287 research outputs found
S matrix from matrix product states
We use the matrix product state formalism to construct stationary scattering
states of elementary excitations in generic one-dimensional quantum lattice
systems. Our method is applied to the spin-1 Heisenberg antiferromagnet, for
which we calculate the full magnon-magnon S matrix for arbitrary momenta and
spin, the two-particle contribution to the spectral function and the
magnetization curve. As our method provides an accurate microscopic
representation of the interaction between elementary excitations, we envisage
the description of low-energy dynamics of one-dimensional spin chains in terms
of these particlelike excitations.Comment: Improved version, extra supplemental materia
Topological nature of spinons and holons: Elementary excitations from matrix product states with conserved symmetries
We develop variational matrix product state (MPS) methods with symmetries to
determine dispersion relations of one dimensional quantum lattices as a
function of momentum and preset quantum number. We test our methods on the XXZ
spin chain, the Hubbard model and a non-integrable extended Hubbard model, and
determine the excitation spectra with a precision similar to the one of the
ground state. The formulation in terms of quantum numbers makes the topological
nature of spinons and holons very explicit. In addition, the method also
enables an easy and efficient direct calculation of the necessary magnetic
field or chemical potential required for a certain ground state magnetization
or particle density.Comment: 13 pages, 4 pages appendix, 8 figure
Faster Methods for Contracting Infinite 2D Tensor Networks
We revisit the corner transfer matrix renormalization group (CTMRG) method of
Nishino and Okunishi for contracting two-dimensional (2D) tensor networks and
demonstrate that its performance can be substantially improved by determining
the tensors using an eigenvalue solver as opposed to the power method used in
CTMRG. We also generalize the variational uniform matrix product state (VUMPS)
ansatz for diagonalizing 1D quantum Hamiltonians to the case of 2D transfer
matrices and discuss similarities with the corner methods. These two new
algorithms will be crucial to improving the performance of variational infinite
projected entangled pair state (PEPS) methods.Comment: 20 pages, 5 figures, V. Zauner-Stauber previously also published
under the name V. Zaune
Particles, holes and solitons: a matrix product state approach
We introduce a variational method for calculating dispersion relations of
translation invariant (1+1)-dimensional quantum field theories. The method is
based on continuous matrix product states and can be implemented efficiently.
We study the critical Lieb-Liniger model as a benchmark and excelent agreement
with the exact solution is found. Additionally, we observe solitonic signatures
of Lieb's Type II excitation. In addition, a non-integrable model is introduced
where a U(1)-symmetry breaking term is added to the Lieb-Liniger Hamiltonian.
For this model we find evidence of a non-trivial bound-state excitation in the
dispersion relation
Transfer Matrices and Excitations with Matrix Product States
We investigate the relation between static correlation functions in the
ground state of local quantum many-body Hamiltonians and the dispersion
relations of the corresponding low energy excitations using the formalism of
tensor network states. In particular, we show that the Matrix Product State
Transfer Matrix (MPS-TM) - a central object in the computation of static
correlation functions - provides important information about the location and
magnitude of the minima of the low energy dispersion relation(s) and present
supporting numerical data for one-dimensional lattice and continuum models as
well as two-dimensional lattice models on a cylinder. We elaborate on the
peculiar structure of the MPS-TM's eigenspectrum and give several arguments for
the close relation between the structure of the low energy spectrum of the
system and the form of static correlation functions. Finally, we discuss how
the MPS-TM connects to the exact Quantum Transfer Matrix (QTM) of the model at
zero temperature. We present a renormalization group argument for obtaining
finite bond dimension approximations of MPS, which allows to reinterpret
variational MPS techniques (such as the Density Matrix Renormalization Group)
as an application of Wilson's Numerical Renormalization Group along the virtual
(imaginary time) dimension of the system.Comment: 39 pages (+8 pages appendix), 14 figure
Symmetry Breaking and the Geometry of Reduced Density Matrices
The concept of symmetry breaking and the emergence of corresponding local
order parameters constitute the pillars of modern day many body physics. The
theory of quantum entanglement is currently leading to a paradigm shift in
understanding quantum correlations in many body systems and in this work we
show how symmetry breaking can be understood from this wavefunction centered
point of view. We demonstrate that the existence of symmetry breaking is a
consequence of the geometric structure of the convex set of reduced density
matrices of all possible many body wavefunctions. The surfaces of those convex
bodies exhibit non-analytic behavior in the form of ruled surfaces, which turn
out to be the defining signatures for the emergence of symmetry breaking and of
an associated order parameter.
We illustrate this by plotting the convex sets arising in the context of
three paradigmatic examples of many body systems exhibiting symmetry breaking:
the quantum Ising model in transverse magnetic field, exhibiting a second order
quantum phase transition; the classical Ising model at finite temperature in
two dimensions, which orders below a critical temperature ; and a system
of free bosons at finite temperature in three dimensions, exhibiting the
phenomenon of Bose-Einstein condensation together with an associated order
parameter . Remarkably, these convex sets look all very
much alike. We believe that this wavefunction based way of looking at phase
transitions demystifies the emergence of order parameters and provides a unique
novel tool for studying exotic quantum phenomena.Comment: 5 pages, 3 figures, Appendix with 2 pages, 3 figure
Co-Creative Action Research Experiments—A Careful Method for Causal Inference and Societal Impact
The rigor-versus-relevance debate in the world of academia is, by now, an old-time classic
that does not seem to go away so easily. The grassroots movement Responsible Research in Business
and Management, for instance, is a very active and prominent advocate of the need to change current
research practices in the management domain, broadly defined. One of its main critiques is that
current research practices are not apt to address day-to-day management challenges, nor do they
allow such management challenges to feed into academic research. In this paper, we address this
issue, and present a research design, referred to as CARE, that is aimed at building a bridge from
rigor to relevance, and vice versa. In so doing, we offer a template for conducting rigorous research
with immediate impact, contributing to solving issues that businesses are struggling with through
a design that facilitates causal inference
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