969 research outputs found
Time Evolution of an Infinite Projected Entangled Pair State: an Efficient Algorithm
An infinite projected entangled pair state (iPEPS) is a tensor network ansatz
to represent a quantum state on an infinite 2D lattice whose accuracy is
controlled by the bond dimension . Its real, Lindbladian or imaginary time
evolution can be split into small time steps. Every time step generates a new
iPEPS with an enlarged bond dimension , which is approximated by an
iPEPS with the original . In Phys. Rev. B 98, 045110 (2018) an algorithm was
introduced to optimize the approximate iPEPS by maximizing directly its
fidelity to the one with the enlarged bond dimension . In this work we
implement a more efficient optimization employing a local estimator of the
fidelity. For imaginary time evolution of a thermal state's purification, we
also consider using unitary disentangling gates acting on ancillas to reduce
the required . We test the algorithm simulating Lindbladian evolution and
unitary evolution after a sudden quench of transverse field in the 2D
quantum Ising model. Furthermore, we simulate thermal states of this model and
estimate the critical temperature with good accuracy: for and
for the more challenging case of close to the quantum
critical point at .Comment: published version, presentation improve
Recent developments in Quantum Monte-Carlo simulations with applications for cold gases
This is a review of recent developments in Monte Carlo methods in the field
of ultra cold gases. For bosonic atoms in an optical lattice we discuss path
integral Monte Carlo simulations with worm updates and show the excellent
agreement with cold atom experiments. We also review recent progress in
simulating bosonic systems with long-range interactions, disordered bosons,
mixtures of bosons, and spinful bosonic systems. For repulsive fermionic
systems determinantal methods at half filling are sign free, but in general no
sign-free method exists. We review the developments in diagrammatic Monte Carlo
for the Fermi polaron problem and the Hubbard model, and show the connection
with dynamical mean-field theory. We end the review with diffusion Monte Carlo
for the Stoner problem in cold gases.Comment: 68 pages, 22 figures, review article; replaced with published versio
Density Matrix Renormalization Group and Reaction-Diffusion Processes
The density matrix renormalization group (DMRG) is applied to some
one-dimensional reaction-diffusion models in the vicinity of and at their
critical point. The stochastic time evolution for these models is given in
terms of a non-symmetric ``quantum Hamiltonian'', which is diagonalized using
the DMRG method for open chains of moderate lengths (up to about 60 sites). The
numerical diagonalization methods for non-symmetric matrices are reviewed.
Different choices for an appropriate density matrix in the non-symmetric DMRG
are discussed. Accurate estimates of the steady-state critical points and
exponents can then be found from finite-size scaling through standard
finite-lattice extrapolation methods. This is exemplified by studying the
leading relaxation time and the density profiles of diffusion-annihilation and
of a branching-fusing model in the directed percolation universality class.Comment: 16 pages, latex, 5 PostScript figures include
Phase Diagram and Conformal String Excitations of Square Ice using Gauge Invariant Matrix Product States
We investigate the ground state phase diagram of square ice -- a U(1) lattice
gauge theory in two spatial dimensions -- using gauge invariant tensor network
techniques. By correlation function, Wilson loop, and entanglement diagnostics,
we characterize its phases and the transitions between them, finding good
agreement with previous studies. We study the entanglement properties of string
excitations on top of the ground state, and provide direct evidence of the fact
that the latter are described by a conformal field theory. Our results pave the
way to the application of tensor network methods to confining, two-dimensional
lattice gauge theories, to investigate their phase diagrams and low-lying
excitations.Comment: 36 pages, 16 figures; referee suggestions incorporated, added Figs.
3, 13 and appendices A,
Numerical continuum tensor networks in two dimensions
We describe the use of tensor networks to numerically determine wave
functions of interacting two-dimensional fermionic models in the continuum
limit. We use two different tensor network states: one based on the numerical
continuum limit of fermionic projected entangled pair states obtained via a
tensor network formulation of multi-grid, and another based on the combination
of the fermionic projected entangled pair state with layers of isometric
coarse-graining transformations. We first benchmark our approach on the
two-dimensional free Fermi gas then proceed to study the two-dimensional
interacting Fermi gas with an attractive interaction in the unitary limit,
using tensor networks on grids with up to 1000 sites.Comment: 9 pages, 9 figures, sample source codes are available at
https://github.com/rezah/cpep
Numerical continuum tensor networks in two dimensions
We describe the use of tensor networks to numerically determine wave functions of interacting two-dimensional fermionic models in the continuum limit. We use two different tensor network states: one based on the numerical continuum limit of fermionic projected entangled pair states obtained via a tensor network formulation of multi-grid, and another based on the combination of the fermionic projected entangled pair state with layers of isometric coarse-graining transformations. We first benchmark our approach on the two-dimensional free Fermi gas then proceed to study the two-dimensional interacting Fermi gas with an attractive interaction in the unitary limit, using tensor networks on grids with up to 1000 sites
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