3,621 research outputs found

### Fast convergence of imaginary time evolution tensor network algorithms by recycling the environment

We propose an environment recycling scheme to speed up a class of tensor
network algorithms that produce an approximation to the ground state of a local
Hamiltonian by simulating an evolution in imaginary time. Specifically, we
consider the time-evolving block decimation (TEBD) algorithm applied to
infinite systems in 1D and 2D, where the ground state is encoded, respectively,
in a matrix product state (MPS) and in a projected entangled-pair state (PEPS).
An important ingredient of the TEBD algorithm (and a main computational
bottleneck, especially with PEPS in 2D) is the computation of the so-called
environment, which is used to determine how to optimally truncate the bond
indices of the tensor network so that their dimension is kept constant. In
current algorithms, the environment is computed at each step of the imaginary
time evolution, to account for the changes that the time evolution introduces
in the many-body state represented by the tensor network. Our key insight is
that close to convergence, most of the changes in the environment are due to a
change in the choice of gauge in the bond indices of the tensor network, and
not in the many-body state. Indeed, a consistent choice of gauge in the bond
indices confirms that the environment is essentially the same over many time
steps and can thus be re-used, leading to very substantial computational
savings. We demonstrate the resulting approach in 1D and 2D by computing the
ground state of the quantum Ising model in a transverse magnetic field.Comment: 17 pages, 28 figure

### Dynamical windows for real-time evolution with matrix product states

We propose the use of a dynamical window to investigate the real-time
evolution of quantum many-body systems in a one-dimensional lattice. In a
recent paper [H. Phien et al, arxiv:????.????], we introduced infinite boundary
conditions (IBC) in order to investigate real-time evolution of an infinite
system under a local perturbation. This was accomplished by restricting the
update of the tensors in the matrix product state to a finite window, with left
and right boundaries held at fixed positions. Here we consider instead the use
of a dynamical window, namely a window where the positions of left and right
boundaries are allowed to change in time. In this way, all simulation efforts
can be devoted to the space-time region of interest, which leads to a
remarkable reduction in computational costs. For illustrative purposes, we
consider two applications in the context of the spin-1 antiferromagnetic
Heisenberg model in an infinite spin chain: one is an expanding window, with
boundaries that are adjusted to capture the expansion in time of a local
perturbation of the system; the other is a moving window of fixed size, where
the position of the window follows the front of a propagating wave

### Particle number conservation in quantum many-body simulations with matrix product operators

Incorporating conservation laws explicitly into matrix product states (MPS)
has proven to make numerical simulations of quantum many-body systems much less
resources consuming. We will discuss here, to what extent this concept can be
used in simulation where the dynamically evolving entities are matrix product
operators (MPO). Quite counter-intuitively the expectation of gaining in speed
by sacrificing information about all but a single symmetry sector is not in all
cases fulfilled. It turns out that in this case often the entanglement imposed
by the global constraint of fixed particle number is the limiting factor.Comment: minor changes, 18 pages, 5 figure

### Magnetism in the dilute Kondo lattice model

The one dimensional dilute Kondo lattice model is investigated by means of
bosonization for different dilution patterns of the array of impurity spins.
The physical picture is very different if a commensurate or incommensurate
doping of the impurity spins is considered. For the commensurate case, the
obtained phase diagram is verified using a non-Abelian density-matrix
renormalization-group algorithm. The paramagnetic phase widens at the expense
of the ferromagnetic phase as the $f$-spins are diluted. For the incommensurate
case, antiferromagnetism is found at low doping, which distinguishes the dilute
Kondo lattice model from the standard Kondo lattice model.Comment: 11 pages, 2 figure

### Biorthonormal Matrix-Product-State Analysis for Non-Hermitian Transfer-Matrix Renormalization-Group in the Thermodynamic Limit

We give a thorough Biorthonormal Matrix-Product-State (BMPS) analysis of the
Transfer-Matrix Renormalization-Group (TMRG) for non-Hermitian matrices in the
thermodynamic limit. The BMPS is built on a dual series of reduced
biorthonormal bases for the left and right Perron states of a non-Hermitian
matrix. We propose two alternative infinite-size Biorthonormal TMRG (iBTMRG)
algorithms and compare their numerical performance in both finite and infinite
systems. We show that both iBTMRGs produce a dual infinite-BMPS (iBMPS) which
are translationally invariant in the thermodynamic limit. We also develop an
efficient wave function transformation of the iBTMRG, an analogy of McCulloch
in the infinite-DMRG [arXiv:0804.2509 (2008)], to predict the wave function as
the lattice size is increased. The resulting iBMPS allows for probing bulk
properties of the system in the thermodynamic limit without boundary effects
and allows for reducing the computational cost to be independent of the lattice
size, which are illustrated by calculating the magnetization as a function of
the temperature and the critical spin-spin correlation in the thermodynamic
limit for a 2D classical Ising model.Comment: 14 pages, 9 figure

### Infinite boundary conditions for matrix product state calculations

We propose a formalism to study dynamical properties of a quantum many-body
system in the thermodynamic limit by studying a finite system with infinite
boundary conditions (IBC) where both finite size effects and boundary effects
have been eliminated. For one-dimensional systems, infinite boundary conditions
are obtained by attaching two boundary sites to a finite system, where each of
these two sites effectively represents a semi-infinite extension of the system.
One can then use standard finite-size matrix product state techniques to study
a region of the system while avoiding many of the complications normally
associated with finite-size calculations such as boundary Friedel oscillations.
We illustrate the technique with an example of time evolution of a local
perturbation applied to an infinite (translationally invariant) ground state,
and use this to calculate the spectral function of the S=1 Heisenberg spin
chain. This approach is more efficient and more accurate than conventional
simulations based on finite-size matrix product state and density-matrix
renormalization-group approaches.Comment: 10 page

### Symmetry fractionalization in the topological phase of the spin-1/2 J(1)-J(2) triangular Heisenberg model

Using density-matrix renormalization-group calculations for infinite cylinders, we elucidate the properties of the spin-liquid phase of the spin-1/2 J(1)-J(2) Heisenberg model on the triangular lattice. We find four distinct ground states characteristic of a nonchiral, Z(2) topologically ordered state with vison and spinon excitations. We shed light on the interplay of topological ordering and global symmetries in the model by detecting fractionalization of time-reversal and space-group dihedral symmetries in the anyonic sectors, which leads to the coexistence of symmetry protected and intrinsic topological order. The anyonic sectors, and information on the particle statistics, can be characterized by degeneracy patterns and symmetries of the entanglement spectrum. We demonstrate the ground states on finite-width cylinders are short-range correlated and gapped; however, some features in the entanglement spectrum suggest that the system develops gapless spinonlike edge excitations in the large-width limit

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