1,677 research outputs found
Frustrated two dimensional quantum magnets
We overview physical effects of exchange frustration and quantum spin
fluctuations in (quasi-) two dimensional (2D) quantum magnets () with
square, rectangular and triangular structure. Our discussion is based on the
- type frustrated exchange model and its generalizations. These
models are closely related and allow to tune between different phases,
magnetically ordered as well as more exotic nonmagnetic quantum phases by
changing only one or two control parameters. We survey ground state properties
like magnetization, saturation fields, ordered moment and structure factor in
the full phase diagram as obtained from numerical exact diagonalization
computations and analytical linear spin wave theory. We also review finite
temperature properties like susceptibility, specific heat and magnetocaloric
effect using the finite temperature Lanczos method. This method is powerful to
determine the exchange parameters and g-factors from experimental results. We
focus mostly on the observable physical frustration effects in magnetic phases
where plenty of quasi-2D material examples exist to identify the influence of
quantum fluctuations on magnetism.Comment: 78 pages, 54 figure
WavePacket: A Matlab package for numerical quantum dynamics. II: Open quantum systems, optimal control, and model reduction
WavePacket is an open-source program package for numeric simulations in
quantum dynamics. It can solve time-independent or time-dependent linear
Schr\"odinger and Liouville-von Neumann-equations in one or more dimensions.
Also coupled equations can be treated, which allows, e.g., to simulate
molecular quantum dynamics beyond the Born-Oppenheimer approximation.
Optionally accounting for the interaction with external electric fields within
the semi-classical dipole approximation, WavePacket can be used to simulate
experiments involving tailored light pulses in photo-induced physics or
chemistry. Being highly versatile and offering visualization of quantum
dynamics 'on the fly', WavePacket is well suited for teaching or research
projects in atomic, molecular and optical physics as well as in physical or
theoretical chemistry. Building on the previous Part I which dealt with closed
quantum systems and discrete variable representations, the present Part II
focuses on the dynamics of open quantum systems, with Lindblad operators
modeling dissipation and dephasing. This part also describes the WavePacket
function for optimal control of quantum dynamics, building on rapid
monotonically convergent iteration methods. Furthermore, two different
approaches to dimension reduction implemented in WavePacket are documented
here. In the first one, a balancing transformation based on the concepts of
controllability and observability Gramians is used to identify states that are
neither well controllable nor well observable. Those states are either
truncated or averaged out. In the other approach, the H2-error for a given
reduced dimensionality is minimized by H2 optimal model reduction techniques,
utilizing a bilinear iterative rational Krylov algorithm
WavePacket: A Matlab package for numerical quantum dynamics. I: Closed quantum systems and discrete variable representations
WavePacket is an open-source program package for the numerical simulation of
quantum-mechanical dynamics. It can be used to solve time-independent or
time-dependent linear Schr\"odinger and Liouville-von Neumann-equations in one
or more dimensions. Also coupled equations can be treated, which allows to
simulate molecular quantum dynamics beyond the Born-Oppenheimer approximation.
Optionally accounting for the interaction with external electric fields within
the semiclassical dipole approximation, WavePacket can be used to simulate
experiments involving tailored light pulses in photo-induced physics or
chemistry.The graphical capabilities allow visualization of quantum dynamics
'on the fly', including Wigner phase space representations. Being easy to use
and highly versatile, WavePacket is well suited for the teaching of quantum
mechanics as well as for research projects in atomic, molecular and optical
physics or in physical or theoretical chemistry.The present Part I deals with
the description of closed quantum systems in terms of Schr\"odinger equations.
