628 research outputs found
Optimum ground states for spin- chains
We present a set of {\em optimum ground states} for a large class of
spin- chains. Such global ground states are simultaneously ground
states of the local Hamiltonian, i.e. the nearest neighbour interaction in the
present case. They are constructed in the form of a matrix product. We find
three types of phases, namely a {\em weak antiferromagnet}, a {\em weak
ferromagnet}, and a {\em dimerized antiferromagnet}. The main physical
properties of these phases are calculated exactly by using a transfer matrix
technique, in particular magnetization and two spin correlations. Depending on
the model parameters, they show a surprisingly rich structure.Comment: LaTeX, 22 pages, 6 embedded Postscript figure
Spin-3/2 models on the Cayley tree -- optimum ground state approach
We present a class of optimum ground states for spin-3/2 models on the Cayley
tree with coordination number 3. The interaction is restricted to nearest
neighbours and contains 5 continuous parameters. For all values of these
parameters the Hamiltonian has parity invariance, spin-flip invariance, and
rotational symmetry in the xy-plane of spin space. The global ground states are
constructed in terms of a 1-parametric vertex state model, which is a direct
generalization of the well-known matrix product ground state approach. By using
recursion relations and the transfer matrix technique we derive exact
analytical expressions for local fluctuations and longitudinal and transversal
two-point correlation functions.Comment: LaTeX 2e, 8 embedded eps figures, 14 page
Mixed Heisenberg Chains. II. Thermodynamics
We consider thermodynamic properties, e.g. specific heat, magnetic
susceptibility, of alternating Heisenberg spin chains. Due to a hidden Ising
symmetry these chains can be decomposed into a set of finite chain fragments.
The problem of finding the thermodynamic quantities is effectively separated
into two parts. First we deal with finite objects, secondly we can incorporate
the fragments into a statistical ensemble. As functions of the coupling
constants, the models exhibit special features in the thermodynamic quantities,
e.g. the specific heat displays double peaks at low enough temperatures. These
features stem from first order quantum phase transitions at zero temperature,
which have been investigated in the first part of this work.Comment: 12 pages, RevTeX, 12 embedded eps figures, cf. cond-mat/9703206,
minor modification
The square-kagome quantum Heisenberg antiferromagnet at high magnetic fields: The localized-magnon paradigm and beyond
We consider the spin-1/2 antiferromagnetic Heisenberg model on the
two-dimensional square-kagome lattice with almost dispersionless lowest magnon
band. For a general exchange coupling geometry we elaborate low-energy
effective Hamiltonians which emerge at high magnetic fields. The effective
model to describe the low-energy degrees of freedom of the initial frustrated
quantum spin model is the (unfrustrated) square-lattice spin-1/2 model in
a -aligned magnetic field. For the effective model we perform quantum Monte
Carlo simulations to discuss the low-temperature properties of the
square-kagome quantum Heisenberg antiferromagnet at high magnetic fields. We
pay special attention to a magnetic-field driven
Berezinskii-Kosterlitz-Thouless phase transition which occurs at low
temperatures.Comment: 6 figure
Accurate determination of tensor network state of quantum lattice models in two dimensions
We have proposed a novel numerical method to calculate accurately the
physical quantities of the ground state with the tensor-network wave function
in two dimensions. We determine the tensor network wavefunction by a projection
approach which applies iteratively the Trotter-Suzuki decomposition of the
projection operator and the singular value decomposition of matrix. The norm of
the wavefunction and the expectation value of a physical observable are
evaluated by a coarse grain renormalization group approach. Our method allows a
tensor-network wavefunction with a high bond degree of freedom (such as D=8) to
be handled accurately and efficiently in the thermodynamic limit. For the
Heisenberg model on a honeycomb lattice, our results for the ground state
energy and the staggered magnetization agree well with those obtained by the
quantum Monte Carlo and other approaches.Comment: 4 pages 5 figures 2 table
Entanglement and quantum phase transitions in matrix product spin one chains
We consider a one-parameter family of matrix product states of spin one
particles on a periodic chain and study in detail the entanglement properties
of such a state. In particular we calculate exactly the entanglement of one
site with the rest of the chain, and the entanglement of two distant sites with
each other and show that the derivative of both these properties diverge when
the parameter of the states passes through a critical point. Such a point
can be called a point of quantum phase transition, since at this point, the
character of the matrix product state which is the ground state of a
Hamiltonian, changes discontinuously. We also study the finite size effects and
show how the entanglement depends on the size of the chain. This later part is
relevant to the field of quantum computation where the problem of initial state
preparation in finite arrays of qubits or qutrits is important. It is also
shown that entanglement of two sites have scaling behavior near the critical
point
Solving Gapped Hamiltonians Locally
We show that any short-range Hamiltonian with a gap between the ground and
excited states can be written as a sum of local operators, such that the ground
state is an approximate eigenvector of each operator separately. We then show
that the ground state of any such Hamiltonian is close to a generalized matrix
product state. The range of the given operators needed to obtain a good
approximation to the ground state is proportional to the square of the
logarithm of the system size times a characteristic "factorization length".
Applications to many-body quantum simulation are discussed. We also consider
density matrices of systems at non-zero temperature.Comment: 13 pages, 2 figures; minor changes to references, additional
discussion of numerics; additional explanation of nonzero temperature matrix
product for
Some New Exact Ground States for Generalize Hubbard Models
A set of new exact ground states of the generalized Hubbard models in
arbitrary dimensions with explicitly given parameter regions is presented. This
is based on a simple method for constructing exact ground states for
homogeneous quantum systems.Comment: 9 pages, Late
Exact ground states of quantum spin-2 models on the hexagonal lattice
We construct exact non-trivial ground states of spin-2 quantum
antiferromagnets on the hexagonal lattice. Using the optimum ground state
approach we determine the ground state in different subspaces of a general
spin-2 Hamiltonian consistent with some realistic symmetries. These states,
which are not of simple product form, depend on two free parameters and can be
shown to be only weakly degenerate. We find ground states with different types
of magnetic order, i.e. a weak antiferromagnet with finite sublattice
magnetization and a weak ferromagnet with ferrimagnetic order. For the latter
it is argued that a quantum phase transition occurs within the solvable
subspace.Comment: 7 pages, accepted for publication in Phys. Rev.
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