetallic state by modest out‐of‐plane compressive pressure. This work establishes 2D hex‐CORFs as a class of versatile single‐layer quantum materials to advance the understanding of low dimensional correlated electronic systems
Designer quantum states of matter created atom-by-atom
With the advances in high resolution and spin-resolved scanning tunneling
microscopy as well as atomic-scale manipulation, it has become possible to
create and characterize quantum states of matter bottom-up, atom-by-atom. This
is largely based on controlling the particle- or wave-like nature of electrons,
as well as the interactions between spins, electrons, and orbitals and their
interplay with structure and dimensionality. We review the recent advances in
creating artificial electronic and spin lattices that lead to various exotic
quantum phases of matter, ranging from topological Dirac dispersion to complex
magnetic order. We also project future perspectives in non-equilibrium
dynamics, prototype technologies, engineered quantum phase transitions and
topology, as well as the evolution of complexity from simplicity in this newly
developing field
Simulating Ising Spin Glasses on a Quantum Computer
A linear-time algorithm is presented for the construction of the Gibbs
distribution of configurations in the Ising model, on a quantum computer. The
algorithm is designed so that each run provides one configuration with a
quantum probability equal to the corresponding thermodynamic weight. The
partition function is thus approximated efficiently. The algorithm neither
suffers from critical slowing down, nor gets stuck in local minima. The
algorithm can be A linear-time algorithm is presented for the construction of
the Gibbs distribution of configurations in the Ising model, on a quantum
computer. The algorithm is designed so that each run provides one configuration
with a quantum probability equal to the corresponding thermodynamic weight. The
partition function is thus approximated efficiently. The algorithm neither
suffers from critical slowing down, nor gets stuck in local minima. The
algorithm can be applied in any dimension, to a class of spin-glass Ising
models with a finite portion of frustrated plaquettes, diluted Ising models,
and models with a magnetic field. applied in any dimension, to a class of
spin-glass Ising models with a finite portion of frustrated plaquettes, diluted
Ising models, and models with a magnetic field.Comment: 24 pages, 3 epsf figures, replaced with published and significantly
revised version. More info available at http://www.fh.huji.ac.il/~dani/ and
http://www.fiz.huji.ac.il/staff/acc/faculty/biha
Simulating Quantum Magnetism with Correlated Non-Neutral Ion Plasmas
By employing forces that depend on the internal electronic state (or spin) of
an atomic ion, the Coulomb potential energy of a strongly coupled array of ions
can be modified in a spin-dependent way to mimic effective quantum spin
Hamiltonians. Both ferromagnetic and antiferromagnetic interactions can be
implemented. We use simple models to explain how the effective spin
interactions are engineered with trapped-ion crystals. We summarize the type of
effective spin interactions that can be readily generated, and discuss an
experimental implementation using single-plane ion crystals in a Penning trap.Comment: 10 pages, 5 figures, to be published in the Proceedings of 10th
International Workshop on Non-Neutral Plasma
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