The emphasis is on discrete variable representations for spatial discretization
as well as various techniques for temporal discretization.The upcoming Part II
will focus on open quantum systems and dimension reduction; it also describes
the codes for optimal control of quantum dynamics.The present work introduces
the MATLAB version of WavePacket 5.2.1 which is hosted at the Sourceforge
platform, where extensive Wiki-documentation as well as worked-out
demonstration examples can be found
Thermodynamics of anisotropic triangular magnets with ferro- and antiferromagnetic exchange
We investigate thermodynamic properties like specific heat and
susceptibility in anisotropic - triangular quantum spin
systems (). As a universal tool we apply the finite temperature Lanczos
method (FTLM) based on exact diagonalization of finite clusters with periodic
boundary conditions. We use clusters up to sites where the thermodynamic
limit behavior is already stably reproduced. As a reference we also present the
full diagonalization of a small eight-site cluster. After introducing model and
method we discuss our main results on and . We show the
variation of peak position and peak height of these quantities as function of
control parameter . We demonstrate that maximum peak positions and
heights in N\'eel phase and spiral phases are strongly asymmetric, much more
than in the square lattice - model. Our results also suggest a
tendency to a second side maximum or shoulder formation at lower temperature
for certain ranges of the control parameter. We finally explicitly determine
the exchange model of the prominent triangular magnets CsCuCl and
CsCuBr from our FTLM results.Comment: 13 pages, 12 figure
N\'eel temperature and reentrant H-T phase diagram of quasi-2D frustrated magnets
In quasi-2D quantum magnets the ratio of N\'eel temperature to
Curie-Weiss temperature is frequently used as an empirical
criterion to judge the strength of frustration. In this work we investigate how
these quantities are related in the canonical quasi-2D frustrated square or
triangular - model. Using the self-consistent Tyablikov approach for
calculating we show their dependence on the frustration control
parameter in the whole N\'eel and columnar antiferromagnetic phase
region. We also discuss approximate analytical results. In addition the field
dependence of and the associated possible reentrance behavior of
the ordered moment due to quantum fluctuations is investigated. These results
are directly applicable to a class of quasi-2D oxovanadate antiferromagnets. We
give clear criteria to judge under which conditions the empirical frustration
ratio may be used as measure of frustration
strength in the quasi-2D quantum magnets.Comment: 16 pages, 14 figures, to appear in Physical Review
Quantum fluctuations in anisotropic triangular lattices with ferro- and antiferromagnetic exchange
The Heisenberg model on a triangular lattice is a prime example for a
geometrically frustrated spin system. However most experimentally accessible
compounds have spatially anisotropic exchange interactions. As a function of
this anisotropy, ground states with different magnetic properties can be
realized. Motivated by recent experimental findings on
CsCuClBr, we discuss the full phase diagram of the
anisotropic model with two exchange constants and , including
possible ferromagnetic exchange. Furthermore a comparison with the related
square lattice model is carried out. We discuss the zero-temperature phase
diagram, ordering vector, ground-state energy, and ordered moment on a
classical level and investigate the effect of quantum fluctuations within the
framework of spin-wave theory. The field dependence of the ordered moment is
shown to be nonmonotonic with field and control parameter.Comment: 13 pages, 14 figure
Thermodynamics of anisotropic triangular magnets with ferro- and antiferromagnetic exchange
We investigate thermodynamic properties like specific heat and
susceptibility in anisotropic - triangular quantum spin
systems (). As a universal tool we apply the finite temperature Lanczos
method (FTLM) based on exact diagonalization of finite clusters with periodic
boundary conditions. We use clusters up to sites where the thermodynamic
limit behavior is already stably reproduced. As a reference we also present the
full diagonalization of a small eight-site cluster. After introducing model and
method we discuss our main results on and . We show the
variation of peak position and peak height of these quantities as function of
control parameter . We demonstrate that maximum peak positions and
heights in N\'eel phase and spiral phases are strongly asymmetric, much more
than in the square lattice - model. Our results also suggest a
tendency to a second side maximum or shoulder formation at lower temperature
for certain ranges of the control parameter. We finally explicitly determine
the exchange model of the prominent triangular magnets CsCuCl and
CsCuBr from our FTLM results.Comment: 13 pages, 12 figure
Supersymmetry and eigensurface topology of the spherical quantum pendulum
We undertook a mutually complementary analytic and computational study of the
full-fledged spherical (3D) quantum rotor subject to combined orienting and
aligning interactions characterized, respectively, by dimensionless parameters
and . By making use of supersymmetric quantum mechanics (SUSY
QM), we found two sets of conditions under which the problem of a spherical
quantum pendulum becomes analytically solvable. These conditions coincide with
the loci of the intersections of the eigenenergy
surfaces spanned by the and parameters. The integer topological
index is independent of the eigenstate and thus of the projection quantum
number . These findings have repercussions for rotational spectra and
dynamics of molecules subject to combined permanent and induced dipole
interactions.Comment: arXiv admin note: text overlap with arXiv:1404.224
Supersymmetry and eigensurface topology of the planar quantum pendulum
We make use of supersymmetric quantum mechanics (SUSY QM) to find three sets
of conditions under which the problem of a planar quantum pendulum becomes
analytically solvable. The analytic forms of the pendulum's eigenfuntions make
it possible to find analytic expressions for observables of interest, such as
the expectation values of the angular momentum squared and of the orientation
and alignment cosines as well as of the eigenenergy. Furthermore, we find that
the topology of the intersections of the pendulum's eigenenergy surfaces can be
characterized by a single integer index whose values correspond to the sets of
conditions under which the analytic solutions to the quantum pendulum problem
exist
Topology of surfaces for molecular Stark energy, alignment and orientation generated by combined permanent and induced electric dipole interactions
We show that combined permanent and induced electric dipole interactions of
polar and polarizable molecules with collinear electric fields lead to a sui
generis topology of the corresponding Stark energy surfaces and of other
observables - such as alignment and orientation cosines - in the plane spanned
by the permanent and induced dipole interaction parameters. We find that the
loci of the intersections of the surfaces can be traced analytically and that
the eigenstates as well as the number of their intersections can be
characterized by a single integer index. The value of the index, distinctive
for a particular ratio of the interaction parameters, brings out a close
kinship with the eigenproperties obtained previously for a class of Stark
states via the apparatus of supersymmetric quantum mechanics.Comment: 22 pages, including 2 tables and 8 figure
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